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            <title>The art of fortification, or architecture militaire as vvell offensiue as defensiue, compiled &amp; set forth, by Samuell Marolois revievved, augmented and corrected by Albert Girard mathematician: &amp; translated out of French into English by Henry Hexam</title>
            <title>Opera mathematica. Part 3.</title>
            <author>Marolois, Samuel.</author>
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               <date>1631</date>
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                  <title>The art of fortification, or architecture militaire as vvell offensiue as defensiue, compiled &amp; set forth, by Samuell Marolois revievved, augmented and corrected by Albert Girard mathematician: &amp; translated out of French into English by Henry Hexam</title>
                  <title>Opera mathematica. Part 3.</title>
                  <author>Marolois, Samuel.</author>
                  <author>Girard, Albert, 1595-1632.</author>
                  <author>Hexham, Henry, 1585?-1650?</author>
               </titleStmt>
               <extent>[4], 48 p. : 40 plates  </extent>
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                  <publisher>For M. Iohn Iohnson,</publisher>
                  <pubPlace>Printed at Amsterdam :</pubPlace>
                  <date>Anno 1631.</date>
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                  <note>A translation of: Marolois, Samuel. Fortification, ou architecture militaire, that offensive que defensive, published in the author's: Opera mathematica.</note>
                  <note>Running title reads: The fortification of Samuel Marolois.</note>
                  <note>With engraved title page.</note>
                  <note>Plates from 1627 Dutch edition.</note>
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         <div type="title_page">
            <pb facs="tcp:1568:1" rendition="simple:additions"/>
            <pb facs="tcp:1568:1" rendition="simple:additions"/>
            <p>
               <figure>
                  <p>THE
ART OF
FORTIFICATION,
<hi>OR</hi>
ARCHITECTVRE MILITAIRE
asvvell Offensiue as Defensiue, compiled
&amp; set forth,
<hi>By</hi>
SAMVELL MAROLOIS
<hi>Revievved, Augmented and Corrected
by</hi>
ALBERT GIRARD
Mathematician:
&amp;
<hi>Translated out of French into
English.</hi>
by
HENRY HEXAM.</p>
                  <p>PRINTED
At <hi>Amsterdam,</hi> for
M. IOHN IOHNSON.
<hi>Anno</hi> 1638.</p>
               </figure>
            </p>
         </div>
         <div type="dedication">
            <pb facs="tcp:1568:2"/>
            <pb facs="tcp:1568:2"/>
            <head>TO
The right honorable, &amp; truely noble,
S<hi rend="sup">r.</hi> HENRY VANE KNIGHT,
MASTER CONTROVLER OF THE KINGS HOVSEHOLD,
&amp; one of his Majesties most honorable privie Coun<g ref="char:EOLhyphen"/>cellours
of State.</head>
            <p>
               <seg rend="decorInit">W</seg>Hen your honor was last here in the <hi>Netherlands</hi> Lord <hi>Am<g ref="char:EOLhyphen"/>bassadour</hi>
extraordinarie for his Ma<hi rend="sup">tie</hi> of <hi>great Brittan<gap reason="illegible" resp="#TECH" extent="1 letter">
                     <desc>•</desc>
                  </gap>e;</hi> with
the Lords the <hi>States Generall</hi> of the United Provinces: It
pleased your honor, to employ your servant in collecting,
and abbreviating some militarie <hi>Abstracts.</hi> Since which
time, in regard of my longe service, I haue gained more ex<g ref="char:EOLhyphen"/>perience,
and studied my profession some what better. To
this end, for the good of my Countrie, and Nation (for every
man by a naturall inclination, ought to add some thing there<g ref="char:EOLhyphen"/>vnto)
I haue of late vndertaken, and written a treatise intituled, <hi>The Principles of the Art Militaire, practised in the vvarres of the Vnited Netherlands, represented by
figure, the vvord of Commaund, an demonstration,</hi> disgesting the same into three parts,
whereof the <hi>first,</hi> showes the dutie, and office of a <hi>Captaine,</hi> his inferiour officers,
the true forme observed amongst vs in the <hi>exercising</hi> of a Companie, the <hi>Ordering</hi>
of a Regiment, and our lawes, and articles of <hi>Marshall discipline.</hi> The <hi>second</hi> part
treats of the severall duties of the officers of the field, and the diverse formes of
ranging horse and foote in battle-ray, showne by Prince <hi>Maurice</hi> of famous me<g ref="char:EOLhyphen"/>morie,
&amp; his brother his highnesse the Prince of <hi>Orange</hi> our Generall that now is,
at sundry times, and in diverse places. The <hi>third</hi> part, handles the place &amp; office
of the <hi>Master</hi> (or <hi>Generall</hi>) of the Ordinance and all the officers vnder his traine
and Commaund, together with the <hi>Ordinance, Munition, Engines, Instruments, Ma<g ref="char:EOLhyphen"/>terials,</hi>
and all necessarie <hi>preparations,</hi> and <hi>Equipage,</hi> belonging to an <hi>Armie</hi> &amp; other
officers depending on the warre. But yet (me thinkes) these three parts, are <hi>de<g ref="char:EOLhyphen"/>fectiue</hi>
and <hi>incompleate,</hi> vnlesse a fourth be added therevnto, which is the excellent
art of <hi>Fortification.</hi> To this effect, I haue translated into English out of French, the
workes of two famous <hi>Mathematicians</hi> of our moderne times, namely Mr. <hi>Samuell
Marolois,</hi> and Mr. <hi>Albert Girard,</hi> who haue written at large vpon this subject.
As for exemple, what valour, and this art haue done, witnesse the famous siege of
<hi>Ostend,</hi> for by the meanes hereof never was <hi>tovvne</hi> so brauely disputed, never <hi>For<g ref="char:EOLhyphen"/>tresse</hi>
(in the memorie of man) so couragiously defended, having to doe with so
braue an Ennemy, who was fainte during the time of three yeeres, three months,
and odd daies Siege, to gett this towne (as it were) by <hi>ynchmeale:</hi> what should I say
by ynchmeale? when they were driven to such <hi>nonpluses,</hi> that they could not gett
a strawes breadth of vs, but held vp many daies, and weekes (finding such a resi<g ref="char:EOLhyphen"/>stance)
their approches, before they could advance them any further: yea which is
more, when they had approched, sapt, and mined into the very bowels of some
<hi>Bulvvarkes,</hi> blowing them vp with the violence of pouder, steeple-high into the
aire, each Ennemy then strived at push of the pike, who should become master of
that falne Earth, to turne it vp one against an other. And at last being master of
the deformed <hi>karkeis</hi> of a torne Bulwarke or two, found presently a new <hi>retrench<g ref="char:EOLhyphen"/>ment,</hi>
or cutting of cast vp before them; being then forced to sapp forward againe,
and make new workes, and mines, which lasted so longe, and was so well disputed,
till they gott the halfe of the towne, before they had the whole. This men, valour,
<pb facs="tcp:1568:3"/>
&amp; <hi>fortification</hi> (by the help of <hi>Almighty God</hi>) can doe. Againe, this was one of Prince
<hi>Maurice</hi> (of blessed memorie) his <hi>master peeces,</hi> for by this <hi>art,</hi> he was so warie, and
carefull of the Liues of his men, that he choose rather, to spend the States a hun<g ref="char:EOLhyphen"/>dred
pound, in casting vp a <hi>trench,</hi> a <hi>Sap,</hi> and a <hi>vvorke,</hi> rather then to hasard &amp; loose
the life of a man, so good a <hi>Menagier</hi> was he for the preserving of his men. This
<hi>Art</hi> then, being of such singular vse, for the makeing of all manner of <hi>Fortresses,</hi> and
<hi>vvorkes</hi> both <hi>Regular,</hi> and <hi>irregular,</hi> even from a <hi>quadrangle</hi> which is a fortresse with
foure points or Bulwarkes, to a <hi>Dodecon,</hi> which is a towne or a fortresse with twelue
<hi>Bastions,</hi> for the preservation of men in a Warre defensiue, comes in most humble
wise, to craue your honours gracious patronage, that vnder your favour, and pro<g ref="char:EOLhyphen"/>tection,
it may come to the view of the world, an maye be helpfull to such, as are
desirous and <hi>ingenious</hi> to studie this noble art, which if it be acceptable vnto your
honor, then I shall think my time well spent, and acknowledg my selfe much bound
vnto your honor, and shalbe obliged not onely to pray vnto the Almightie, to
preserue yow and yours in health; but also to crowne you hereafter with everla<g ref="char:EOLhyphen"/>sting
felicity, resting<g ref="char:punc">▪</g>
            </p>
            <closer>
               <signed>Iour honors humble, and devoted
servant
HENRY HEXHAM.</signed>
            </closer>
         </div>
      </front>
      <body>
         <div n="1" type="part">
            <pb n="1" facs="tcp:1568:3"/>
            <head>THE FIRST PART
OF
REGVLAR
FORTIFICATION,
DEMONSTRATED
BY THE DECEASED
SAMVEL MAROLOIS,
And
Reviewed, corrected &amp; augmented
BY
ALBERT GIRARD,
SANMIELOIS.</head>
            <p>
               <seg rend="decorInit">G</seg>Od having found good to create Man, did
with all prepare his affection for societie, that by this meanes he
might the longer preserue him, and so make him become more
stronge &amp; able. According to which &amp; to the same end, there were
first built howses, and lodgings, to keepe men from the injurie of
the aire, as windes, stormes, raine, excessiue heate, and colde, as the
situation of their dwellings, and the commodiousnesse of those places did afford.
And as by divine blessing, and their owne industrie, they attayned unto many
Earthly riches, as famillies, cattell, and other goods: so by the instinct of nature,
they sought alwaies to strengthen &amp; defend themselues with the best fortifications
they could, that thereby they might not onely preserue their bodies against the
violence of their Adversaires; but also their goods, kindred, and Associates. To
this end (as we may obserue as well in ancient histories, as also at this day in some
East and West Indian Nations) they droue in piles of timber, and made Empale<g ref="char:EOLhyphen"/>ments
closse one to an other, that enclossing themselues so narrowly together, they
might be the better able to defend and resist the furie of their Ennemies. But in
<pb n="2" facs="tcp:1568:4"/>
processe of time, the defects of such enclossure being well marked, they began after<g ref="char:EOLhyphen"/>wards
to make their Fortifications of a more solid, firme, and durable matter, as
stone, brick, earth and such like. And though experience taught them, that these
their Empalements of wood, were not able to <gap reason="illegible" resp="#TECH" extent="1 letter">
                  <desc>•</desc>
               </gap>esist fyre, &amp; diuerse other accidents,
which might befall them: yet it is certaine, they used these and the like fortifica<g ref="char:EOLhyphen"/>tions,
till they found the harme &amp; conveniencie, which they receiued by them. But
necessitie, the Inventrix of Arts, found that walls built with stones and bricks were
better. These were in use and traine, till such time also, as their imperfections were
knowne, and that by the force of man, and Engines they were diuerse wayes attem<g ref="char:EOLhyphen"/>pted;
yea many times beaten downe &amp; overthrowne: which made them seeke from
time to time to remedie their defects: for perceiving that their walls were hereto<g ref="char:EOLhyphen"/>fore
subject to be beaten downe (by Rames) and other ancient Engines; they made
them (upon the right line of the wall) Spures, and roundles to hinder the beating of
them downe, and to preserue them the better from a breach, and tumbling downe,
they gaue them the Talude, that is, a slooping towards the inside of the place, that
they might be the more able to resist the violence &amp; force of these Engines. Finally
these walls were made after diverse manners: first in a round forme, which, as on
the one side, it was held the strongest; because these Engines beating against the
wall crushed the stones, &amp; made them stick the closser together, in regard the circle
exteriour was greater then the interiour, and that the Engines could not unfasten,
loose and breake them but with great difficultie. So on the other side, it was impos<g ref="char:EOLhyphen"/>sible
to defend such walls, when approches was made unto them; because no part of
them could be discouvered, or flancked: so that afterward they built the<g ref="char:cmbAbbrStroke">̄</g> in a square
forme, with small squares in their angles, for the defense of their Curtaines. Then
made them also Demycircles with angles interiour, and exteriour, and lastly trian<g ref="char:EOLhyphen"/>gular
wise, on the one side to resist the force of the furious Canon, used at this day;
and on the other side, that they might be the more capable to defend themselues
by discovering euery part of the wall, euen to the very foundation. And as invention
of attempting is growne to the highest degree in these dayes, by reason of the longe
experience of the warrs in these parts (which is the Schole of all military actions) and
the abilitie, and capacitie of the Assaillants &amp; Defendants: So am I of the opinion,
that the Fortifications made in these Low Countryes, are the strongest, exactest, &amp;
perfectest, which can be invented, and which haue bene made and practized, not by
a simple Generall, but by one of the greatest Captaines of the World, endowed with
a singular courage and spirit, an excellent Mathematician, and is not onely a Prince
of a great howse; but also experienced &amp; beaten in all militaire actions, and strata<g ref="char:EOLhyphen"/>gems;
aswell offensiue, as defensiue: of which Fortification, we haue undertaken to
treate briefly at this present, and as succinctly as possibly may be.</p>
            <div type="section">
               <head>Of the definitions.</head>
               <head type="sub">I.</head>
               <p>Forasmuch then as the definitions of Fortification are by the dayly use of armes
growne so common: it were in vaine for me (in my opinion) to make any further
explication thereof: yet to satisfie the ignorant, we will marke out the angles, and
sides of a Fortresse, by the Letters of the Alphabeth, and opposite to the said letters,
ye shall finde their names, and appellations, as we may note by the figures 1. and 2,
following.</p>
            </div>
            <div type="section">
               <pb n="3" facs="tcp:1568:4"/>
               <head>Icnographie, or ground-markeing.</head>
               <list>
                  <head>1. Figure.</head>
                  <item>N. O. The side of the Polygone,
that is many angles.</item>
                  <item>N. D. The line of the gorge,</item>
                  <item>D. C. The line of the flanke,</item>
                  <item>B. N. The Capitall line.</item>
                  <item>B. C. Q. R. The Moate.</item>
                  <item>P. The Raveline, or halfe mone.</item>
                  <item>Q. S. The covert way.</item>
                  <item>T. S. The Parapett thereof.</item>
                  <item>B. I. The line of defence.</item>
                  <item>D. K. The Curtaine.</item>
                  <item>K. F. The Parapett.</item>
                  <item>K. M. The Rampart.</item>
                  <item>A. N. The semy-diameter.</item>
                  <item>V. C. The flanke lengthned.</item>
                  <item>C. N. D. The angle forming the flank.</item>
                  <item>B. C. D. The angle of the shoulder.</item>
               </list>
            </div>
            <div type="section">
               <head>Orthographie, or the Profile.</head>
               <list>
                  <head>2. Figure.</head>
                  <item>A. B. The foote or basis of the Rampart.</item>
                  <item>G. H. The heigth of the Rampart.</item>
                  <item>H. B. The talud (or slooping) of the infiel
of the Rampart.</item>
                  <item>A. Y. The Talud on the outside of the
Rampart, or scharfe.</item>
                  <item>Z. D. The foote of the Parapett.</item>
                  <item>Z. E. The Parapett itselfe.</item>
                  <item>D. F. The foote-banke.</item>
                  <item>F. G. The Terra-plaine or bredth of the
Rampart.</item>
                  <item>K. A. The way for the round, or the false<g ref="char:EOLunhyphen"/>bray.</item>
                  <item>I. K. The foote banke thereof.</item>
                  <item>I. M. The Parapett of the falsebray.</item>
                  <item>M. N. The Scharfe.</item>
                  <item>P. O. N. M. The moate.</item>
                  <item>P. O. The Counterscharfe.</item>
                  <item>P. Q. The Covert way.</item>
                  <item>R. Q. The foote banke thereof.</item>
                  <item>T. S. R. The Parapett of the Covert
way.</item>
               </list>
               <p>The other names, which haue neede of explanation shalbe declared in their due
places.</p>
               <p>Before we come to instruct yow particularly in the Art of Fortification; we will
briefely treate of the calculation thereof: In which supputation, ye shall haue first
sett downe the knowne termes, and under them the disposition of the Characters
or Letters: beginning with a square fortresse with foure angles, or Bulwarks, and
proceede on to a <hi>Dodecagone,</hi> a fortresse with twelue angles, or Bulwarks, makeing
upon every <hi>Polygone,</hi> 3 or 4 Trialls, that afterwards one may choose the best of
them: and because the angles will not be much altered by the diversitie of the trials:
I haue thought good to giue this generall rule for them following.</p>
               <p>It is a thing generally received of all men, that a square fortresse with foure Bul<g ref="char:EOLhyphen"/>warks,
is not so good as a <hi>Pentagonall</hi> with fiue angles, nor a <hi>Pentagonall</hi> so stronge as
an Exagonall with sixe, and so consequently of the rest. If the cause thereof be
sought out; one may obserue that this proceedes from the smallnesse of their an<g ref="char:EOLhyphen"/>gles;
as not being able to beare such a body of a Bastion, as the subsequent <hi>Polygones:</hi>
so that a square fortresse for this reason, wilbe more defective, then the <hi>Pentagonall,</hi>
                  <pb n="4" facs="tcp:1568:5"/>
and this lesse defensive then the Hexagonall, and so well the rest following even
to a <hi>Dodecagone,</hi> which hath the angle of the Bastion right, which is the cause, that
constraines one to make the angles flanked lesser, then the reason of building well
doth require, that is, the flanks too litle, the Gorge too narrow, and the line of de<g ref="char:EOLhyphen"/>fence
too longe. To encrease then proportionally the angles of Fortresses, accor<g ref="char:EOLhyphen"/>ding
as the angle of their <hi>Polygone</hi> augmenteth; we will take then the halfe of their
angles, and adding thereunto 15 degrees, the summe wilbe the angle of the Bul<g ref="char:EOLhyphen"/>warke,
which we terme the angle-flanked, and if the angle-flanked be substracted
from the angle of the <hi>Polygone,</hi> there will remayne the double of the angle flanking
interiour, which double being substracted from 180 degrees, `then will remayne the
angle flanking exteriour, called the <hi>Tenaille,</hi> and if ye add to the angle flanking
interiour 90 degrees, then the summe wil be the angle of the Shoulder.</p>
               <p>To finde out the angle of the <hi>Polygone</hi> from the number of its substract, namely 2,
the remaynder must be multiplyed by 2. and the product wil be the number of the
right angles, which such a <hi>Polygone</hi> containeth, as ye maye see by this exemple
following.<gap reason="math">
                     <desc>〈 math 〉</desc>
                  </gap>
               </p>
               <p>Or thus.<gap reason="math">
                     <desc>〈 math 〉</desc>
                  </gap>
               </p>
               <p>And by the same rule ye shall finde the angles of the Subsequent <hi>Polygones,</hi> be<g ref="char:EOLhyphen"/>ginning
from a square Fortresse to a <hi>Dodecagone.</hi>
               </p>
               <p>
                  <pb n="5" facs="tcp:1568:5"/>
                  <table>
                     <row>
                        <cell>4.</cell>
                        <cell>5.</cell>
                        <cell>6.</cell>
                        <cell>7.</cell>
                        <cell>8.</cell>
                        <cell>9.</cell>
                        <cell>10.</cell>
                        <cell>11.</cell>
                        <cell>12</cell>
                     </row>
                     <row>
                        <cell>90.</cell>
                        <cell>72.</cell>
                        <cell>60.</cell>
                        <cell>51 3/7.</cell>
                        <cell>45.</cell>
                        <cell>40.</cell>
                        <cell>36.</cell>
                        <cell>32 8/<gap reason="illegible" resp="#TECH" extent="2 letters">
                              <desc>••</desc>
                           </gap>.</cell>
                        <cell>30 the angl. of the center.</cell>
                     </row>
                     <row>
                        <cell>90.</cell>
                        <cell>108.</cell>
                        <cell>120.</cell>
                        <cell>128 4/7.</cell>
                        <cell>135.</cell>
                        <cell>140.</cell>
                        <cell>144.</cell>
                        <cell>147 <gap reason="illegible" resp="#TECH" extent="1 letter">
                              <desc>•</desc>
                           </gap>/11.</cell>
                        <cell>150 the angle of the Polig.</cell>
                     </row>
                     <row>
                        <cell>45.</cell>
                        <cell>54.</cell>
                        <cell>60.</cell>
                        <cell>64 2/7.</cell>
                        <cell>67 1/2.</cell>
                        <cell>70.</cell>
                        <cell>72.</cell>
                        <cell>73 7/11.</cell>
                        <cell>75 The halfe.</cell>
                     </row>
                     <row>
                        <cell>15.</cell>
                        <cell>15.</cell>
                        <cell>15.</cell>
                        <cell>15.</cell>
                        <cell>15.</cell>
                        <cell>15.</cell>
                        <cell>15.</cell>
                        <cell>15.</cell>
                        <cell>15.</cell>
                     </row>
                     <row>
                        <cell>Sum.</cell>
                        <cell>60.</cell>
                        <cell>69.</cell>
                        <cell>75.</cell>
                        <cell>79 2/7.</cell>
                        <cell>82 1/2.</cell>
                        <cell>85.</cell>
                        <cell>87.</cell>
                        <cell>88 7/11.</cell>
                        <cell>90 The angle flanked.</cell>
                     </row>
                     <row>
                        <cell>Remaines 30.</cell>
                        <cell>39.</cell>
                        <cell>45.</cell>
                        <cell>49 2/7.</cell>
                        <cell>52 1/2.</cell>
                        <cell>55.</cell>
                        <cell>57.</cell>
                        <cell>58 7/11.</cell>
                        <cell>60 the double of the ang.</cell>
                     </row>
                     <row>
                        <cell>180.</cell>
                        <cell>180.</cell>
                        <cell>180.</cell>
                        <cell>180.</cell>
                        <cell>180.</cell>
                        <cell>180.</cell>
                        <cell>180.</cell>
                        <cell>180</cell>
                        <cell>180 The flanke interiour.</cell>
                     </row>
                     <row>
                        <cell>150.</cell>
                        <cell>141.</cell>
                        <cell>135.</cell>
                        <cell>130 5/7.</cell>
                        <cell>127 1/2.</cell>
                        <cell>125.</cell>
                        <cell>123.</cell>
                        <cell>121 4/11.</cell>
                        <cell>120 The flank exteriour.</cell>
                     </row>
                     <row>
                        <cell>15.</cell>
                        <cell>19 1/2.</cell>
                        <cell>22 1/2.</cell>
                        <cell>24 9/14.</cell>
                        <cell>26 1/4.</cell>
                        <cell>27 1/2.</cell>
                        <cell>28 1/2.</cell>
                        <cell>29 7/22.</cell>
                        <cell>30 The flank interiour.</cell>
                     </row>
                     <row>
                        <cell>90.</cell>
                        <cell>90.</cell>
                        <cell>90.</cell>
                        <cell>90.</cell>
                        <cell>90.</cell>
                        <cell>90.</cell>
                        <cell>90.</cell>
                        <cell>90.</cell>
                        <cell>90</cell>
                     </row>
                     <row>
                        <cell>105.</cell>
                        <cell>109 1/2.</cell>
                        <cell>112 1/2.</cell>
                        <cell>114 9/14.</cell>
                        <cell>116 1/4.</cell>
                        <cell>117 1/2.</cell>
                        <cell>118 1/2.</cell>
                        <cell>119 1/22.</cell>
                        <cell>120 the ang. of the should.</cell>
                     </row>
                  </table>
               </p>
               <p>And seing the angle flanked of a <hi>Dodecagone</hi> is right, and able to resist a batterie,
which is also made alwayes with right angles to shake the more the face of the Bul<g ref="char:EOLhyphen"/>warke;
one must fortifie the <hi>Polygones,</hi> which are aboue the <hi>Dodecagone,</hi> with a right
angle, that the line of defence may come the more into the curtaine, that one
may giue the more fire upon it: but the <hi>Polygones,</hi> which are under a <hi>Dodecagone,</hi>
must be fortified, according to the precedent Table, and the calculation thereof
shalbe made hereafter.</p>
               <p>Some times we augment, aswell the angles of the Bulwarkes, as the <hi>Octogone,</hi> a
Fortresse with 8 angles or Bulwarks, with a right angle, and those aboue are alwayes
right, &amp; those under diminishing to the square fortresse (which hath the angle of its
Bulwarke onely of 60 degrees.) According to which the Bulwarks are somewhat
larger, and the gorges and flanke greater then the former, but the second flanks
lesser. Now for the finding out of every angle, ye must doe this following, where
ye may observe, that in the manner aboue sayd, the angles flanking interiour are
the fourth part of the angle flanked, or the 1/<gap reason="illegible" resp="#TECH" extent="1 letter">
                     <desc>•</desc>
                  </gap> of the angle of the <hi>Polygone.</hi>
               </p>
               <p>
                  <table>
                     <row>
                        <cell>IIII.</cell>
                        <cell>V.</cell>
                        <cell>VI.</cell>
                        <cell>VII.</cell>
                        <cell>VIII</cell>
                        <cell>the angle</cell>
                     </row>
                     <row>
                        <cell>90.</cell>
                        <cell>108.</cell>
                        <cell>120.</cell>
                        <cell>128 4/7.</cell>
                        <cell>135.</cell>
                        <cell>the angle</cell>
                        <cell>of the Polygone.</cell>
                     </row>
                     <row>
                        <cell>60.</cell>
                        <cell>72.</cell>
                        <cell>80.</cell>
                        <cell>85 5/7.</cell>
                        <cell>90.</cell>
                        <cell>the angle</cell>
                        <cell>Flanked.</cell>
                     </row>
                     <row>
                        <cell>90.</cell>
                        <cell>72.</cell>
                        <cell>60.</cell>
                        <cell>51 3/7.</cell>
                        <cell>45.</cell>
                        <cell>the angle</cell>
                        <cell>of the center added thereunto.</cell>
                     </row>
                     <row>
                        <cell>150.</cell>
                        <cell>144.</cell>
                        <cell>140.</cell>
                        <cell>137 1/7.</cell>
                        <cell>135.</cell>
                        <cell>the angle</cell>
                        <cell>Flanking exteriour.</cell>
                     </row>
                     <row>
                        <cell>30.</cell>
                        <cell>36.</cell>
                        <cell>40.</cell>
                        <cell>42 <gap reason="illegible" resp="#TECH" extent="1 letter">
                              <desc>•</desc>
                           </gap>/7.</cell>
                        <cell>45.</cell>
                        <cell>the angle</cell>
                        <cell>double of the angl. flank. interiour.</cell>
                     </row>
                     <row>
                        <cell>15.</cell>
                        <cell>18.</cell>
                        <cell>20.</cell>
                        <cell>21 3/7.</cell>
                        <cell>22 <gap reason="illegible" resp="#TECH" extent="1 letter">
                              <desc>•</desc>
                           </gap>/2.</cell>
                        <cell>the angle</cell>
                        <cell>Flanking interiour,</cell>
                     </row>
                     <row>
                        <cell>90.</cell>
                        <cell>90.</cell>
                        <cell>90.</cell>
                        <cell>90.</cell>
                        <cell>90.</cell>
                        <cell>the angle</cell>
                        <cell>which is the flanke alwayes</cell>
                     </row>
                     <row>
                        <cell>105.</cell>
                        <cell>108.</cell>
                        <cell>110.</cell>
                        <cell>111 3/7.</cell>
                        <cell>112 1/2.</cell>
                        <cell>the angle</cell>
                        <cell>of the shoulder.</cell>
                     </row>
                  </table>
               </p>
               <p>In the same manner also may be made right the angle flanked of the <hi>Decagone,</hi>
a Fortresse of ten Bulwarks, where ye must note also, that before wee proceede
<pb n="6" facs="tcp:1568:6"/>
further, we will make use in the supputation following of the tenths or decinall
numbers; which though it gives some imperfection: yet seing the things, which we
omit therein are of no great consequence, it were ridiculous to make any further
search thereof; considering likewise that the tables of <hi>Sines, tangents,</hi> and <hi>secants,</hi>
are one and the same; I thought it good therfore to make use of these following.</p>
            </div>
            <div type="section">
               <head>THE I. QUESTION.
The 1. Figure, &amp; 1. Plate.</head>
               <p>Let there be made upon a Square a fortification of foure
Bulwarkes, so that the line of the Gorge be 7 parts: DI the
curtaine 21, and IF, which is the flanke of 5, and from the
angle of the flanke is drawne the line of defence by the angle
of the Shoulder, to giue it a face. The question is how many
the angles will be, and every line of the same fortresse, when
as the line of defence will take up 600 feete. Now the length
of a foote is sett downe in the 25 modell of Geometrie, noted
by 1, and is divided into 12 ynches, &amp; the ynch into 10 equall
parts, and is the same foote, whereof 12 makes a rodd, which
his Excell, useth in all his Fortifications.</p>
            </div>
            <div type="translators_note">
               <head>ALBERT GIRARD.</head>
               <p>THe Authour hath here aboue so disposed his calculations, that in stead of explaining
them briefly, he confounds them teadiously, as if heretofore there had bene noe certaine
rule sett dovvne in vvriting, to calculate lines and angles as is ordinarily done by the <hi>Tri<g ref="char:EOLhyphen"/>gometrie</hi>
of plaine Triangles, although there haue bene a number of Authours, vvhich
haue treated of them, th' one after one manner, th' other after an other; and the most part of
them commixed vvith longe discourses, vvhich moved me not longe since, to putt into light
some tables of <hi>Sines</hi> in a portable volume, vvith the most succinct method that possibly could,
touching the supputation of such plaine triangles, reducing them into foure diverse cases,
vvhere I did insert in their places, some of my ovvne inventions to the purpose, knovvne as
I suppose to none others heretofore; so that it cannot be, but having 3 knovvne termes, in a
triangle, but that one maye knovve the other three, or one of them onely, vvhich one desires,
as the Reader may knovve it; the manner &amp; order thereof being much more facile, &amp; easier
to conceiue, then the reading of our Authour in his former editions, being obscure, trouble<g ref="char:EOLhyphen"/>some,
and hard to be attayned unto. For this reason the Learners of this science, are required
to be forevvarned before they come to the reading of this booke; &amp; are advertized hereby,
that vvhen it is sayd, a triangle hath three termes, he must understand knovvne, or given,
and that vvhen I say that a triangle right-angle hath three termes, that then I am bound
but to shevv tvvo of them; seing that this vvord (right-angle) presupposeth that the triangle
hath a right angle, to vveet of 90 degrees: moreover, that touching this present question,
these 7, 21, 5 parts, demonstrate the reason of the lines <hi>ND, DI, IF,</hi> and not the quantitie
of the same in feete, as is necessary to finde in the manner follovving.</p>
            </div>
            <div type="section">
               <pb n="7" facs="tcp:1568:6"/>
               <head>To finde out the Angles.</head>
               <p>IN the triangle right angle CDI, the side CD, is to DI, as 5 to 21, (for CD being
of 5 parts; then DI wilbe the 21 thereof) therefore the angle DIC, wilbe found
for 13:24 its double CLD 26:48, and its adjunct CLF flanking exteriour, wilbe of
153:12. Now in the figure <hi>quadrilatere,</hi> or of foure-sides, ABLH; the angle exteriour
BLH is alwayes equall to the 3 interiours B, A &amp; H; now A 90, the angle of the
center, being taken from BLH, 153:12, there will remaine the two Demy-flankes
ABL, &amp; LHA 63:12. for one entire flank ZBC: &amp; seing that the angle of the Shoul<g ref="char:EOLhyphen"/>der
BCD, is exteriour in the triangle CDI, it wilbe equall to the two interiours
D.90. and 1. 13; 24, and therefore the Shoulder C, wilbe 103. 24.</p>
            </div>
            <div type="section">
               <head>To finde out the Lengths.</head>
               <p>IN a triangle <hi>ambligone</hi> BNI, the side BI is 600 feete, &amp; the angles are found, there<g ref="char:EOLhyphen"/>fore
the other termes shall be found, to wit BN the Capitall line 196, 64, &amp; NI,
444, 62, but ND is the third of DI (for ND being 7, DI is 21 by the <hi>Hypotheses</hi>) there<g ref="char:EOLhyphen"/>fore
the fourth part of the found NI, wilbe ND, 111, 15 the Gorge, &amp; the rest wilbe
333, 46, for DI, the Curtaine, now DI to DC is as 21, to 5: therefore one may say, if
21 giues me 5, how many DI 333, 46, giue me? facit for CD 79, 40. &amp; so CI wilbe 343,
84, which taken from BI 600, there will remaine BC 257, 16, for the face.</p>
               <p>Finally, the triangle right-angle VDH hath three termes, DH 600, and the angle
H equall to HDI. 13:24 (because of the parallels DI; VH) then yow shall know VD
139, 05, &amp; VH 583, 67, from which side substract VP (equall to Demy DI) 166, 73,
there will remaine PH 416, 94, whereof the double wilbe for BH 833, 88, and PA
wilbe 416, 94, for it is equall to PH, and thus must ye doe with the rest following.</p>
            </div>
            <div type="section">
               <head>The 3. Figure, 1. Plate.</head>
               <p>Let there be a square Fortresse, whereof the curtaine DI being 4
parts; the flanck CD shall haue 1 of them, and also the Gorge 1: The
defence running from the angle of the flanke, formeth the face, &amp; the
length BI is of 600 feete, one requires the greatnesse of the other lines
of the same Fortresse.</p>
            </div>
            <div type="section">
               <head>To finde out the Angles.</head>
               <p>THe triangle right-angle CDI hath three termes, as the reason of the sides CD, 1,
to DI, 4, therefore the flancking interiour CDI wilbe 14 degrees &amp; 2 mi<g ref="char:EOLhyphen"/>nutes,
whereunto add D 90 degrees, then the Shoulder BCD wilbe 104: 2; now if
ye double the angle CID, it wilbe 28:4, CMD, and its adjunct CMF, 151: 56 for
the angle flancking exteriour, from which substract the angle of the center A 90:
there will remaine 61: 56 for the angle flancked entire B, and thus much for the
angles.</p>
            </div>
            <div type="section">
               <pb n="8" facs="tcp:1568:7"/>
               <head>For the sides.</head>
               <p>THe triangle BNI, hath three termes, to witt, BI 600 feete, and the angles B, 30:
58. &amp; N, 135. I, 14. 2, so one shall finde the lines BN 205, 76 &amp; NI 436, 59; but in
regard that ND to DI is as 1, to 4, according to the Hypotese, then ND will be the
fifth of NI, where will follow that ND wilbe 87, 32 (and DC as much) and DI the
rest 349, 27. Now seing that in the triangle right-angle CDI, the sides CD, DI are
notified, one shall finde the Hypotenuse CI of 360, which taken from BI 600. there
remaines the face BC 240. Finally, in the triangle right-angle VDH, which hath 3
termes DH 600, the angle H, equall to CID 14.2, ye shall haue VD 145, 49: also
VH 582. 09, from which take VP 174, 64. (equall to the demy-curtaine DI) there
will remaine PH 407, 45, also PA its equall: then in the triangle right-angle APH,
ye shall finde AH 576, 22 from whence take BN or HO, the capitall line 205, 76,
there will remaine AO 370, 46, &amp; in takeing VD, from AP, there will remaine the
perpendicular of the Center, A upon the middest of the curtaine 261, 96. Now BH
wilbe 114, 90. as being the double of PH.</p>
            </div>
            <div type="section">
               <head>4. Figure. &amp; 1. Plate.</head>
               <p>In this square Fortresse, the defence BI is 600 feete, and the angle
flanked 60 degrees, whereof DBC is the fourth part, which is 15 de<g ref="char:EOLhyphen"/>grees,
the question is what the quantity of the parts of such a Fortresse
wilbe?</p>
            </div>
            <div type="section">
               <head>For the angles.</head>
               <p>SEing that the line flanked is 60, then in the triangle BNI the angle B wilbe 30, &amp; N
135, (the adjunct of ANI 45:) whereof the angle remayning BIN wilbe 15 degrees:
therefore the triangle BDI wilbe <hi>Isosceles,</hi> that is, two sides a like, such that DBI is
aswell 15; as BID; The Shoulder C wilbe 105, and in the triangle DMI, the angles
upon the basis are each of them 15 degrees, the remaynder M will be then 150 for
the flanking exteriour BMH.</p>
            </div>
            <div type="section">
               <head>For the sides.</head>
               <p>THe triangle <hi>Isoceles</hi> BDI hath three termes, the defence BI 600 feete, and the
pointed angles every of them 15 degrees. Therefore DI the Curtaine wilbe
310, 584. Also the triangle CDI, hath three termes, the angle D right; I 15. and the
curtaine DI, then CD the flanke 83, 217, &amp; CI 321, 535, which being taken from BI
600, there will remaine BC the face 278, 465. Moreover in the triangle IBN, the
angles B 30, I, 15, &amp; the defence 600: so then BN the Capitall line wilbe 219, 623,
&amp; NI 424. 268. from whence DI being taken there will remaine the gorge ND, 113.
684. Moreover, the triangle BIL having three termes, L right, B equall to CID 15.
and BI 600, then IL wilbe 155, 292, &amp; BL 579, 558, and takeing from it PL 155. 292.
(which is the halfe of the curtaine) there will remaine BP 424, 266 for AP; also its
double being BH 848, 532, one may also easely knowe BA 600.
<q>
                     <pb n="9" facs="tcp:1568:7"/>
The 5. Figure. &amp; 2. Plate.</q>
               </p>
            </div>
            <div type="translators_note">
               <head>ALBERT GIRARD.</head>
               <p>Heitherto of the defence dravvne from the angle of the flanke, but in those follovving,
there is a second flank, and the distance of the angle of the flank, euen to the angle flanked,
vvhich is called <hi>Fichant.</hi>
               </p>
               <p>The 5 figure is the dessigne or draught of a square Fortresse, whereof
the line of defence fichant DH maketh 600 feete, the angle flanked 60
degrees, the line HB is divided into 7 equall parts; whereof the one
which is betweene the Characters 1. 2. is subdiuided into 5 equall parts,
and from the center B, is made the Arch, 4 N cutting the capitall line
at N, from which point is drawne NDZ parallel to BH, and from the
point V (which is in the character 2) the perpendicular VD, the question
is how many these lines, and the angles of such a Fortresse, will make?</p>
            </div>
            <div type="section">
               <head>For the lines in parts indetermined.</head>
               <p>FOrasmuch as BH contayneth 35 such parts as BN 9; BV 10, VH 25, ye shall haue
in the triangle right-angle BTN termes enough to knowe BT, or TN 6, 364, and
TV or, ND 3, 636: Also the triangle right-angle DVH, had three termes, VD
equall to TN, 6364, &amp; VH 25, then DII wilbe 25, 797 parts or the same DH is 600
foote. We must then calculate according to this reason, the lines aboue mentioned
to bring them into feete, saying, as followeth.</p>
            </div>
            <div type="section">
               <head>For the lines in parts determined, to vvit, brought into feete.</head>
               <p>THe 25, 797 parts, make 600 foote, how many then will BH 35. come to? There
wilbe for BH 814, 04 foote, likewise VL, or DZ the curtaine may be made soe;
BH 7 parts make 814, 04 foote, how many VL 3? it will come for the curtaine to 348,
87, &amp; for BN the Capitall line ye shall say, if 35 giues 814, 04: how many 9? ye shall
haue for BN 209.32: and so of the other: for TN, or BT, or VD wilbe 148. 02, &amp; TV,
or the Gorge ND 84 57. and seing that BH is knowne, also VL the halfe of the
remainder wilbe BV 232, 58. In the triangle right-angle BVC, the angle B wilbe 15
degrees: (for PBO is 45, &amp; CBO 30:) and BV being knowne, therefore BC the
face wilbe 240, 78, and VC 62, 32, which being taken from VD, there will remaine
CD the flanck 85. 7; and therfore the triangle right-angle CDI, shall haue 3 termes,
the angle C 75, &amp; CD 85, 7. soe DI wilbe 319, 84, CI 331, 15, likewise BI flancking
571, 93. &amp; I, Z 29. 03 for the second flancke. Now OP is knowne as being the halfe
of BH.</p>
               <p>Now of the Pentagons, or Fortresses with fiue angles or Bulwarks.</p>
            </div>
            <div type="section">
               <head>6. Figure. &amp; 2. Plate.</head>
               <p>In the Pentagone, a Fortresse with fiue Bulwarks, KFBDL, let the
<pb n="10" facs="tcp:1568:8"/>
line, KL be 63 rods, &amp; divided into 7 equall parts, whereof the Capitall
line KA is 2 of them, also LE, and from the Character 2 (or G) let GB
be the perpendicular. Also the angle flancked is 69 degrees, according
to the precedent table, how many then wilbe the lines and the angles of
such a Fortresse?</p>
            </div>
            <div type="translators_note">
               <head>ALB. GIRARD.</head>
               <p>Before vvee come to the Construction hereof, take notice, that <hi>KA</hi> in this figure is not
ansvverable to the length of <hi>KG,</hi> yet ye must suppose them to be equall, asvvell as the cipher
1, and the letter <hi>H,</hi> are tvvo differing points, vvhich vvould haue bene the better discerned,
if the figure had bin vvell made, vvhich may serue as a fore-vvarning for some figures
follovving, upon vvhich one ought not to stand so much as upon the Suppositions, or <hi>Hypo<g ref="char:EOLhyphen"/>teses</hi>
of the Propositions.</p>
               <p>The triangle right-angle KHA hath three termes, KA 18 rodd, the angle AKH
54 degrees, which being of KH wilbe 10, 5802, &amp; HA or GB 14, 5623. Now if ye take
away KH from KG, there will remaine for AB the Gorge, 7. 4198. Item the curtaine
BD wilbe 27 rodd, being equall to GM. And because the angle flancked is 69
degrees, if ye add thereunto the angle of the Center, which is 72, ye shall haue the
angle flancking exteriour, 141 degrees, the halfe of its adjunct for the interiour
19 1/2 degrees. The triangle right-angle KGF, hauing 3 termes, KG 18, GKF 19 1/2: the
face KF wilbe 19, 0953, and FG 6. 3741, which being taken from GB 14, 5623. there
will remayne FB (the flanck) <gap reason="illegible" resp="#TECH" extent="1 span">
                     <desc>〈…〉</desc>
                  </gap>, then the triangle right-angle FBI may be
knowne, seing that FB is found, and the angle <gap reason="illegible" resp="#TECH" extent="1 span">
                     <desc>〈…〉</desc>
                  </gap> 1/2 the complement of 1; therefore
BI wilbe 23.1227, which taken from BD 27, there will remayne ID for the second
flanck 3, 8773, also FI wilbe found to be 24, 5297, whereunto add KF 19. 0953, and
ye shall haue KI, the defence flancking 43. 6250, finally the triangle right-angle
LGB, hauing three termes, to wit LG 45 rodd, and GB 14, 5623; one may easely
know BL, and the distance of the Center of the Fortresse by K, because that KP is
31 1/2 rodd, and the angle AKP 54 degrees.</p>
            </div>
            <div type="section">
               <head>The 7. Figure, &amp; 2. Plate.</head>
               <p>In a Fortresse Pentagonall, BOV, let AB the deffence flancking be
50 rodd, the Flanck ED 9 rodd, and the angle of the Bulwarke 72 de<g ref="char:EOLhyphen"/>grees.
How many then will the other parts of the same make, when the
second flanck AG makes fiue rodd.</p>
               <p>THe angle of the <hi>Polygone</hi> is 108, the halfe is 54 for FBQ, to which add CBF 36
degrees by the Hypoteses, you shall haue 90 for CBQ, but CF is paralell to BQ
therefore BCA right, the triangle BCA wilbe then the right-angle, and BA of 50,
and the angle B of 72 degrees, then ye shall finde BC, or QD to be of 15, 451, and CA
47, 553, and the angle A 18 degrees. Also in the triangle right-angle EDA, the angle
A is giuen, and the side ED 9 rodd, by the <hi>Hypotese,</hi> then EA wilbe 29, 12463, &amp; DA
27, 69912; now if ye take EA from DA, there will remaine BE the face 20, 87537, and if ye substract DA from AC, there will remaine CD, or BQ, 19. 854. Also the
<pb n="11" facs="tcp:1568:8"/>
triangle right-angle BCF, hath 3 termes, BC and the angles; in fine BF the capitall
line wilbe 19, 097 &amp; CF, 11, 226, which being taken from CD, there will remaine
FD 8, 628, the Gorge; now if to DA, ye add AG 5 rodd, the second flanck, ye shall
haue the curtaine DG 32. 69912, to which add twise BQ, and ye shall haue BV 72,
40711 its half BK 36, 20355, and so the triangle right-angle BKO, hauing 3 termes,
the angle KBO wilbe 54 degrees, ye shall finde BO 61, 593099, and KO 49, 82984.
Finally VB, BQ being knowne, then the triangle right angle DQV, hauing 3 termes
giuen VQ, &amp; QD; ye shall finde the fichant DV easely.</p>
            </div>
            <div type="translators_note">
               <head>ALB. GIRARD.</head>
               <p>IF one vvill consider the difference vvhich is betvveene this operation, and that of our Au<g ref="char:EOLhyphen"/>thour
published in his former Editions, he shall finde that this question is defectiue, for I
haue added thereunto (that the second flanke <hi>AG</hi> is rodd) seing that in all such questions,
vvhere there is a second flank, he ought to haue set dovvne 5 knovvne termes &amp; neither more
nor lesse, vvithout the one depending on the other, as in this present, the name of the Fortresse,
to vvit, <hi>Pentagonall</hi> is a terme, in the second place there is the defence; then the flanck, the
angle flancked, and the second flancke, vvhich are fiue termes: vvhere ye must note, that
vvhen there are reasons in the proposition, and that though a reason hath tvvo numbers,
neverthelesse it is but one terme; but vvhere there is no second flanck (as in the figures of the
first plate, then 4 termes vvill suffice.) Finally, my Authour had so ordained his Supputation,
that in stead of makeing an addition, or a substraction; he made the rules of three very great,
so that ye must imagine it vvas easier for me to change all, then to recorrect it, hauing no other
respect, but to the explication of the figures, and as much as is lavvfull and possible to shevv
his intention, vvhich I am bound to doe: Moreouer, if peradventure same one should finde
this manner of operation strange, vvhich I <gap reason="illegible" resp="#TECH" extent="1 span">
                     <desc>〈…〉</desc>
                  </gap> heitherto, it is requisite for him to
knovv also (be it spoken under <gap reason="illegible" resp="#TECH" extent="4 letters">
                     <desc>••••</desc>
                  </gap>ection) that he understandeth not much, if he doth not
practize it soe himselfe in other Subjects, yea though I had not sett dovvne one onely number;
vvhich I should haue done already heretofore, if I had not had regard to the obscuritie, vvhich
students might pretend to finde, vvhich hauing cleared heitherto, ye may goe on vvith the
more assurance in the rest follovving: and must also knovv, that the 8 figure vvas left
vvithout explication by the Authour.</p>
            </div>
            <div type="section">
               <head>The 8. 9. 10 Figure. &amp; 3. Plate.</head>
               <p>In this figure Pentagonall, the angle ELO is divided into 2 equall
parts by LD, the flanck FB 9 rodd, the angle flancked 69 degrees, and
the curtaine 30 rodd, how many then will the other lines &amp; angles be?</p>
               <p>THe angle of the <hi>Polygone</hi> is parted in the midst by KA, and the angle AKF is
knowne, also the rest shalbe FKG, or its equall FB, whence followes that the
triangle right-angle FBI shall haue 3 termes FB, and the angles; therefore the other
3 termes wilbe knowne, also the whole line DB, and the part BI, ergo the rest ID is
the second flanke. The triangle KBI hath three termes, the angle found, BI &amp; K
(the fourth part of the flanck by consequence the 3 termes remayning are knowne,
and the difference of the found lines KI, IF wilbe for the face KF; which makes that
in the triangle right-angle KGF wilbe knowne KG. GF; and if to KG doubled,
ye add the curtaine, ye shall haue KL; also KG to the curtaine is for GL, or XB if to
GF ye add FB, ye shall haue LX, and therefore in the triangle right-angle LB wilbe
<pb n="12" facs="tcp:1568:9"/>
knowne; seing that LX, XB are found. Moreouer, in the triangle right-angle LXE,
the angle E is a demy <hi>Polygone,</hi> and the line LX being knowne, ye shall haue LE the
Capitall line, and XE taken from XD (equall to KG) there will remayne DE the
Gorge.</p>
               <list>
                  <item>BI 25, 4151</item>
                  <item>FI 26, 9617</item>
                  <item>ID 4, 5848</item>
                  <item>KI 51, 2795</item>
                  <item>KF 24, 3178</item>
                  <item>KG 22, 9229</item>
                  <item>GF 8, 1175</item>
                  <item>KL 75, 8459</item>
                  <item>XB 52, 9233</item>
                  <item>LX 17, 1175</item>
                  <item>LB 55, 6227</item>
                  <item>LE 21, 1583</item>
                  <item>XE 12, 4366</item>
                  <item>DE 10, 4863</item>
               </list>
            </div>
            <div type="section">
               <head>The 9. Figure, vvhich is the 8, 9. 10. &amp; 3 Plate.</head>
               <p>In the former figure Pentagonall, there are other <hi>Hypoteses</hi> BL, fichant
60 rodd, the angle DLM 36 degrees, and 45 minutes, DM 17 rodd, and
the angle OLE parted in the midst by LM.</p>
               <p>THe angle MLE is 54: from which take DLM 36, 45; there will remaine
17, 15; for DLE its quadruple or fourefould for the angle flancked 69: ye
must first calculate the traingles right-angles MDL, QEL, whereby is found DE
the Gorge, LE the Capitall line, and ML in the triangle right-angle LGB; the line
of defence LB 600, and GB 17; therefore ye shall finde GL, which added to KG
equall to ML, ye shall haue <gap reason="illegible" resp="#TECH" extent="1 span">
                     <desc>〈…〉</desc>
                  </gap> take ML, from it, there will remaine GM
for the curtaine BD, in the triangle MLO, ye shall find the face OL, &amp; MO, which
taken from 17, there remaines OD for the flanck, &amp; the triangle right-angle ODC
may be knowne, because the angle C, is equall to MLO 19 1/2, then CO &amp; CD being
notified, ye shall find CL &amp; BC, and from the Center of the Fortresse wilbe knowne
the distances towards K, P, A.</p>
               <list>
                  <item>DE 10, 41454</item>
                  <item>LE 21, 01319</item>
                  <item>ML 22, 76572</item>
                  <item>GL 57, 54128</item>
                  <item>KL 80, 30700</item>
                  <item>BD 34, 77556</item>
                  <item>OL 24, 15101</item>
                  <item>MO 8, 06179</item>
                  <item>OD 8, 93821</item>
                  <item>OC 26, 77657</item>
                  <item>CD 25, 24075</item>
                  <item>CL 50, 92758</item>
                  <item>CB 9, 53481</item>
                  <item>A (†) 47, 30000</item>
               </list>
            </div>
            <div type="section">
               <head>The 10. Figure, vvhich is the 8, 9. 10.</head>
               <p>In the figure Pentagonall, let LB fichant be 60 rodd, and LC the de<g ref="char:EOLhyphen"/>fence
flancking 50, 92758 fifth-parts. Also BC the second flancke 9,
53481, and the angle OLE parted in the midst by LD.</p>
               <p>THe triangle BCL hauing the three sides giuen, then ye shall finde the angle C,
or the lengthning of the basis BC unto the perpendicular X, as followeth here,
the basis BC, 9, 53481 giueth me the Summe of both the other sides, 110, 92758,
<pb n="13" facs="tcp:1568:9"/>
how much then will their difference 9, 07242 giue? it will come to 105, 54816,
from which take the basis (because that the perpendicular falls without, which is
seene, when the sayd quotient is more then the basis) there will remaine one
number, whereof the halfe is CX 48, 00668, this being done ye must calculate the
triangle right-angle CLX, by which ye shall know the angle C, or LMO, which
taken from LME, the remainder wilbe OLE, 34 1/2, and the angle flancked wilbe
the double of it 69; also ye shall haue LX, or MD, and then shall ye calculate the
triangle MDL (for the angle MLD is knowne) seing it is equall to MLO 19 1/2, and
OLD 17 1/2: Also the triangle LQE, whereby ye shall finde the Gorge, the Capitall
line, &amp; CD, then by the triangle ODC is found the flanke, &amp; after that the face: &amp;
if to CX aboue sayd, ye put BC being giuen, there will come out BX, or GL, to
which add ML by addition, then by substraction ye shall haue KL, and the curtaine
BD, whereof the numbers agree with those of the precedent question.</p>
            </div>
            <div type="section">
               <head>The 11. Figure. 3. Plate.</head>
               <p>In this figure <hi>Hexagone,</hi> that is, a Fortresse with sixe angles or Bulwarks,
let the Curtaine be sesquialtere, or halfe as much againe to the face, &amp;
the face to the flancke doubled-sesquialtere, the angle flancked 75
degrees, and DP distant from the points 70 rodd. Wee must finde out
the rest.</p>
               <p>SEsquialtere, or one and a halfe, is as 3 in respect of 2; twise sesquialtere is as 5 to 2:
so that BH, DC, CB wilbe as 15, 10, 4. whereunto if yee add 4 cifphers to each of
them, DC wilbe 100000 sines of the right-angle. Now ADF is 60, and ADC 37 1/2,
then CDF wilbe 22 1/2 degrees; therefore CF 38268, and DF 92388 also KP; but BH,
or FK is 150000, then DB wilbe 334776 parts, which make 70 rodd by the <hi>Hypoteses,</hi>
wee will bring then these lines into Rodds, according to this reason following;
because 334776 parts make 70 Rodd.</p>
               <list>
                  <head>How many partes. they will come to.</head>
                  <item>150000 31, 364 BH</item>
                  <item>100000 20, 909 DC</item>
                  <item>40000 8, 364 CB</item>
                  <item>38268 8, 002 CE</item>
                  <item>92388 19, 318 DF</item>
               </list>
               <p>And seing that PD, DF are knowne, FP wilbe also; and by FC, CB, wilbe knowne
FB, or AE, 16. 366, now by the 47 pro.1 of Euclide BP fichant wilbe 53, 259: And if
one calculates the triangles CBG, DEA, ye shall finde DG, 42, 765; and DE, 9, 448,
ergo EF, or AB the Gorge wilbe 9, 87; the distance from the Center to D, is equall
to DP, 70 rodd.</p>
            </div>
            <div type="section">
               <head>The 12. Figure. &amp; 4. Plate.</head>
               <p>Let DP be 72 rod, the angles of the Bulwarks are 72 degrees, the
curtaine BH 32 rod, the flancks of 8, 3638, fourth of rodds, how many
then wilbe the other parts of this Fortresse Hexagonall?</p>
               <p>
                  <pb n="14" facs="tcp:1568:10"/>
Seing that DP is 72, &amp; BH, or FK 32, then the halfe of the rest wilbe 20 for DF,
and also the angle ABF being 60 degrees, and ADC 37 1/2, then CDF wilbe 22 1/2 de<g ref="char:EOLhyphen"/>grees:
whereby ye shall know then the triangle right-angle CDF. Secondly, FC
found, with CB giuen, will make knowne FB, but PF is 52, then the triangle
right-angle BFP hath the sides BF, FP knowne, &amp; BP wilbe knowne in the triangles
right-angles ADE, CBG, their termes will suffice to make the rest to be understood.
when ye haue DA, its halfe wilbe for DE, which taken from DF, there will remaine
AB.</p>
               <list>
                  <item>DG 21, 64780</item>
                  <item>FB 16, 64800</item>
                  <item>BP 54, 60000</item>
                  <item>AD 19, 22344</item>
                  <item>DE 9, 61172</item>
                  <item>AB 10, 38828</item>
                  <item>GH 11, 80804</item>
                  <item>DG 43, 50349</item>
               </list>
            </div>
            <div type="section">
               <head>The 13. Figure.</head>
               <p>In this Figure <hi>Hexagonall,</hi> the second flanke is in the flanke as 6 to 7,
the flanke hath its gorge as 7 to 10, the Gorge to the line of the <hi>Polygone,</hi>
as 2 to 9. the question is how many they, &amp; the other dimensions wilbe,
when as DH makes 60 rodd.</p>
               <p>IF ye make GH 6, then HO wilbe 7, &amp; HI 10, the Curtaine wilbe 25; Then ye shall
calculate the triangles CBG, DAG by which ye haue the angle G, or his equall
CDF, &amp; the face D<gap reason="illegible" resp="#TECH" extent="1 letter">
                     <desc>•</desc>
                  </gap> and then in the triangle DCF, the lines DF, FC, FB, FP, and
finally BF 44, 93555, which make <gap reason="illegible" resp="#TECH" extent="1 word">
                     <desc>〈◊〉</desc>
                  </gap>
                  <g ref="char:punc">▪</g> for which reason one must reduce the
parts into rodds: but this reason may be sett downe more easie, in takeing but 7,
48926, which make 1000000 parts; Now if ye had rather worke it by multiplication,
without division, then ye must take but 100000 parts, which make 13352 rodd, and
so ye shall finde</p>
               <list>
                  <item>DC 25, 38302</item>
                  <item>CB 9, 34672</item>
                  <item>BA 13, 35246</item>
                  <item>DP 81, 01484</item>
                  <item>BH 33, 38115</item>
                  <item>The angle flancked 79. 33.</item>
               </list>
            </div>
            <div type="section">
               <head>The 14. Figure, the 1. of the tvvo.</head>
               <p>In this Fortresse <hi>Hexagonall,</hi> let EH be 60 rodd, and EI, BC, KH equall,
the flanke KC 8 rodd, it behoues us to finde out the rest.</p>
               <p>BY the help of the rule of <hi>Algeber,</hi> ye shall finde that the angle EIF wilbe 69 de<g ref="char:EOLhyphen"/>grees,
4 1/2 minuts; then in the triangle IBC, the angle I, &amp; the side IB 8 rodd being
giuen, ye shall finde BC 20, 9229 for the face EI; also IC wilbe 22, 4002, then EC
will make 43, 3231, the rest is easie, without the second flanck.</p>
            </div>
            <div type="section">
               <head>The 15. Figure.</head>
               <p>This figure hath for the flanke 10 rodd; the rest being like to the
former they shalbe put in order in the Tables following.</p>
            </div>
            <div type="section">
               <pb n="15" facs="tcp:1568:10"/>
               <head>The 16. Figure. &amp; 5. Plate.</head>
               <p>The flanke of this <hi>Heptagone,</hi> that is, A Fortresse with seuen angles, or
Bulwarks, maketh 10 rodd, the distance of the points 72 rodd, and the
angle flanked 80 degrees, how many then will the rest make, when as the
second flanke is 10 rodd.</p>
               <p>SEing that the angle of the Bulwarke makes 80 degrees, and the angle of the <hi>Poly<g ref="char:EOLhyphen"/>gone</hi>
128:34, 17 the difference divided in the halfe wilbe the angle flanking inte<g ref="char:EOLhyphen"/>riour
24, 17, 18 1/2, the flanck CB 10 rodd, whence the triangle CBG wilbe knowne, &amp;
by adding GH giuen to BG, ye shall haue the curtaine 32, 1623, which taken from
DP 72 rod, and then take the halfe of the rest, ye shall finde DF, and also DC. CF,
for the face DC 21, 8525, &amp; DG 46, 1666, also in the triangle DAE; ye shall haue
DE, &amp; consequently EF, or AB. Moreouer ye shall finde DH in the triangle DKH,
to be 55, 4345.</p>
            </div>
            <div type="section">
               <head>The 17. Figure, &amp; 5. Plate.</head>
               <p>This <hi>Heptagone</hi> hath the flanke of 9 rodd, the angle flanked 79 degrees
25. 43, DP <gap reason="illegible" resp="#TECH" extent="1 letter">
                     <desc>•</desc>
                  </gap>2 rodd, and the choice of the second flanke.</p>
            </div>
            <div type="translators_note">
               <head>ALB. GIRARD.</head>
               <p>HAuing calculated the angles as in the former. OM wilbe 21, 6436, and HM, 19
6836, let us make the second flanke 7, 3164, and then the curtaine wilbe 26; DF,
23; the face OP 25, 2901. MP 46, 9337. <hi>Marolois</hi> had giuen here 80 degrees, but
tooke no more then 79, 25, 43, for the angle flanked, which he did without pre<g ref="char:EOLhyphen"/>meditation.</p>
            </div>
            <div type="section">
               <head>The 18. Figure. &amp; 5. Plate.</head>
               <p>In this present <hi>Heptagone</hi> the angle flanked is 79 degrees, the gorge 12
rodd, &amp; the curtaine 32 rodd, how much will the other lines &amp; angles
make of this Fortresse.</p>
               <p>TO resolue this question, ye must suppute from the triangle CBG, the lines CG,
GB, and ye shall haue GB the second flanke; now if to BG, ye add AB, ye shall
haue AG, then the triangle DAG wilbe knowne; afterward the triangle DAE, and
finally the triangles DCF, and DHK.</p>
            </div>
            <div type="translators_note">
               <head>ALB. GIRARD.</head>
               <p>NOte that in this Question <hi>Marolois</hi> had sett downe the angle flanked 79 and 2
seuenths, yet did not followe this number, but 79 degrees: the same errour
also was committed in his supputation of the former, and in the 14 figure. One
cannot gesse well his Supposition: neuerthelesse that needes not to stay the reader;
for I haue sett downe the question, as it seemes he would haue propounded it, but
<pb n="16" facs="tcp:1568:11"/>
the worst is, he made 2 figures, and one cannot understand well of which of either of
them he would speake, but we will speake more thereof hereafter; howsoeuer those
which are most intricate (aswell by reason of the faults escaped in the impression of
the former Editions, as by the errour of his disciples, which did calculate them)
shalbe partly omitted, and shall giue no impediment, but that the rest may giue con<g ref="char:EOLhyphen"/>tentment
to the Readers, for that which they are desirous to finde out in this booke:
(in the 20 figure following the Letters ye were sent unto were wholly repugnant.)</p>
            </div>
            <div type="section">
               <head>The 19. Figure.</head>
               <p>In this <hi>Heptagone</hi> let the angle flanked be 80 degrees, &amp; the angle from
the Capitall line, &amp; from the imagined DB (to wit ADB) let be 22 ½ de<g ref="char:EOLhyphen"/>grees,
DP 82 rodd, &amp; the flank CB 10 rodd.</p>
               <p>FRom the angle of the <hi>Polygone</hi> 128, 34, 17, take the flanked 80, the halfe of there<g ref="char:EOLhyphen"/>mainder
wilbe 24, 17, 9: for the angle flanking interiour DGA: beginn then the
triangles CBG, DBG. (whereof the angle in D maketh 17 ½) ye shall finde BG 22,
1621, CG 24, 3138; &amp; BD 30, 3118, then GD wilbe 49, 1096, and DC the face 24,
7958, afterward the triangle BDF, the line BF wilbe found to be 20, 1982, and DF
22, 6014, whereof the double taken from DP 82, there will remaine for the curtaine
BH 36, 7972, and consequently for the second flanke GH, 14, 6350. Now knowing
the triangle DEA, ye shall finde the Capitall, also the gorge AB 12, 8744. If in the
triangle DKH, yee seeke DH, then ye shall finde it to be 62, 7388. Now the reason
of the Demy-diameter or middle line in the side of this <hi>Heptagone,</hi> is as 1000000000,
to 867767478.</p>
            </div>
            <div type="section">
               <head>The 20. Figure.</head>
               <p>This present <hi>Octogone,</hi> that is a Fortresse of 8 angles or Bulwarks, hath
the distance DP divided into 7 equall parts, whereof DF, &amp; FB make
each of them 2, &amp; BP fichant is 60 rod, the angle flanked 82 ½ degrees.</p>
               <p>THe line BF being 2, and FP 5, then the square of BP wilbe 29, and seing that BP
is 60 rodd, its square wilbe 3600 rod, by which reason ye may knowe one part of
the 7 of DP, saying, if 29 giues me 3600, how many will 1 giue me (the square of an
other part?) it will come to 124, 1379310345, whereof the square roote substracted
wilbe 11, 14172, and its double 22, 28344 for DF, or FB, the triple is 33, 42516 for the
curtaine BH, and the seventhfould 77, 99204 for DP. Moreouer, the angle flanking
interiour, or its equall FDC wilbe 26, 15; so that DC wilbe 24, 84581, also FC 10,
98907, the flanke then wilbe 11, 29437 (for FB was knowne) in the triangle right<g ref="char:EOLhyphen"/>angle
DRG, the angle D is also 26. 15; and RC equall to FB, then DG the line of
defence flanking, wilbe 50, 38218; finally, the Capitall wilbe found 24, 11937, and the
gorge AB 13, 05342, if ye calculate the triangle DEA.</p>
            </div>
            <div type="section">
               <head>The 21. Figure.</head>
               <p>In this <hi>Octogone</hi> let the face be 24 rod, the flanke 12, &amp; the curtaine 36
rod, &amp; the angle flanked, right, it is required how many the other lines &amp;
angles wilbe?</p>
               <p>
                  <pb n="17" facs="tcp:1568:11"/>
The angles ADF 67 ½, &amp; ADC 45, will make knowne CDF to be 22 ½ Now DC is
24 rod, by consequence DF, FC, DP, FB wilbe knowne; also seing that FB is found (or
EA) ye haue also the triangle DEA, by which ye shall finde DA, AB, &amp; shall finde
DG in the triangle CBG: for hauing CG, ye add unto it DC) finally DH in the
triangle DKH.</p>
               <list>
                  <item>DP 80, 34624</item>
                  <item>DG 55, 35756</item>
                  <item>DH 61, 91032</item>
                  <item>GH 7, 02948.</item>
                  <item>AB 13, 39837.</item>
                  <item>AI 62, 39837.</item>
               </list>
            </div>
            <div type="section">
               <head>The 22. Figure.</head>
               <p>In this present <hi>Octogone,</hi> the flanke is 11 rod, the angle flanked 82 ½ de<g ref="char:EOLhyphen"/>grees,
the line DP 76 rod, &amp; the second flanke to be choosen, how many
then wilbe the other parts of this Fortresse?</p>
               <p>THe angle of the <hi>Octogone</hi> is knowne, and the angle flanked, also their halfe ADF,
ADC, therefore the rest, and the triangle CBG wilbe knowne, and BG wilbe
found 22, 3058, suppose the second flanke GH is 9, 6942, then BH 32 rod, likewise as
much for FK; but DP is 76, therefore DF makes 22, and after ye haue calculated
the triangles DCF, DAE, ye shall finde DC, 24, 52978, DG 49, 40045, AB 12, 94981,
and finally in the triangle DKH the fichant DH, 58, 25283.</p>
            </div>
            <div type="section">
               <head>The 23. Figure.</head>
               <p>Let the angle flanked be 82 ½ of this present Octogone, the line of
defence DG 50 rod, DP 76, and CAB the halfe of the angle flanked.</p>
               <p>AFter ye haue carryed AC, which was forgetten, if ye count the triangles DAG,
ACG, ye shall finde the Capitall, the face, and the gorge, and BG, then the trian<g ref="char:EOLhyphen"/>gles
CBG, DCF, afterward ye shall haue CB, CF, DF, and therfore FK, or the cur<g ref="char:EOLhyphen"/>taine,
and the second flanke, then DH, 58, 3498.</p>
               <list>
                  <item>The Capitall 23, 93655</item>
                  <item>The Gorge 12, 84323</item>
                  <item>The Flanke 11, 26362</item>
                  <item>The second flanke 9, 15324</item>
                  <item>The face 24, 53340</item>
                  <item>The Curtaine 31, 99346</item>
               </list>
            </div>
            <div type="section">
               <head>The 24. Figure.</head>
               <p>Let there be an <hi>Enneagone,</hi> A fortresse with nine Angles or Bulwarks,
(that is with 9 sides) whereof the angle flanked is 85 degrees, the face 24
rod, the flanke 12, and the curtaine 36 rod.</p>
               <p>THe angle of the <hi>Polygone</hi> is 140 degrees, seeke the triangles, DCF, CBG, DEA,
DKH, and then ye shall finde the lines GH 12, 94824: DP 78, 57648: AB 12,
88709.</p>
            </div>
            <div type="section">
               <pb n="18" facs="tcp:1568:12"/>
               <head>The 25. Figure.</head>
               <p>As in the tables aboue let the angle flanked of the Enneagone be 85
degrees, the fichant 60 rod, and DP being 7 parts, then let DF be two of
them, afterward FB the perpendicular 2, for the makeing of the flanke
CB, wee require the rest.</p>
               <p>DK being 5 parts, and KH 2. the square DH wilbe 29. which makes 3600, whereof
1 makes 124, 13793103 for the square of one part, its root substracted wilbe 11, 14172
for one part, whereof the double wilbe for DF, or FB, and the triple for FK, or the
curtaine 33, 42516 BH, and after ye haue calculated the triangles DFC, CBG, DEA,
ye shall finde the other lines DC 25, 1219, DG, 48, 25855, GH 12, 9026, BC wilbe 10,
68335, the seuen parts of the number aboue sayd wilbe for DP, 77, 99204.</p>
            </div>
            <div type="section">
               <head>The 26. Figure.</head>
               <p>In this present <hi>Enneagone,</hi> let the angle flanked be 85 degrees, the de<g ref="char:EOLhyphen"/>fence
50 rod, the other 60, &amp; the gorge in the flanke as 4 to 3. the rest is
required.</p>
               <p>IF ye take away the angle ADC 42 ½ from ADF 70, the angles GDR will remaine,
and DG makes 50 rod, then the triangle DGR wilbe knowne, to wit, DR, &amp; RG,
or KH 23. 0875, which will make ye knowe the triangle DKH (for DH is 60) then
RK, or GH wilbe 11, 0301. Moreouer, in the triangle DEA the side EA is equall to
KH, by DE &amp; DR, ye shall haue AG 35, 94735, then in carrying AC, ye shall seeke
the angle A from the triangle ABC, setting downe AB 4, and BC 3 parts, according
to the <hi>Hypatese,</hi> ye shall finde then the angle A of 36 degrees, 52 min. &amp; 12. seconds.
Then let us goe to the triangle ACG, hauing AG knowne, the angle A &amp; G, equall
to CDF 27 ½ degrees, to finde CG afterward the face, and consequently DF, FK, EF
or AB the Gorge, which wilbe 14, 72808, therefore if 4 giues 3, how many then AB?
ye shall haue BC for the flanke 11, 04606, &amp; DP 78, 51183, DA 24, 56925.</p>
            </div>
            <div type="section">
               <head>The 27. Figure.</head>
               <p>The distance DP being 7 parts, DF &amp; FB each of them 2 parts, the
defences 50 &amp; 60 rod, and the angle flanked 85 degrees, how many will
the other dimensions be of such a Fortresse non angular?</p>
            </div>
            <div type="translators_note">
               <head>ALB. GIRARD.</head>
               <p>THis question is impossible to resolue being exceeding, seing that there is a condition in it
more then one desires, &amp; vvhich is vvorst, repugnant to the others, for vvhich fault the
Authour may be excused, seing that in his time, there vvere no such advertisements giuen as
vvee haue giuen thereof in the beginning of the <hi>Trigonometrie,</hi> cited in the first question
going before, the vvhich though they may seeme to be of litle consequence to some; yet one must
acknovvledg, that those that knovve them shall not fall into the like errours, as these vvhich
may be explained thus; There are tvvo reasons giuen <hi>DP</hi> to <hi>DF,</hi> and <hi>DF</hi> to <hi>FB</hi> (a reason of
<pb n="19" facs="tcp:1568:12"/>
equality) tvvo lines of defence the angle flanked, &amp; the name of the figure of nine-side figure,
vvhich are sixe termes, yet one needes but 5 (as ye shall finde it noted in the 7 figure, vvhere
the question vvas defectiue, and of some others aftervvard) finally, the proofe of this may be
seene in makeing comparaison of this vvith the 25 figure, vvhere the same question is pro<g ref="char:EOLhyphen"/>pounded,
and vvhere ye shall finde that the defence flanking ought to be 48, 25855, and here he
vvill haue it 50, vvhich is absurd, as is said.</p>
            </div>
            <div type="section">
               <head>The 28. Figure.</head>
               <p>In this present <hi>Decagone,</hi> a Fortresse with ten angles or Bulwarks, let
the angle flanked be 87 degrees, the Gorge in the flanke in reason
sesquitertia, the defences 50 and 60 rod, it is required how many the
other parts thereof will make?</p>
               <p>THe reason <hi>sesquitertia</hi> is, as 4 to 3, for AB to BC, then the imaginall angle BAC
wilbe 36 degrees, 52 minutes, 12 seconds. Moreouer, the angle ADC being 43 ½
then CDF wilbe 28 ½, which is an angle of the triangle GDR, and which may be
knowne, seing that DG is 50 rod, therefore GR 23, 858, or its equall KH, and for as
much as DH is 60, then DK wilbe knowne, and also DR withall, and so ye shall finde
RK for the second flanke: likewise the triangle DEA wilbe knowne, then ED and
DR will make knowne ER, or AG, &amp; consequently ye shall haue the triangle ACG
for the angle A was found aboue, and the angle G is 28 ½ degrees, then the face wilbe
26, 11334, and hauing found out DF, ye shall finde EF, or the gorge 15, 197: Also FK
for the curtaine 32, 10821; DP 78, 00619.</p>
            </div>
            <div type="section">
               <head>The 29. Figure.</head>
               <p>In this <hi>Decagone</hi> the angle flanked maked 87 degrees, the defence
fichant 60 rod, the flanke 12 rod, and the gorge 16 rod, it is required how
much the other parts make?</p>
               <p>THe <hi>quadrangle</hi> ABCD hauing fiue termes giuen, ye shall finde the other parts;
also the triangle DFC, whereby ye haue FB, or KH, &amp; consequently the triangle
DKH, and hauing FD &amp; DK, their summe and difference wilbe for DP, 78, 65, and
BH 30, 32633; the face shall be 27, 49377: DG 52, 64265.</p>
            </div>
            <div type="section">
               <head>The 30. Figure.</head>
               <p>In this <hi>Decagone,</hi> let the curtaine be 36 rod, and the flanke 12, the face
24, and the reason of the Bulwarke in the flanking interiour, as 58 to 19.</p>
               <p>THe halfe of 58 is 29, then the angles ADG to AGD, or CDF, wilbe as 29 to 19,
therefore setting downe ADF to CDF, it wilbe as 48 to 19; but ADF is 72 de<g ref="char:EOLhyphen"/>grees,
then CDF wilbe 28 ½ degrees, &amp; then the angle flanked 87 degrees, the rest is
easie, for the triangles DCF, CBG will make knowne CF, FD; DG is 49, 14888, DH
61, 68324; DP 78, 18336, AD 24, 52336.</p>
            </div>
            <div type="section">
               <pb n="20" facs="tcp:1568:13"/>
               <head>The 31. Figure.</head>
               <p>Let there be a <hi>Decagone,</hi> whereof the face is 24 rod, the flanke 12, and
the curtaine 36, how many will those parts make, when the defence flan<g ref="char:EOLhyphen"/>king
is doubled to the Capitall.</p>
               <p>IF DG be sett downe 2. then DA wilbe 1. Now the angle DAG is 108 degrees, then
the angle flanking interiour G wilbe 28. 23. 38, and the angle flanked 87, 12, 44<gap reason="illegible" resp="#TECH" extent="1 letter">
                     <desc>•</desc>
                  </gap>
the rest is easie, &amp; is found in the same manner, as the end of the former, &amp; therefore
<hi>Marolois</hi> leaues its so for this reason.</p>
            </div>
            <div type="section">
               <head>The 32. Figure.</head>
               <p>In this present <hi>Vndecagone,</hi> a fortresse with eleuen Bulwarks, let the
face be 24 rod, the flanke 12, the curtaine 36, and the capitall DA to AG
as 5 to 7, the unknowne parts are required.</p>
               <p>SEt downe DA 5, and AG 7, and the angle DAG is 106 degrees, and 4 eleuenths:
that is 106, 21, 49, and hence ye shall know the angles remayning ADC, 43, 55, 48,
and the other or CDF 29, 42, 23, therefore in the triangle CDF, the angle D is then
so, and DC 24 rod, and then DF, DK, DP wilbe knowne, likewise FC, FB, BP, &amp; AD,
DE &amp; EF for the gorge. Here is nothing but that which is ill calculated by the
Autheur, or rather by his disciples, as from the beginning (without all doubt)
seekeing to help themselues with the figure put here under, which was needlesse;
supposing that they had skill in <hi>Trigonometrie.</hi> I will onely set downe here the reason
of the raid (or semy-diameter) in the side of the <hi>Vndecagone</hi> inscribed in the Circle, is
<q>
                     <l>as 100000000000000</l>
                     <l>to 563<gap reason="illegible" resp="#TECH" extent="1 letter">
                           <desc>•</desc>
                        </gap>46511368285.</l>
                  </q>
So that ye may take here the reason or proportion as precisely as ye will.</p>
            </div>
            <div type="section">
               <head>The 33. Figure.</head>
               <p>In this <hi>Vndecagone</hi> let the face of the curtaine be as 2 to 3: &amp; the gorge
in the flanke as 4 to 3, the distance of the points of the Bastions 75 rod,
and the angle flanked 88 degrees, 38 min. 11 seconds, the question is
how ye shall finde out the other dimensions?</p>
               <p>SEing that ADC, and ADF are knowne, the rest CDF wilbe also, being 29, 19, 6, &amp;
setting downe DC 2 parts, (then the curtaine, or FK wilbe 3) the triangle CDF
wilbe knowne by the parts, namely DF 1, 74384, as much also is KL, and FK 3, then
DP wilbe (in parts) 6, 48768, which make by the Hypotese 75 rod, &amp; by this reason,
ye shall finde out the face, and the curtaine, saying, if 6, 48768 parts make 75 rod,
how many then will make aswell 2, as 3? DC 23, 12075, &amp; BH 34, 68112 as much makes
FK, which taken from 75, the halfe of the rest wilbe for DF, ye shall finde then also
FC, afterward AB, being set downe upon 4. BC wilbe 3, then the triangle BAC wilbe
36, 52, 12; which taken from DAB, there will remaine DAC, &amp; so the triangle DAC
<pb n="21" facs="tcp:1568:13"/>
shall haue 3 termes, ye shall then seeke DA, or AC, by which ye shall come to haue
AB 13, 7969, &amp; BC 10, 34743, then in the triangle CBG, ye shall finde BG, afterward
DR, or CG being knowne ye shall haue DG 41, 54579, GH 11, 57496, and finally
DH the fichant 58, 96636.</p>
            </div>
            <div type="section">
               <head>The 34. Figure.</head>
               <p>Moreouer for this <hi>Vndecagone</hi> let the angle flanked be 88 degrees 38,
11, &amp; the face to the curtaine as 2 to 3, and the gorge in the flanke as 8
to 5. &amp; the fichant 60 rod, how many will all these lines make?</p>
               <p>YE must first finde out the <hi>Quadrangle</hi> ABCD, whereof the angles are knowne, &amp;
sett downe AB, 8 parts; then BC wilbe 5, &amp; DC being found, ye shall finde DF,
FC, also BH, seing that DC is to BH as 2 to 3; hauing DK, and KH ye shall haue DH
in parts, which make 60 rod, by which reason ye haue the lines required, AB, 14, 6,
CB 9, 127, DG 42, 374, DC 23, 7363, BH 35, 604, &amp; DP 76, 99675.
<q>Vpon the 35. Figure.</q>
               </p>
            </div>
            <div type="translators_note">
               <head>ALB. GIRARD.</head>
               <p>THis question is defectiue, in regard it hath but foure termes knovvne, <hi>DP</hi> 70 rod, &amp; <hi>CB</hi> 10, the reason of <hi>DC</hi> to <hi>BG</hi> is as 10 to 9, and the name of the figure <hi>Undecagonall,</hi>
vvhich are but 4 termes, he comes to the <gap reason="illegible" resp="#TECH" extent="1 word">
                     <desc>〈◊〉</desc>
                  </gap>
                  <g ref="char:punc">▪</g> setting dovvne the face 20 rod, to see
if there be not in it repugnanci<gap reason="illegible" resp="#TECH" extent="1 letter">
                     <desc>•</desc>
                  </gap>, as if the question vvere exceeding, so that he in this search
committeth the faulth, vvhich is called <hi>petitio principij.</hi> VVhich is spoken not to defame
the Authour, but to shevv, hovv this proceeded from hence, that in this time many thought
that <hi>Geometrie</hi> hath attained to her highest degree; though vvee haue had but the <hi>A, B, C</hi>
of it: till that some undertakeing the restauration thereof, haueing in part made it flourish
againe, could neuerthelesse escape the blame of some envious &amp; ignorant men in this divine
science, as happens often, haue let passe the most difficult of the <hi>Analitica,</hi> vvhich ought to
adorne those, that make profession thereof, vvho contraryvvise setting dovvne the limits of
their pretensions from the beginning of their course; by emulating one an other, content them<g ref="char:EOLhyphen"/>selues
to grope together vvithout learning to goe forvvard vvith a solide, and a firme pace in
a faire vvay.</p>
            </div>
            <div type="section">
               <head>The 36. Figure.</head>
               <p>In this <hi>Dodecagone,</hi> let the face be 24, the flanke and the curtaine 36
rod, the angle flanked right, how many will the remayning lines make?</p>
               <p>LEt DF be found, also FC, ye shall haue DK, &amp; KH for to haue DH, afterward in
the triangle DGR, hauing the angles &amp; RG, ye shall finde DG. Finally ye shall
finde DE in the triangle DEA, for to haue EF, or the gorge: Now seing that GCB
is 60 degrees, then of necessity GC wilbe 24, as being asmuch againe as CB, then
DG wilbe 48, and GR, or KH the halfe is 12, therefore DH wilbe 61, 648, DP, 77, 56944.</p>
            </div>
            <div type="section">
               <pb n="22" facs="tcp:1568:14"/>
               <head>The 37. Figure.</head>
               <p>In this present <hi>Dodecagone,</hi> let the angle flanked be right, the defences
flanking, &amp; the fichant 45, &amp; 60 rod, the gorge in the flanke is as 4 to 3.</p>
               <p>SEing that the angle DCF is 60 degrees. DH 45 wilbe the double of GR 22 ½ rod,
DH, HK being knowne, DK wilbe 55, 621, DR 38, 971, then the second flanke 16,
65. Also DE wilbe found by the triangle DAE, &amp; taken from DR, there will remaine
AG the basis of the triangle ACG, the angle A thereof wilbe 36, 52, 11, because of the
reason giuen, and G 60 degrees, then the sayd triangle ACG will make knowne
CG 21, 4933, &amp; also the face 23, 5067 (for DG is 45) the halfe of GC is CB 10, 7466,
which multiplyed by 4/3, ye shall haue BA 14, 3289, DP 75, 979, BH 35, 2637.</p>
            </div>
            <div type="section">
               <head>The 38. Figure.</head>
               <p>Let the curtaine be 36 rod, the line of defence flanking 45, the angle
BAC 36, 45, &amp; the flanked right. How many will the other parts of this
Fortresse <hi>Dodecagonall</hi> come to?</p>
               <p>THe triangle DAG, afterward ACG wilbe knowne, and also CBG, DCF, DKH,
whereby DC wilbe found 23, 974, GR 22 ½ (the halfe of DG) 10, 5127, DH 61,
0593. DP, 77, 52516, AB 14, 733.</p>
            </div>
            <div type="section">
               <head>The 39. Figure.</head>
               <p>In this <hi>Dodecagone</hi> the angle BAC makes 37 degrees, the flanked right,
the face 24 rod, the fichant 62, how many makes then the other lines?</p>
               <p>THe line DC 24 shalbe the double of CF 12; the angle BAC being giuen, the
triangle DAC, wilbe knowne, therefore DA, AC, and the triangles DAE, ACB
DGR, DHK wilbe knowne; and consequently the lines required, as AB, 14, 6179.
BC, 11, 01525, BH 36, 7851; DP 78, 3547. DA 23, 82709; He failed herein to calcu<g ref="char:EOLhyphen"/>late
them a new together: but the reason of this was, that wee agree not, seing that
in the construction, in stead of 37 for the angle BAC, (as he sett downe) he tooke 38.</p>
               <p>All questions comming after this are defectiue euen to the discourse, which
endeth the order of the same questions; but seing I know whither it tends, I will
explane them, in adding thereunto the things, that were wanting passing ouer the
figures 40, 41, and so we will beginn with the 42, as followeth.</p>
            </div>
            <div type="section">
               <head>The 42. Figure.</head>
               <p>In a square Fortresse with foure Bulwarks, let the angle flanked be 60
degrees, the angle forming the flanke FID 40 degrees, the face 24 rod,
hauing the reason to the curtaine as 4 to 5, the other lines are required.</p>
               <p>
                  <pb n="23" facs="tcp:1568:14"/>
Seeke the triangles DAL: AID, IFD, DFP, ye shall finde also PH, for FH wilbe 30:
IO 48, 45532: AK 76, 6464, IF 9, 22766: FD, 7, 74298, IA 19, 73479, the fichant
AH 54, 98265.</p>
            </div>
            <div type="section">
               <head>The 43 Figure.</head>
               <p>Is a <hi>Pentagone,</hi> the angle flanked 69 degrees, the angle forming the
flanke <gap reason="illegible" resp="#TECH" extent="1 letter">
                     <desc>•</desc>
                  </gap>0 degrees, the curtaine to the face as 5 to 4, the face 24 rod; wee
desire to know the other lengths.</p>
               <p>Ye must doe as before, and then there wilbe no difference in the operation,
Touching the number of the names of the figures in this 9 plate, ye shall finde them
marked about the angle flanking exteriour, the reason of the face to the curtaine is
marked on the point of the Bastions, the length aswell of the face, as of the curtaine
next themselues, and must be proposed as the two former, hauing alwayes the angle
forming the flanke of 40 degrees: the opening of the flanked angles, is according
to the manner of the first table, to wit 15 degrees more then the demy-angle of the
<hi>Polygone,</hi> sauing that in the figures 2, 43, &amp; 2, 44, afterward an other time the 45, 46,
he taketh for the angles flanked the ⅔ of the angle of the <hi>Polygone,</hi> according to the
second table in the beginning placed before: Of these things ye shall finde 2 tables
in the end of this booke, setting downe the faces to the curtaines, as 2 to 3, the faces
24 rod, which make the former-flankes 40 degrees, and the flanked according to the
two manners abouesaid, where ye must knowe, that the lines of defence fichant
are about 60, 61 rod. The said tables are both calculated <gap reason="illegible" resp="#TECH" extent="1 word">
                     <desc>〈◊〉</desc>
                  </gap>; because of the
errours escaped in the other editions. Moreouer, after the <hi>Dodecagone</hi> ye shall haue
ouer and aboue following a Fortification upon a right line, which is called upon a
right curtaine. Now let us marke what the Authour saith.</p>
            </div>
            <div type="section">
               <head>Note 1.</head>
               <p>NOw not to take so much paines in remembering the diverse proportions of the
face to the curtaine, whereof the Fortresse <hi>quadrangular,</hi> &amp; <hi>Pentagonall</hi> Fortresse
is as 4 to 5, and the <hi>Exagonall</hi> as 3 to 4, it will not be amisse (seing that the line of de<g ref="char:EOLhyphen"/>fence
will beare it) to make also the said Fortresses of the same proportion, as the
subsequent, to wit, in reason <hi>sesquialtere,</hi> as appeareth by the 3 figures of the 9 plate,
quoted by the numbers 2, 42. 2, 43. 2, 44. where the lines of defence doe not much
exceede 60 rod, which is as farre as a musket can well carry, &amp; therefore one ought
not to exceede this number; because that alwayes from the flanke reciprocally the
entrance into the moate must be defended, which is often done, and most commo<g ref="char:EOLhyphen"/>diously
by the Muskettiers, because that Canon cannot so suddenly (by reason of
the weight) be brought thither, many good occasions are neglected, for which cause
they are preferred before Canon, and in regard a Musket will but carrie some 700
feete point-blanke, Bulwarkes ought to be made noe further one from another, for
otherwise the line of defence would be too long, which should cause imperfection.</p>
            </div>
            <div type="section">
               <head>Note 2.</head>
               <p>IF in stead of takeing the face 24 rod, for the line of the <hi>Polygone</hi> exteriour take 80
rod, and the rest according to the former proportion, the parts wilbe brought very
<pb n="24" facs="tcp:1568:15"/>
neere together, as appeareth by the precede<g ref="char:cmbAbbrStroke">̄</g>t Examples, according to the figures of
the 10 plate, marked with the numbers 51. 52. 53. 54. 55. 56. 57. 58, 59, whereof we haue
made no calculation; because they are easely done by the former supputations.</p>
            </div>
            <div type="section">
               <head>Note 3.</head>
               <p>THat in all our designes and calculations, we are resolued to use but one measure
onely, which is in the 25 plate of our <hi>Geometrie</hi> upon the rule of the instrument
marked number 1, which is a foote deuided into 12 equall parts, whereof 12 foote
makes a <hi>Rheneland</hi> rodd in the territoire of <hi>Leyden.</hi>
               </p>
            </div>
            <div type="section">
               <head>Designes &amp; plat formes of diverse Fortifications.</head>
               <p>WE might according to the former supputations giue diuerse constructions of
the platformes of Fortifications; but considering the great diversity of rules,
(which often causes confusion, and that time will not permit us) wee will giue but
one simple and generall rule for them, which is this following.</p>
            </div>
            <div type="section">
               <head>The 9 Plate, and the 42, 43, 44, 45, 46, 47, 48, 49, 50 Figures.</head>
               <p>FIrst, if the face be giuen (suppose it to be 24 rod) then ye must doe as followeth:
Ye shall draw a right line infinite AC from the point A, the angle CAB shalbe
made according to the forme of the <hi>Polygone,</hi> upon which A, B shalbe sett downe the
24 rod abouesayd, as from A to D, and by D is drawne the line, which formeth the
angle of the Center of the Bulwarke 40 degrees, then must ye sett downe upon A, C
and A, B, the reason of the curtaine to the face that by the same ye may draw the
line infinite A, E, makeing from the point D, a parallell with A, C, cutting the said
AE, at G, by which point is drawne the line, that formeth the other face G, K, in such
sort that the angle G, K, A, wilbe equall to the angle D, A, K, and so the figure wilbe
drawne, according to the said proportion.</p>
            </div>
            <div type="section">
               <head>The 10. Plate, &amp; the 51, 52, 53, 54, 55, 56, 57, 58, 59, Figures.</head>
               <p>SEcondly, if the line from angle to angle be giuen AB (for example 80 rod) ye shall
then proportion out the face to the curtaine <hi>sesquialtera,</hi> as 2 to 3. Then in con<g ref="char:EOLhyphen"/>formitie
of the table of angles set downe before, wilbe made the angle CAB, accor<g ref="char:EOLhyphen"/>ding
to its forme, to wit, in a square of 15 degrees, in a <hi>Pentagone</hi> of 89 ½ degrees, in the
<hi>Exagone</hi> 22 ½ degrees, and so consequently of the rest, then for the forming of the
abouesaid proportion of the face to the curtaine, which is (as we haue said) as 2 to 3.
aswell in a square Fortresse as in a <hi>Pentagone,</hi> and others following ye shall take upon
a scale of a reasonable greatnesse 2. which shalbe sett from A to C, and 3 from A to
D, suppose that it be at C &amp; D, then from the point D wilbe made the arch G of the
distance of 2, (to wit CA) &amp; from C of the distance of D, A, 3, wilbe made the arches,
which cutt betweene each other at G, by which a right line being drawne to A,
where the same cutting the line FB, as here at F ye haue the face of the Bulwarke,
and by that the curtaine wilbe knowne. To knowe also the line of the gorge, and
the flanke, and all the other parts, ye must make the angle forming the gorge, and
the flanke of 40 degrees, as is here the angle KIE, cutting the diameter P, A, at I,
from which point I a right line parallel being drawne from A, B, as is I, N, ye shall
drawe the line perpendicular to be E, K, which shalbe the flanke, and K, I, the line of
the gorge of this Fortresse, and then ye haue the thing required.</p>
               <p>
                  <pb n="25" facs="tcp:1568:15"/>
In like manner ye shall finde, and marke out the other Fortresses, according to
their seuerall formes, takeing heede that as here ye take 2 &amp; 3, ye must in the others
also take 2 &amp; 3, to place them aswell upon A, B, as upon A, C, and the rest being the
same; as is in the former construction it wilbe needelesse, to giue yow here any
further particular instruction for them.
<q>The 3, 50. Figure, and the 9. Plate.</q>
               </p>
            </div>
            <div type="translators_note">
               <head>ALBERT GIRARD.</head>
               <p>THirdly, VVhen upon the line of the <hi>Polygone</hi> interiour AB, ye desire to construe, or ex<g ref="char:EOLhyphen"/>plane
a Fortresse, hauing 5 termes, to vvit, the name of the figure, the angle of the bastion
M, The angle forming the flanke GBH, and the reason of the face DG, to the curtaine HL,
conceiuing therein that AB is giuen.</p>
               <p>This figure is in stead of the 2, 50, being vvorth nothing. I am so constrained to make a
nevv figure, and a nevv explanation. Let then NBA be equall to the demy-angle of the <hi>Poly<g ref="char:EOLhyphen"/>gone,</hi>
and let the angle forming the flanke be HBG, LAK, so ye shall haue the intersection or
cutting betvveene C, then DBF the halfe equall to the demy-angle flanked, and finding the
point F, so that AB, to BF is the reason of the curtaine to the face, and hauing dravvne CF,
cutting NB at D, and makeing DG a paralell vvith FB, meeting vvith BC, at G, ye haue
finally GH the perpendicular vvith BA, and doing the like also on the other side, ye shall haue
all the parts required; the demonstration is manifest, seing that C is the common point of
the like figures FBA, DGK: then as FB, to BA: so DG the face, vvilbe to GK, or HL.</p>
            </div>
            <div type="section">
               <head>The 11. Plate, and 60, 61, 62, 63, 64, 65, 66, <gap reason="illegible" resp="#TECH" extent="1 letter">
                     <desc>•</desc>
                  </gap>7, <gap reason="illegible" resp="#TECH" extent="2 letters">
                     <desc>••</desc>
                  </gap>, Figures.</head>
               <p>IF there be a question to proportion out the face to the curtaine, and the gorge to
the flanke, when the line EF is giuen, ye shall doe as the figures in appearance de<g ref="char:EOLhyphen"/>monstrate
to the eye, namely, ye shall first proportion out the face to the curtaine
by the former rules, and make it soe that the curtaine of a square Fortresse be 300
foote, and the face HF, 250 foote, hauing reason as 5 to 6, according to which ye shall
finde the point G, which is the angle of the shoulder. To finde then afterward the
gorge &amp; the flanke, ye shall make the couert line GH, which must be diuided into
4 equall parts (in foure, because ye would haue the reason of the gorge in the flanke
as 4 to 3) whereof ye must place three of them from H to I, and then drawe I, G,
cutting through the <hi>semy-Diameter</hi> of the <hi>Polygone,</hi> which is here squared into A,
and then the line AB being drawne it wilbe parallell with EF, and so ye haue the side
of the <hi>Polygone</hi> interiour, upon which the 2 perpendiculars being drawne GC, HD,
ye haue the 2 flankes, and consequently the essentiall parts of a square fortification
knowne: ye must also obserue the same in the other figures following.</p>
               <p>If the line EF, which is the side of the <hi>Polygone</hi> exteriour (or the distance of the
angles of the Bulwarks) be not giuen, but onely the line AB, the side of the <hi>Polygone</hi>
interiour, ye shall seeke out in the tables a Fortresse of such a forme, whereof the
face to the curtaine is as 5 to 6, and shall worke it by the rule of proportion, <hi>or else let
it be made after the former manner, vvhich is much more easie, then all the figures of the 11. Plate.</hi>
               </p>
               <p>If such a side of a <hi>Polygone</hi> interiour, giueth such a side of a <hi>Polygone</hi> exteriour, what
will such a side interiour giue? &amp; ye shall haue the thing required; to wit, the <hi>Polygone</hi>
                  <pb n="26" facs="tcp:1568:16"/>
exteriour, whereby one may easely know the other parts of the Fortresse, when the
line AB of the <hi>Polygone</hi> interiour is giuen. But if in the tables the proportion be not
found, make first upon the line AB the triangle ARB, whereof the halfe of the basis
hath the like reason to the perpendicular, as ye will haue proportioned out the
gorge of the flanke, demonstrated by this exemple as 4 to 3, which wilbe done in
setting downe upon the said line AB foure equall parts (4 because ye desire to haue
proportioned out the gorge to the flanke, as 4 to 3) to wit from A to D, raising out
of the point D a perpendicular, and put 3 of the said parts from D to I, then doing
the like on the other side, by this meanes wilbe formed the triangle ARB, and from
the points A &amp; B, the angles flanking interiour wilbe made according to the forme
of the <hi>Polygone,</hi> (which is a <hi>Pentagone</hi>) conformable to the table of angles described
heretofore, as appeareth by the letters SBA and TAB, which cutt the lines infinite
A, L. L, B at the points S, T, and the line S, &amp; T being drawne, the angles T, S, B, and
S, T, A wilbe equall to the angles S, B, A, and T, A, B, as appeareth by the 28 proposi<g ref="char:EOLhyphen"/>tion
of the first part of <hi>Euclide.</hi>
               </p>
               <p>According to which the reason of the face being putt to the curtaine, upon T, S,
and T, A, namely, the face upon TA, and the curtaine upon T, S; ye haue the like
distances, and from the points I &amp; X, the arches which cuts betweene them in a
certaine place, by which intersection the line T, V, shalbe drawne cutting the line
S, B, at V, then the right line V, L. being drawne passing through the center L, &amp; cut<g ref="char:EOLhyphen"/>ting
A, R at G, ye shall haue all the parts of this Fortresse: for hauing sett downe the
distance R, G, from R to H, from the same point G is drawne a paralell to S, B, as E, G,
cutting the <hi>Diagonall</hi> line L, A, at E, the like ye shall finde for F, and consequently all
the other parts of the said Fortresse <hi>Pentagonall.</hi> The same must ye also understand
of the other figures following, from the figure 60, to the figure 68. Also ye may finde
the point V, in setting downe upon T, A, 2 equall parts, such as ye require, and from
the extremity or utmost end, hauing made it a parallell to S, T, and upon the same,
3 of those parts, and drawne from the extremity the line TV, the said point will con<g ref="char:EOLhyphen"/>sequently
be knowne thereby.</p>
               <p>NOte that the proportion giuen here, betweene the face and the curtaine is not
so much to relye fast upon it, as to show that the generall rule sett downe here
before in the 9 and 10 plates, take place also in all other reasons, which may be pro<g ref="char:EOLhyphen"/>pounded.
For otherwise wee are of the opinion; that the former figures would rather
be accepted then these here, because that the reason of the curtaine to the face is
(as wee haue said aboue, sesquialtera as well in square Fortresse, as of <hi>Pentagonall,</hi> and
others following. Which for the facility, &amp; simplicity together with the goodnesse
of them ought to be preferred before the figures 60, 61, 62, 63, 64, 65, 66, 67, and 68,
of the 11 Plate aboue said. Whereof the face to the curtaine is (as the exemples
shew) of diuerse reasons; in such sort, that hence forward one ought to resolue, that
the reason of the curtaine to the face ought in all formes of Fortification to be <hi>sesqui<g ref="char:EOLhyphen"/>altera,</hi>
and the face 24 rod, each rod containing 12 foote, the length whereof is sett
downe in the 25 plate of our Geometrie, noted with the character or the figure 1, &amp;
is diuided into 12 ynches, which rod is used in the Fortifications of the United Pro<g ref="char:EOLhyphen"/>vinces,
to the end that the line of defence may not exceede much aboue 60 rod,
which is about as farre as a Musket can well beare, the gorge to the flanke may be
made by the rule giuen in the 11 plate, according to the reason giuen, but forasmuch
as it is more convenient to make the angle forming the flanke GAC (plate the 11)
of 40 degrees which giueth the reason almost as 6 to 7, in my opinion one ought to
rest thereupon, and so ye shall haue a generall rule for all manner of Fortifications,
<pb n="27" facs="tcp:1568:16"/>
whither they be <hi>Quadrialtera, Pentagonall, Hexagonall,</hi> or the others following, as ye
may perfectly understand by that which shalbe said hereafter. In the meane while
note that I giue here the reason of the gorge to the flanke as 7 to 6, which ought to
be understood in Fortresses without Casemates, but if it were my intention to make
some of them, I would then alter somewhat of the said proportion.</p>
            </div>
            <div type="section">
               <head>The manner how to describe succinctly the designes or Plots
of some regular Fortifications.</head>
               <div type="subsection">
                  <head>The 12. Plate, and the 69. Figure.</head>
                  <p>ALthough one may (by that which we haue taught) sufficiently now understand
the order, and Method requisite to be held in all manner of Fortifications: yet I
haue thought it good to trace out here some from among the rest, to make the
louers of this Art to conceiue the better my intention, and will begin with a regular
<hi>Pentagone,</hi> whereof the angle of the center maketh 72 degrees, and the angle of the
<hi>Polygone</hi> 108 degrees, and seing the angle flanked according to the table before
mentioned, maketh 69 degrees: It wilbe easie to finde the angle C, A, D, which is
alwayes equall to the angle flanking interiour, and shall finde the same to be 19 ½ de<g ref="char:EOLhyphen"/>grees,
setting then your graduate Instrument upon 19 ½ degrees, it makes the angle
CAD, and drawing first the covert line infinite AB, takeing upon the scale 24 parts,
or rod: and sett then from A to C, drawing from the point C a perpendicular upon
A, B, as is CD afterward hauing sett on DE the length of the curtaine, which is here
onely 34 rod (because the false brayes makes the lines of defence too great) &amp; then
the distance AD, from B to E, raysing from the E the <gap reason="illegible" resp="#TECH" extent="1 word">
                        <desc>〈◊〉</desc>
                     </gap>cular EF, being equall
to D, C, and FB drawne out, the two faces wilbe knowne; for to knowe the
center of the Bulwarke, shalbe made of 2 lines GA, &amp; GB the Demy-diameter of
the <hi>Polygone,</hi> then your instrument being sett upon 40 degrees, ye shall finde the
angle HKA, cutting the said demy-diameter at the same point H: from which
point the line HI being drawne; ye shall haue the side of the <hi>Polygone</hi> interiour upon
which out of the points C, and F, shalbe drawne the perpendiculars CL &amp; FM,
which will forme the flanks, and the gorges of the said Fortresse <hi>Pentagonall,</hi> in the
inside of the side of the <hi>Polygone</hi> interiour shalbe drawne a parallell of 5 ½ rod for the
thicknesse of the rampart, as N, O N, R, and RS, and ye must draw for the parapett
of the rampart a parallell of 20 feete (also in the inside of the said side of the <hi>Polygone</hi>
HI) and on the outside thereof ye shall drawe a parallell of 20 foote for the falsebray
as LX, and yet more outward 20 other foote for its parapet, &amp; so all the other parts
wilbe traced out, which are within the moate; for seing that there is here noe Case<g ref="char:EOLhyphen"/>mates,
the falsebray is carried not onely about the curtaines; but also about the
flankes, and the faces of the Bulwarks, in such sort, that the falsebray serueth as a
Casemats to the said flankes, the entrance or sallies ought in my opinion to be made
in the midst of the curtaines, as covertly as possibly may be; the Bulwarkes are made
either massiue, or hollow from Earth; at this present wee haue drawne them out as
being hollow from earth, &amp; so the superficies, or plaine in the midst of the bulwarke
N, R, S, H. is of the same heigth, as the rest of the enclosure of the <hi>Pentagone</hi> is, the
moate shalbe 10 rod broad, which is traced out as followeth: In the point A, or the
angle of the Bulwarke, shalbe made an arch of the distance of 10 rod, &amp; in the point
V make an other arch of somewhat a lesser extention then the former about 10 or 12
foote, then drawe upon the back thereof a covert line infinite; the like must be done
on the otherside of the Bulwarke, and so from place to place, with covert lines being
<pb n="28" facs="tcp:1568:17"/>
drawne as abouesaid, the intersections of them will bring forth the angles of the
said moate, aswell on the interiour as on the exteriour parts, ye must make upon the
brinke of the moate exteriour a parallell of 20 or 24 foote; for the bredth of the
covert way, and besides somewhat more towards the exteriour part, ye shall make a
parallell of 50 foote for the thicknesse of the parapet thereof, which shall goe
downe sloaping being onely raised towards the covert way, or the Coridor of 6
foote, and diminishing litle by litle to the furthest part of the 50 foote, &amp; so ye shall
haue finished the <hi>Icnographia,</hi> or ground-draught of this Fortresse <hi>Pentagonall,</hi> the
streets betweene the ramparts and the housen ought to be 30 foote, that with the
more convenience they may be entrenched in the time of neede, and that the
souldiers may stand there in battle-ray. The streets ought to be made of 24 or 30
foote, and for the market place every side shalbe made 12 rod, and of the same forme,
as the <hi>Polygone</hi> is, which is fortified, being a <hi>Pentagone,</hi> in which the towne-house is
to be made, &amp; other publick buildings, &amp; thus we haue finished the forme thereof.</p>
               </div>
               <div type="subsection">
                  <head>The 70. Figure.</head>
                  <p>THe <hi>Profile</hi> or draught shalbe made in this ma<g ref="char:cmbAbbrStroke">̄</g>ner: first a privie line is drawne from
the utmost part thereof, then ye shall beginne to lay out the breath of the ram<g ref="char:EOLhyphen"/>parts,
moates and wayes, &amp; as wee haue sett downe in our <hi>Icnographia</hi> for the bredth
of the rampart 66 foote, which make 5 ½ rod, we will take upon the skale joyned to
the <hi>Profile</hi> 66 foote, for to place them upon the said covert line as from A to B: then
as the way of the rounds, which we otherwise terme the falsebray, is counted 20
foote, which one may take upon the said skale, &amp; remoue them upon the said covert
line, as from B to I, and the same 20 foote from I to M, for the bredth of the parapet,
then ye shall make an edge MN of 6 foote, which is called in flemish the Teen, or the
toe of the foote of the parapet, the better to prevent the falling of the same into the
moate: from whence ye must take the bredth of the moate, which shalbe 120 foote;
for so much makes the 10 rod as from N to Q, from Q to R, ye must drawe out 20 or
24 foote for the covert way, and from R to T 50 foote for the parapet; and so ye haue
all the dimensions required. For their heigths aboue AB ye shall make a parallell
of 14 foote, which shalbe the height of the rampart, and underneath a parallell of 10
foote for the depth of the moate, the talud or slooping interiour of the rampart
A, V, ought to be 14 foote, and the talud exteriour XB, must be the halfe of its heigth,
which is 7 foote, and the trapeze, or unequall sides giuen A, D, C, B, being the profile
of the rampart: for its parapet ye shall take 20 foote from C to E, and from the point
E draw a perpendicular of 6 foote, which shalbe the height of the said parapet, and
upon the said perpendicular EG shalbe layd out 4 foote to drawe a parallell to DC,
cutting the line B, H, at H, which shalbe the heigth of the said parapet in this place,
and for the superiour part ye shall draw the line GH. Your foote banke shalbe made
as followeth: from E is drawne the line FE of 3 foote, and 1 ½ foote high, then from
the upper part of the footebanke make the line G 2. in such sort, that the said foot<g ref="char:EOLhyphen"/>banke
shall not be broader in heigth then 2 foote, and shall haue the talud 1 foote,
which shalbe the talud interiour of the said parapet. The parapet of the falsebray
IM shalbe made as is aboue said; to wit, from the point I, is raised the perpendicular
IK of 6 foote, which shalbe the height of the said parapet, and from I towards B draw
3 foote for the footebanke, being a foote and a halfe high, and so drawe out the line
K2, that the bredth of the upper part of the footebanke be not (as wee haue said)
aboue 2 foote, in such sort that the Talud interiour (after ye haue drawne out the
said line K 2) of the said parapet shalbe but a foote: for from the point I, the foote
<pb n="29" facs="tcp:1568:17"/>
banke is 3 foote broad, but in the point 3 it is found to be but 2 foote broad. For the
moate first draw out NO, which is the brinke interiour thereof, hauing the talud, as
much as is the depth of the moate, to wit, of 10 foote, likewise the line Q, P, is taken,
which is the brinke exteriour of the said moate, the parapet of the covert way Q, P,
is made by rising from the point R, the perpe<g ref="char:cmbAbbrStroke">̄</g>dicular line RS of 6 foote, takeing from
the said point R towards the left hand 3 foote for the bredth of the footbanke, and
to make it a foote and a halfe high; To giue the more firmenesse to the said parapet,
there shalbe made from the upper part of the point S an oblique line upon the said
footebanke, which is (as is before said) three foote broad; in such sorte, that the said
line declining a foote upon the said footebanke, maketh the said footebanke to be
noe broader then 2 foote. Finally a right line is drawne from S to T, which makes
the slooping of the said parapet.</p>
               </div>
               <div type="subsection">
                  <head>Note.</head>
                  <p>WE haue made the rampare no higher then 14 foote, upon the upper part whereof
is made a parapet of 6 foot high, all upon a plaine field, which is a convenient
heith for a place, that hath noe hils or heigths about it, but in case there be any hils,
that doe commaund the said place, it wilbe then necessarie to raise the rampart
somewhat higher, then is here described, answerable to the heigth of the said hill,
which otherwise would commaund the Fortresse, &amp; for the better blinding of such
places, sometimes one makes upon the upper part of the rampart an other parapet
about 7 foote broad, or there abouts &amp; 6 foote high, which Parapet serueth so much
the better to blinde the said place, and to discouver the fields about it, but when an
Ennemy hath approched neere unto such places, then the said parapet can doe
them no further seruice, so that necessity will compell them to take it away for their
more safegard, and to lye under the said parapet of 20 foote broad: for Canon shott
comming every time to pierce the said parapet being but 7 footebroade; they
cannot safely lodge behinde it, without extreame danger; and therefore is necessary
to be razed, to make use of the other, which is able to resist the force of Canon.</p>
                  <p>Wee haue not made here in this 79 figure any Ravelins or halfe moones, which
are loose peeces on the further side of a moate, neither any Catts, or high plat<g ref="char:EOLhyphen"/>formes
to plant ordinance upon, which are usually made in divers places within
Forts, and upon Bulwarks; because we intend to speake of them hereafter. In the
meane while it wilbe good to note, that the said Cats, Ravelins, and other workes,
may be applyed to this present Fortification, but in this place is omitted for the
avoyding of prolixity, because we are minded to treate of them briefly in an
other place.</p>
               </div>
            </div>
            <div type="section">
               <head>The description of the designe or the plate forme of a
Fortresse Hexagonall.</head>
               <div type="subsection">
                  <head>The 13. Plate, and 71. Figure.</head>
                  <p>LEt there be giuen a Fortresse <hi>Hexagonall</hi> to be fortified, whereof the face AC ma<g ref="char:EOLhyphen"/>keth
24 rod, and the angle flanked 80 degrees, according to which the angle
flanking interiour will make 20 degrees, and the exteriour 140 degrees, and let the
curtaine be 30 rod, which giueth the reason of the face to the curtaine, as 3 to 4. To
doe this, ye shall draw the covert line infinite, A, B, &amp; by the helpe of an instrument
<pb n="30" facs="tcp:1568:18"/>
graduate, the other angle CAD of 20 degrees (of 20, because that the angle flan<g ref="char:EOLhyphen"/>king
interiour, which is alwayes equall to it maketh here 20 degrees) by meanes of
the line indefinite AC, upon which ye make the length of the face 24 rod, as
from A to C, from which point C, the perpendicular CD being drawne upon the
line A, B, shalbe placed from D, the length of the curtaine, which is here 32 rod as
from D to E, finally the distance AD from E to B, and the perpendicular EF the
distance of CD as from E to F, drawing the line FB, ye haue the other face, so that all
the parts of the reason giuen are described; and for to finde the curtaine, ye must
make first the angles GAB, &amp; GBA of 60 degr. seing the whole angle of the <hi>Polygone</hi>
maketh 120 degr. by the lines AG, GB, which cutting through on an other at G, is
the center of the <hi>Polygone,</hi> and seing the gorge, when as ye would make casemates in
them or in a bulwarke where Cats or mounts are raised, they had neede of a larger
extent, then otherwise; we suppose that it were requisite, to make Casemates in
them, to that end we make the angle HKA, which otherwise might be but 40 de<g ref="char:EOLhyphen"/>grees
onely of 35, according to which the gorge in the flanke wilbe almost as 4 to 3,
or somewhat more by reason of the line H, K, cutting the line <hi>Diagonall</hi> AG at H,
from which point H the line HN being drawne, parallell to AB, ye shall haue the
<hi>Polygone</hi> interiour, upon which the lines CL, and FM, being drawne in length the
lines DC to L, and EF to M; in so doing all the essentiall parts of the said Fortresse,
wilbe described; Now to continew the same draught or platforme in every place ye
shall make from the center G a privie circle from the distance GB, and shalbe sett
upon the privie circumference the distance AB, which being the 6 part of the
said figure <hi>Hexagonall,</hi> the said circumference will contayne justly still fiue parts,
which finally will come to end at A. In the like manner is the privie circle made out
of the same center G, and from the distance G, N, upon the circumference thereof
shalbe set the line of the <hi>Polygone</hi> interiour HN, afterward ye must onely coppie out
the rest. Moreouer, the parapet wilbet 20 foote, which shalbe made in the inside of
ACL. MFB, and as the way of the rounds, or the falsebray, is on the outside of the
body of the Fortresse, we will make parallells towards the moate of 20 foote broad,
&amp; then 20 foote more for the parapet thereof, on the outside of the parapet, before
ye come to the moate, is made an edge, or a toe of 6 or 8 foote, to keepe the said para<g ref="char:EOLhyphen"/>pet
from falling into the moate, which is made of 140, or 150 foote or thereabouts,
as necessitie, and the bottome requires; for it must be fitted according to this con<g ref="char:EOLhyphen"/>sideration,
because the ground lying lowe, it will not beare much digging before ye
come to water, and therefore in this place one is forced to make the moate to gett
earth enough for the rampart, but when the ground lies high, then ye may digg very
deepe before ye come to the water, &amp; so by this meanes ye may haue asmuch earth,
as possibly ye can well use, &amp; seing without it cannot be but hurtfull, it wilbe better
not to make the moate so broad, that ye may receiue noe hindrance or hurt by the
store of Earth that it affordeth; which may be cast upon the outside: For to beleeue
that the ramparts being raised higher then the dimension giuen in the former figure
to wit of 14; or at least 15 foote, that they were better as some haue mainteyned, yet
experience hath showne many times the contrarie, for an ennemie hauing once ap<g ref="char:EOLhyphen"/>proched
to the brinke of the moate, the bredth of the parapet hinders one from
makeing any defence upon it, which notwithstanding is most necessarie: because
the neerer an ennemie comes with his approches towards us, we ought the more to
defend our selues, and this being committed by our default, it is too manifest that
one ought to take heede of it, and to remedie this errour by the former way: namely
in makeing the rampart of the heigth abouesaid. Some are of the opinion by a sim<g ref="char:EOLhyphen"/>ple
co<g ref="char:cmbAbbrStroke">̄</g>maund that one ought to heigthen the ramparts aboue the said 14 or 15 foote,
<pb n="31" facs="tcp:1568:18"/>
and not the Bulwarks, for which they haue some reason; for indeede the Bulwarkes
make the greatest defence, and when an ennemy is become master of the said bul<g ref="char:EOLhyphen"/>warke,
there were a meanes to co<g ref="char:cmbAbbrStroke">̄</g>maund the said bulwarke more absolutely, so that
an ennemy could not hinder the use of them, if he raised not his works aboue the
said rampart, to hinder the defences of the besieged, which they might make with
the said ramparts so raised by a simple commaund, which in some manner might
hinder the intents &amp; approches of the besiegers, the more easie would the entren<g ref="char:EOLhyphen"/>chements
be made, and seing the more the bulwarks are raised, the more one ought
to use diligence about the entrenchment; hence would follow this difficulty, that
the comming to the rampart or the bulwarke, would not be so easie, as otherwise,
neither could one make any great defence from such ramparts by reason of their
too much heigth, in such sort that one bulwarke ought to defend an other, &amp; in such
a case the second flanke would be of noe use after an ennemy is entred into the
moate, at which time it is then most needfull to giue the greatest resistance that may
be, seing that when they are gotten ouer the moate, and taken in the foot of the bul<g ref="char:EOLhyphen"/>warke,
then the courage of the besiegers begins to encrease, &amp; the besieged to faile
them, for it is too apparant, that many times resistance failes in such and the like
accidents.</p>
                  <p>Betweene two bulwarkes are commonly made ravelins or halfe moones, which
are Quadrangular figures, euery face containing 12, 15, or sometimes 20 rod, which
beginn at the brinke of the moate: so that its angle interiour, or the tenaille O, lies
just upon the brinke and angle of the moate, the reason why their faces P, Q, and
Q, R, are made of a greater distance, is that the deffence may be the better: for
otherwise their could be noe defence made but from one part of the face of the
bulwarke, which otherwise would not be sufficient to hinder the assaults of an enne<g ref="char:EOLhyphen"/>mie,
which ravelins or loose peeces li<gap reason="illegible" resp="#TECH" extent="1 letter">
                        <desc>•</desc>
                     </gap> so open and are raised aboue the plaine field
some foure foote, that one may the easier discouer the said field, and so also to pre<g ref="char:EOLhyphen"/>vent
the inconveniences which might happen, when one would giue fire from
them upon the besiegers, (if the said ravelin had not bene raised) which would haue
annoyed those which were under the covert way. Upon the said Ravelin being so
raised, is made a parapet of 20 foote broad, and 6 foote high, which wilbe able to
resist Canon, the moate whereof ought to be made 50, or 60 foote, and as deepe, as
possibly may be about the said moate, ye must make also a cover way of some 20
foote broade, as hath bene noted before; Afterward ye must make a parapet of 50
foote broade &amp; six foote high, ending at the end of the 50 foote towards the plaine
field; as the profile doth show in the 72 figure, and to the intent ye may the better
understand my meaning, we haue made the said <hi>Hexagone</hi> in perspectiue, with the
falsebrayes, Ravelins, covert wayes, and their parapets apart, as appeareth by the
second 71 figure, but ye must note, that the said Ravelins must be in respect of Ram<g ref="char:EOLhyphen"/>parts,
which haue a double height, to see in them the more perfection, also a double
height, to make them show the better: for otherwise they would seeme too little
for the reason abouesaid against our intention.</p>
               </div>
               <div type="subsection">
                  <head>The 72. Figure.</head>
                  <p>THe Profile shalbe made as in the 12 Plate of the former figure 70, by drawing a
privie line infinite, and takeing upon it all the dimensions, as first the bredth of
the ramparts, the parapets, the falsebrayes, its parapet, the bredth of the moate, the
covert way, and the other parts of the said profile; and seing wee haue here ordained
Ravelins, wee will make this profile from the midst of the rampart, passing also
<pb n="30" facs="tcp:1568:19"/>
                     <gap reason="duplicate" extent="1 page">
                        <desc>〈1 page duplicate〉</desc>
                     </gap>
                     <pb n="31" facs="tcp:1568:19"/>
                     <gap reason="duplicate" extent="1 page">
                        <desc>〈1 page duplicate〉</desc>
                     </gap>
                     <pb n="32" facs="tcp:1568:20"/>
through the midst of the Raveline, that ye may the better understand our meaning.
According to which ye shall take the bredth of the Rampart 68 foote from A to C,
from C to D 20 foote, from D to E 20 foote, and from E to F 6 foote, the bredth of
the moate shalbe 150 foote, as from F to G, which ought to be broader, but seing the
distance falls out too litle, it shalbe made but of 150 foote, the Raveline ought to
haue in this place 180 foote, but seing the ground faile us, wee haue made the dimen<g ref="char:EOLhyphen"/>sion
thereof 180 foote, but this hindrance would not permit us, to make it of that
competent greatnesse as it ought, which I speake to giue noe stop to the Reader,
which Ravelin is raised 4 foote aboue the plaine field from 6 to T, upon which a
parapet is made, whereof the basis shalbe 20 foote broad, and 6 foote high, to wit its
bredth from Q to R, and the height from Q to S, the footebankes are made of the
same bredth &amp; heigth, &amp; therefore I will make here no mention of them, neither of
the taluds or sloopings of Ramparts, Parapets, &amp; moates; aswell the interiour, as the
exteriour parts are made according to the nature of the soile; for by how much the
ground is leane &amp; sandie, by so much ye ought to giue it the talud, &amp; by that meanes
ye shall hinder the falling downe of the workes, for which reason often times ye must
giue on the exteriour side, being a sandie ground, as much talude as heigth, and if the
said Ravelin be also raised 4 foote aboue the plaine field, me thinks it will not be
amisse, to raise the rampart thereof, which is 15 foote, some 6 foote higher to com<g ref="char:EOLhyphen"/>maund
the better the said Raueline, &amp; leaue the Bulwarks of the height of 15 foote,
that all inconveniences may be prevented: on the outside of the Raveline is made
the edge HI of 6 foote, and a moate of 50 foote, then the covert way 20 foote, &amp; the
parapet LN 60 foote, with a footebanke of the ordinary bredth of 3 foote in that
manner, as the 72 figure demonstrateth.</p>
               </div>
            </div>
            <div type="section">
               <head>The description of the plote of a Fortresse Heptagonall.</head>
               <div type="subsection">
                  <head>The 14. Plate, and 73. Figure.</head>
                  <p>LEt there be giuen to be fortified a <hi>Heptagone,</hi> whereof the side of the <hi>Polygone</hi> ex<g ref="char:EOLhyphen"/>teriour
maketh 63 rod, and the angle flanked 80 degrees. To doe this, ye shall
first divide the said side AB into 7 equall parts, as ye see by the points 1. 2. 3. 4. 5. 6. 7.
and from the points of the 5 and 2 parts the perpendiculars D, N, and E, O shalbe
drawne being equall to A, D, and E, B, to wit, either of them 2 seuenth parts of the
line A, B, then ye shall draw from the extremities, or the utmost parts of these per<g ref="char:EOLhyphen"/>pendiculars,
the privie line infinite H, I. which shalbe the side of the <hi>Polygone</hi> inte<g ref="char:EOLhyphen"/>riour,
and by consequence N, O the curtaine. The angles C, A, B, and C, B, A, shalbe
made by the helpe of a graduate-instrument, as our compasse is, or an other; either
of 64 ½ degrees; in such sort that the intersection of the lines A, C. C, B, which is C,
shalbe the center of the said Fortresse <hi>Heptagonall.</hi> Afterward I, B, 8, of the 40 degr.
which is the halfe of the angle flanked, that ye may haue the whole angle of 80 degr.
according to the <hi>Hypotheses,</hi> and where the said lines cutt the said perpendiculars
D, N, and E, O, in the points 2. &amp; 8, ye shall haue the faces A 2. &amp; B 8, the flanks N. 2.
&amp; O. 8, and also the gorges H, N. &amp; O, I, the Parapets, Ramparts, Falsebrayes &amp; for
the other parts of this Fortresse, ye shall doe the like as hath ben taught in the for<g ref="char:EOLhyphen"/>mer
figure <hi>Hexagonall,</hi> the faces in this present Raveline shalbe made of 15 rod, the
moate of 10 rod, and the moate to the Ravelin of 15 foote, then about it shalbe made
a covert way of 20 foote, &amp; a parapet of 60 foote broad descending (as we haue said
before) sloopingly. According to this forme the flanke wilbe then made of a rea<g ref="char:EOLhyphen"/>sonable
greatnesse, but the gorge so much the lesser, which may be made so, seing
<pb n="33" facs="tcp:1568:20"/>
ye intend not to make any flankes in the Casemates, but in case ye would, ye must
then make the flanke the lesser, and consequently the gorge the greater, to the end
ye may haue space enough for to make within them the said Casemates. The like is
to be understood when ye meane to make a Catt upon the Bulwarke, for the gorge
being so litle (besides other inconveniences) it is impossible to make there such a
bodie, in reserving sufficient space for the flanks, which me thinks in such places,
that haue such narrow gorges, it were better to make the said Cats upon the Cur<g ref="char:EOLhyphen"/>taine,
yet so that they be noe hindrance to the Rounds going along the Ramparts,
for which reason they ought to be made more inward, and so that they may lie as
neere the rampart as possibly may be, the better to discouver, and commaund the
fields about them.</p>
               </div>
               <div type="subsection">
                  <head>The 74. 75. Figures.</head>
                  <p>THe figure 74 is the profile of the Rampart, Falsebray, its Parapet, moate, covert
way, and its parapet, whereof the length, bredth, heigth and depth are marked
out in the said figure 74, which is a section of the Bulwarck, as the figure 75, the
section of the midst of the Rampart, and because all the profile cannot commo<g ref="char:EOLhyphen"/>diously
be drawne out, we haue represented but a part of the moate, the forme of the
Raveline, its heigth, and the forme of its parapet, the bredth and the depth of its
side, with their taluds or sloopings, the covert way with its parapet &amp; footebanke,
as ye may exactly note by the figures hereunto annexed.</p>
               </div>
               <div type="subsection">
                  <head>The 2. of the 14. Plate.</head>
                  <p>ANd for the better facilitating of that <gap reason="illegible" resp="#TECH" extent="1 word">
                        <desc>〈◊〉</desc>
                     </gap> we haue spoken of this present figure
73. we haue added hereu<g ref="char:cmbAbbrStroke">̄</g>to the platforme of the Fortresse of <hi>Coverden in Frizland,</hi>
whereby ye may the better understand our intention, being accounted the master
peece, and the most regular, and royall Fort in the Low-Countries, hauing a False<g ref="char:EOLhyphen"/>braye,
Rauelins, or half moones, covertwayes, with which wee will put an end to the
description of our regular Fortresses.</p>
               </div>
            </div>
            <div type="section">
               <head>A succint description of some other works in the said Heptagone,
which are of an other manner of makeing then the former.</head>
               <div type="subsection">
                  <head>The 15. Plate, &amp; 76. Figure.</head>
                  <p>LEt the side of the <hi>Polygone</hi> interiour be B, C, upon which ye would haue a part of a
Fortresse <hi>Heptagonall</hi> made, whereof the face to the curtaine is as 3 to 4. and the
gorge to the flanke as 13 to 9. To doe this, ye must doe as we haue taught yow in the
11. <hi>Plate, or in the 9. Plate, and Figure</hi> 3. 50, where ye shall finde the proportion requi<g ref="char:EOLhyphen"/>site:
on the outside of the same face, shalbe made the parallells each of 20 foote, aswell
for the parapet, as for the falsebray, the like is to be done in the flanks, and curtaines,
and on the inside a parallell of 20 foote, with an other parallell of 72 foote for the
bredth of the Rampart in the basis, in the same manner as this 76 figure sheweth, on
the outside ye shall make a parallell of 10 rod for the bredth of the moate, and upon
the brinke of it to the <hi>tenaille,</hi> ye shall lay out the Ravelins, as we haue said in the for<g ref="char:EOLhyphen"/>mer
figure 73, in the angles of the Bulwarks ye shall make also Ravelins, such as ye
see here marked with I, K, L, M, which shalbe defended by the Ravelins E, F, G, H,
&amp; the better to defend the said ravelins, which are in the angles of the Bulwarks, ye
<pb n="34" facs="tcp:1568:21"/>
shall make the other works N, O, P, &amp; Q, which are called Horne-works, which are
made in such a manner, that the moates of these Horneworks comes to answere to
the Falsebray, which is in the flanks of the Bulwarks: so that their bredth S, T, ma<g ref="char:EOLhyphen"/>keth
about 32 rod, of which distance the two demy-Bulwarks V, X, are made
(whereof the face, and the curtaine are of a like greatnesse) according to the rule
prescribed in the 10. Plate, the flanks wilbe found, makeing from the angle of the
shoulder, two lines perpendicular upon the curtaine, which is directly opposite to it.
euen as the figures 77, 78 demonstrate. The utmost angles of the said Horneworks
ought not to be further from the curtaine of the Fortresse, then a Musket can
carry point-blanke, which is 60 rod or there abouts, and if the Rauelins EF, GH, are
not made in the tenailles, then ye may cut the said Hornworke, as is here marked
out in the 78 figure: the bredth of the moate shalbe 24 or 25 foote: The Rampart
here is noe otherwise then the parapet of the same bredth.</p>
                  <p>The depth of the moate may be made 6 foote in case the ground lies low; but
otherwise the deeper it is made it wilbe so much the better, the bredth will not hinder
it, though it were made but 36 foote; for according to the same bredth &amp; depth ye
may enlarge the Rampart, aswell in height as in bredth, upon which afterward ye
may make a parapet as great as it can well beare: but when haste requireth, I would
make noe Rampart, but onely a Parapet of 24 foote thick, as wee haue made here
being 6 foote high, and a footbanke of 3 or 4 foote.</p>
                  <p>The figure 79 marketh out a <hi>Profile,</hi> which is a section or cutt drawne through the
midst of a curtaine passing through the midst of the Ravelines G, and traversing
through the Horneworke P, and the Rampart and the moate. The true dimen<g ref="char:EOLhyphen"/>sions
thereof are clearely expressed in the said <hi>Profile,</hi> by the helpe of the scale; joy<g ref="char:EOLhyphen"/>ned
to it: as also by the meanes of the <hi>Alphabeticall</hi> letters, shewing the feete to be
12 ynches, whereof the length is <gap reason="illegible" resp="#TECH" extent="1 span">
                        <desc>〈…〉</desc>
                     </gap> in the 25 Plate of our Geometrie.</p>
                  <p>The benefit of such workes are well knowne, when they are made in places of ad<g ref="char:EOLhyphen"/>vantage
for deffence, or where noe men, victualls, and amunition of warre are wan<g ref="char:EOLhyphen"/>ting,
as also where the ground is of a reasonable largenesse, to wit at the least 32 rod,
that the faces of the said horneworkes may be about 12 rod, which is the least length
that one can giue to such workes, against the attempt, which may be giuen by an
Army: &amp; as a great assault, cannot be resisted with a few men, but up a small roome:
so is it manifest that the greatnesse &amp; largenesse of such a place, must be answerable.
Therefore in my opinion, it is a thing repugna<g ref="char:cmbAbbrStroke">̄</g>t to the rule of Fortification, to make
such Horneworkes in the angles of Bulwarkes, where they are so straightned. For
Demy-bulwarkes cannot (by reason of their smallnesse) be vvell mainteyned and
defended, and on the other side, their tvvo vvings cannot be defended from the
maine Fortresse, but vvith great disadvantage, as vvee intend to discusse: thereof
more at large hereafter in the plateforme of <hi>Gulick.</hi>
                  </p>
               </div>
            </div>
            <div type="section">
               <head>How Citadels, or Castles may be joyned to Townes, or
Townes to Castles,</head>
               <div type="subsection">
                  <head>The 16. Plate, and the 81. 82. Figures.</head>
                  <p>FOr to build a Castle (or a <hi>Citadell</hi>) to a Towne, either to help to defend it the
better, or to curbe it: ye must finde out first the most advantagious place: in case
there be a river, then ye shall build your Castle upon the side of it, where it may best
<pb n="35" facs="tcp:1568:21"/>
commaund, with all the advantage that possibly may be, also takeing heede that it
be built in such a place, that the Castle may receiue noe disadvantage thereby, but
that the Rampart of the Towne where the letters A, G are, be the weakest part; to
the end that by this meanes, ye may frustrate the desire of the inhabitans of the said
towne, from opposing themselues against the said Castle: but if ye feare noe such
inconvenience, ye may make the places A, G, as strong as the other: saving that
the Ramparts in the said angles be noe thicker in the angles A, G (which are angles
of imperfect Bulwarkes) then in other places, and not massiue or full of earth, as the
Bulwarkes B, &amp; C, D, are. Let there be a towne then contayning 8 angles, whereof
7 of them are marked out with these Alphabeticall letters A, B, C, D, E, F, &amp; G, and
that you are desirous to make a <hi>Pentagonall</hi> Citadell. For the doing whereof ye must
first make a mapp of the said towne <hi>Octogonall:</hi> in case it be not made, according to
the methode giuen heretofore in our Geometrie, which is here marked out by these
letters A, B, C, D, E, F, &amp; G, with the Falsebrays, Parapets, Moates, Covert way, &amp; its
Parapet. Then upon a paper of the same scale, whereof the mapp of the said towne
is made, being traced out in a <hi>Pentagone</hi> with all the outworkes, such as the figure
marked H, I, K, L, M, demonstrats, according to the method giuen yow before in the
10 and 11 Plates, then the same figure <hi>Pentagonall</hi> must be cutt perfectly, and so fitted
to the towne, remouing it so longe till yow haue at length found out the most ad<g ref="char:EOLhyphen"/>vantagious
place to make there your Castle <hi>Pentagone,</hi> takeing heede that the
<hi>tenailles</hi> N and O, fall out right, to answere the curtaines P, O, and Q, N, to the end
that the entrance into the towne may be the more commodious, &amp; that the towne
in the places N, R, S, T, O, be not discouered without, whereof one ought to haue a
singular care: for there where the said angles of the tenaille, be not well joyned to
the Ramparts, those places will alwayes be badly defended in the said joynings, as
ye may obserue in the Castle of <hi>Gulick,</hi> which platforme followes next. It is true;
that when ye make these angles in the curtaines, that the parts N, R, S, T, O, take
up a great deale of the towne, which may be prevented in setting the Castle more
outward, and makeing the said curtaines meete neerer the faces of the Bulwarks of
the Castle. But the side of the towne N, R, S, T, O, will in noe wise be guarded, as
the Platforme of the Castle of <hi>Gulick</hi> sheweth: so that necessity will require, for the
preventing of such an inconveniencie, to make some Ravelins, or some other works
without the said place, as the commodiousnesse of the ground may afforde, which
would make mee resolue rather to approue of the forme of the 80 figure, then of the
other, were it not for some cause more urgent, then is here alledged, which reason
would moue mee to change my opinion.</p>
                  <p>If the towne or Cittie A, B, C, D, E, F, G, were greater, then were it vnnecessary to
take so much care for the place, which the Castle taketh up: for then ye might make
the curtaines P, O, &amp; Q, N, longer, to wit some 50 rod, that the flanks V, X, and Y, Z,
might not come so neere the Bulwarks E, M: from whence one may easely discouer
the Falsebray of the Castle, for the preventing of which inconvenience, it wilbe
good to raise the Bulwarkes of the Castle, which looks into the towne, somewhat
higher aboue the Ramparts thereof, but the towne being of a small circuit (as wee
haue said) one shalbe constrained to use for it the same figures as are demonstrated
by the figures 80. &amp; 81.</p>
                  <p>If one would built a towne to a Castle, first ye must obserue diligently the site of
the place, and if it may be made regular, to take care, how many Inhabitants this
place will containe, the nature and quality of them, and whether the towne may in
processe of time be enlarged: which ye shalbe able to judge, when ye see the countrie
that lies about it, what wayes, avenues and passages there are to come to it, as also to
<pb n="36" facs="tcp:1568:22"/>
consider the goodnesse of the aire, and of the soile of all which things (as <hi>Vitru<g ref="char:EOLhyphen"/>vius</hi>
saith) one ought to haue a most speciall care. According to all which one
ought to gouerne themselues: for to enclosse a great peece of ground, where
there is none, or little appearance of Inhabitants, this were rather to ruinate,
then to edifie, to which takeing heede then, ye must resolue of the Circuit, or Capa<g ref="char:EOLhyphen"/>city,
which ye would giue to the said towne, and suppose ye would make the forme
thereof <hi>Octogonall,</hi> and regular: ye must trace out then an <hi>Octogonall</hi> Fortresse regu<g ref="char:EOLhyphen"/>lar,
according to the former method, with covert wayes, and what ye require more
upon the same scale, as you made your Castle <hi>Pentagonall,</hi> then ye must cutt the said
forme <hi>Octogonall,</hi> and joyne it to the said Castle, removing it so long, till yow haue
found out &amp; chosen out (with all circumspection requisite) the most convenientest
place, and staying there ye may trace out the said towne, as the figures 80 and 81 de<g ref="char:EOLhyphen"/>monstrate,
joyned to the Castle. But as we haue said, it will loose much of its capa<g ref="char:EOLhyphen"/>city,
because the curtaines of the towne will come to meete with the angles of the
tenailles of the Castle in the points marked O, and N.</p>
               </div>
               <div type="subsection">
                  <head>The 17. Plate, and the 82. 83. Figure.</head>
                  <p>IF ye will not tye your selfe so precisely to this forme <hi>Octogonall,</hi> ye may make the
towne much better by the meanes which wee will now speake of. Let first be
drawne the lines D, D, and A, A. &amp;c. right perpendiculars upon the midst of the
curtaines N, M, and K, Y, of some 60 rod, or there abouts, then let there be made
the perpendicular line infinite in the midst, and upon the curtaine D, E; in which ye
haue the center of the circle, which makes the circle of all the figure, and suppose ye
desire to make a forme regular of nine Bulwarks, whereof the angles flanked, are
distant one from an other 80 rod, from the utmost end Q, shalbe made an arch, in
such sort, that within the circuit thereof the distance N, P, is contained 9 times,
which shall make the point of the center C, C. then upon the circumference of the
said arch the said 9 points, being marked as they are noted here by the letters Q, R,
S, T, V, X, Y, Z, &amp;c ye shall make the angles interiour flanking, according to their
forme, that ye may haue the angle flanked right, &amp; that ye may the better make the
angle flanking, or the tenaille pointed and small, which is accounted the best, as that
skilfull, and diligent man <hi>M. Iohn Errard of Barleduke,</hi> Ingenier to the King of France
hath obserued well, and to know how much the said angle flanking will make, ye
must substract the halfe of the angle from the Bulwarke, or flanked from the halfe
of the angle of the <hi>Polygone,</hi> the rest shalbe the angle flanking interiour. But if the
angle of the <hi>Polygone</hi> be lesser then 150 degrees, which is the angle of a <hi>Dodecagone,</hi>
ye shall then governe your selfe according to the table giuen before, takeing heede
that the angle of the <hi>Polygone</hi> agreeth most with the angle to be fortified, and in its
columne is found the angle flanking interiour, necessary to the said angle, by which
ye may come to the angle of the <hi>tenaille,</hi> &amp; seing in this exemple wee haue set downe
the dista<g ref="char:cmbAbbrStroke">̄</g>ce fro<g ref="char:cmbAbbrStroke">̄</g> angle to angle, as wel of the <hi>Pentag.</hi> as of the towne 80 rod, wee wil set
downe upon the lines, which make the <hi>tenailles</hi> 2 equall parts, &amp; from the said 2 parts
in the line which formeth the angle flanking, a parallell line being drawne to that of
80 rod, &amp; placed upo<g ref="char:cmbAbbrStroke">̄</g> the 3 equall parts, a privie line infinite, must be drawne through
the said 3 point, &amp; through the angle, and where the same comes to cutt the other
side of the <hi>tenaille</hi> in the point O, ye shall haue the shoulder, through which the line
A, B, being drawne, makeing the angle forming the flanke 40 degrees, ye shall haue
the center of the Bulwarks justas wee haue taught heretofore in the 10 &amp; 11 plates.
If the Castle had bin made with foure angles, the construction would haue ben the
<pb n="37" facs="tcp:1568:22"/>
same, and if the lines D, D, Q, and A, A, &amp;c. had bene somewhat more then 60 rod,
the forme would haue bene better, for though we haue made the lines of defence,
to be 60 rod in the former Fortresses, there is an other consideration in this present
building; in regard the Bulwarkes Q, &amp;c. advance themselues towards the angles
Q, &amp;c. from whence the said curtaines Q, E, E. &amp; B, B &amp;c. maye be sufficiently de<g ref="char:EOLhyphen"/>fended,
when they doe not exceede aboue 70 rod, the moates, covert wayes, false<g ref="char:EOLhyphen"/>brayes
and other workes, must be made in that forme as we haue sett them downe
before in the 16. plate.</p>
               </div>
            </div>
            <div type="section">
               <head>How to describe the order which is obserued in makeing of a
platforme, and of some other appendances.</head>
               <p>THe draught being made upon a paper, ere ye make a platforme of it, ye ought
first to ouercast, aswell the lines, as the body of the Fortresse, in that manner as
we haue showne yow before in our <hi>Geometrie,</hi> that ye may know pertinently all the
particular dimensions, &amp; so committ noe errour, in makeing a plateforme thereof:
Before ye lett it out, according to our Method giuen in the conclusio<g ref="char:cmbAbbrStroke">̄</g> of the practize
of <hi>Geometrie,</hi> which being done before the Inginier begins the worke, he shall de<g ref="char:EOLhyphen"/>clare
the particular conditions, which he would haue obserued in the makeing and
finishing of this worke, as the time when they are to beginn, how long it wilbe before
it be finished, how many men he must ordinarily haue to worke, what instruments
they must use for the driving in of piles, and the laying of the foundation, how many
foote, and what edge they are to giue to the wall, or the parapet of the falsebray, the
thicknesse of the parapet, and how broad the falsebray ought to be, how much the
talud (or slooping) on the inside and on the outside must be<g ref="char:punc">▪</g> and that according
to the goodnesse or weaknesse of the matter upon which one builds, how many
bundles of brush in a sand<gap reason="illegible" resp="#TECH" extent="1 letter">
                     <desc>•</desc>
                  </gap>e Earth he is to lay in the parapet of the falsebray, and in
the Rampart, the height, the Talud or slooping, both on the inside, &amp; on the outside,
the bredth and depth of the moate, &amp; its slooping, and generally and specially all
things touching the makeing of such a Castle, whereof he hath made his platforme.
And some dayes before they come to the place, or that the forme be drawne out,
they shall sett up billets in the next adjoyning townes to giue notice to the Worke
masters, that upon such and such a day, one is resolued to hire and let out such &amp; such
works, to him that will take them on upon the least price: and before the day pre<g ref="char:EOLhyphen"/>fixed
the said Inginier shall come thither himself with some one of the Deputies, or
some other that hath the managing of that worke, to draw a draught of the said
Fortresse, and to prepare all things necessarie against that day assigned. Then tho
day being come, all the Worke-masters &amp; Undertakers shall come together, either
upon the place where the worke is to be made, or else in some other place where
the conditions and couenants are read, according as they will haue the worke
hastned: this done, they shall demaund, who will take it on for the least money, then
one of the Workemasters will say for so much, an other for so much lesser, which is
done till noe man will take it on at a lesser rate, then underneath they signe unto
the articles of the conditions, that I N, N, haue undertaken the worke upon such
and such conditions, for the summe of so much money: sometimes ye shall haue
two or three Undertakers joyne together and undertake the whole worke, all of
them signing to the articles, as also the Commissioners, and Inginier must doe on
their part: then they beginn the worke, and commonly the Undertakers are bound
by the said articles and Contracts, to deliuer all the materialls necessarie for the said
worke, which they receiue from the Master of the Magazin there or else, where
<pb n="38" facs="tcp:1568:23"/>
giving him a note under their hands for the restitution of them back againe, when
the worke is finished, and to make good whatsoeuer they either breake or loose.</p>
               <p>Then the Workemaster placeth his men in order, as he knowes the quality of the
worke requireth best, some to digg, and cast up the Earth, others to fill Karrs, and
Wheele-barrowes, others to levell the ground which is pricked out; for in the be<g ref="char:EOLhyphen"/>ginning
it wilbe necessary to carry the Earth away, with a Horse and a Karre, which
is cast up on the outside of the moate upon the basis of the Rampart, &amp; not with
Wheele-barrowes as they must doe at the last, when the worke growes high, and that
ye are come to the depth of the moate, for then ye cannot so well use Horse and
Karrs; by reason of the difficulties knowne to all men, namely, that the treading of
the horses and the Karrs spoyle the groundworke, and cannot be laid so well, as
when men brings the Earth up in Wheele-barrowes upo<g ref="char:cmbAbbrStroke">̄</g> away ascending with plan<g ref="char:EOLhyphen"/>cies,
as hath bene found by experience often times by the undertakers of such
workes.</p>
            </div>
            <div type="section">
               <head>Of the Foundations.</head>
               <div type="subsection">
                  <head>2. The 17. Plate.</head>
                  <p>WHen the foundation is bad, it wilbe your best course to driue in piles, along the
foote of the Rampart, just where the said Rampart beginneth, some piles 25, or
30 foote, or else yong Alders-trees, about foure or fiue yeares growth along the
worke about 18 or 20 foote long, closse one to an other, and the closser the better,
and though this be a great charge, and a long worke; yet this is the best foundation
ye can choose: But as we haue said oftentimes, seing it hapneth that one cannot
stay so long, ye must then take bundles of brush, and binde them up in fagots, &amp; lay
them crossewise, driving them into the Earth with stakes to fasten them together,
that they may lie firme, and if ye lay the foundation in a ditch or a quagmire, ye must
make use of such fagots bound and tyed up together with cords, &amp; if it be in a river,
then ye must binde brickbats, or stones betweene two bundles, to make them sinke
to the botome: ye may make them as long, or as short as ye please, and so necessity
requires, till ye haue filled up the water with these sinkers, upon which yow must lay
your foundation, then ye must also driue in some piles about 18 or 20 foote longe,
(according to the depth) to make them lie the more firme and solid together. Now
these bundles are made in the forme of <hi>Saucidges,</hi> as here followeth.</p>
                  <p>First, ye driue into the ground stakes of the heigth &amp; bredth as ye desire to make
these <hi>Saucidges,</hi> either great or small, the one a foote high, the other a foote and a
halfe, and sometimes two foote, then ye lay betweene these stakes bulrushes, boughs
or small bundles of brush bound fast together, and in the midst of them ye must lay
brick-bats, when ye sinke them in a river, but of Earth if ye will lay them as a foun<g ref="char:EOLhyphen"/>dation
in a moate all along the said worke, then ye binde the said bundles with
stones, or Earth in them, fastning them with withs in the same manner, as ye binde
up a fagot, or a bavin, and in this forme are your <hi>Saucidges,</hi> or sinkers made, which
being done, the letters A are bound one to another, as strong as possible may be, as
ye may perceiue by the letter B in the 2. 17. Plate.</p>
                  <p>Then ye sinke these downe to the bottome, that ye may afterward build your
Fortresse upon them, according to the former platforme, whereof a Plate is made
before, which groundworks among the Ingeniers of the united Provinces are much
used, because these parts are maritimate, moorish, and subject to bad foundations, so
that in some places the foundations cost more then the rest of the building it self,
<pb n="39" facs="tcp:1568:23"/>
yea in diuerse places of these Countries, the Inhabitants are driuen to keepe
their grounds from the violence of the Sea and Rivers, by such and such
like meanes and remedies, to their great and unspeakeable charges, for one
would haue thought it had ben impossible for them so many yeares to doe it, since
the times that these Provinces were united, had not the superintendants, &amp; Dike<g ref="char:EOLhyphen"/>graues
used great care and diligence in continuing the same preservation for the
good of the inhabitants, and common weale, whereof wee will speake more at large
hereafter.</p>
                  <p>When the worke is raised aboue the water, and that the Earth in the moate di<g ref="char:EOLhyphen"/>minisheth,
the Worck-master shall then beginn to lay his edge, or border upon the
line drawne out for the Rampart. Now the line being drawne out upon the ground,
as ye see in the line C. by the 2. of the 17. Plate, being fiue or six ynches broad, and
as deepe, which is done by the Ingenier himself to take away all excuse from the
Work-masters, that he may likewise carrie a right line, aswell on the inside as on the
outside of the Rampart, as also for the moate, and the other parts of the said For<g ref="char:EOLhyphen"/>tresse,
represented in the plat-forme: Besides if the condition of the undertaker
containes, that the outside of the Rampart must be raised with sodds, which are
ordinarily 4 or 5 ynches square, and 14 or 15 ynches long diminishing towards the
inside, as ye may see here by the figure D, to the end that betweene the said rowes of
sodds, one may lay a litle earth to settle them the better together to the bodie of the
Rampart. Moreouer, they are so laid together that the rowes aboue must lie euen
in the midst of the joynture of the rowes beneath, makeing them settle together
according as the condition beares, and as the articles are which the undertaker
hath signed unto. Now for his better ease, he must make use of a triangular Instru<g ref="char:EOLhyphen"/>ment,
such a one as the letter F demonstrats, being <gap reason="illegible" resp="#TECH" extent="1 word">
                        <desc>〈◊〉</desc>
                     </gap> 
                     <gap reason="illegible" resp="#TECH" extent="2 letters">
                        <desc>••</desc>
                     </gap>de A, B, about 2, or 3 foote
more or lesse, according to the quality of the worke, and the rest so consequently:
For as ye desire to haue the Talud, either great or little, so ye must enlarge the line
A, G, or lessen it: If it be needefull to lay bundles of brush to strengthen your works
of the Fortresse, ye must lay them so that the ends touch the former sodds, to wit the
one row half a foote aboue the other, and betweene each of them halfe a foote of
Earth, continuing the worke so untill it be finished: upon the top of the Earth of
the Rampart, ye shall raise the parapet with such a Talud and bredth, as the condi<g ref="char:EOLhyphen"/>tions
imports, in the same manner as before, raising it with sodds, as we haue said. If ye
make your Fortresse in a fatt and a clayie soile, then ye may (in stead of sodds) make
a cruste of 3, or 4 foote, or more, stamping it well with a stamper made to that end,
and of such an inclination as your agreement beares, in which crust ye may sett a
certaine kinde of grasse, called in Flemish <hi>Queeckcruyt,</hi> in Latin <hi>Gramen,</hi> &amp; in English
<hi>Meddovv grasse,</hi> which roote is of such a nature, that it will spread itfelfe ouer the
whole Rampart, and binde the Earth fast together: so that it will make the said
crust of a long durance, and almost perpetuall: on the outside of the said brust, ye
may sowe Oats or Hay-seed: they use also to sett upon the Bulwarke, roots of seuen-leaued-grasse,
which is likewise very good: but the leaues doe not spread themselues
ouer the exteriour superficies, or this crust, as the abouesaid grasse doth: for this
reason some yeares since his Excellencie hath found it good, to repaire all the Forti<g ref="char:EOLhyphen"/>fications
of such a crust without sodds; because experience hath taught us, that
the said sodds bindes not the rest of the Earth, so well as the said crust doth, which
being moist by that meanes joyneth so much the better the rest of the wall or Ram<g ref="char:EOLhyphen"/>part
together, which is of very great use, and is quickly done.</p>
                  <p>
                     <pb n="40" facs="tcp:1568:24"/>
The talud of the Rampart is made somewhat greater, that one may stand an end
the better upon it, as ye may see by the profiles here before, aswell of Ramparts as
Falsebrayes. This being done, ye must make the parapet of the covert-way of earth
digged out of the moate, whereof good store was layd on the outside of the moate,
to that purpose: and the said undertaker ought to that end make an exact calcu<g ref="char:EOLhyphen"/>lation
of the quantity of Earth, which is necessary for that use. But seing oftentimes
the undertakers are not skillfull in casting up such accounts: It were good that the
Ingenier himself should make an exact calculation, not onely of this part, but also
of the whole worke, which may be done in that manner, as wee haue showne in our
<hi>Geometrie,</hi> or else in this easie manner following.</p>
               </div>
               <div type="subsection">
                  <head>The second 17. Plate, and Letters G, H, R.</head>
                  <p>LEt the 12 part of the Fortresse be <hi>Dodecangular</hi> G, and AB the face 24 rod; the
flanke AD 12, and the curtaine 36. and for the Rampart H. Let the talud inte<g ref="char:EOLhyphen"/>riour
be 15 foote, and the height asmuch, the talud exteriour 10 foote, the bredth
upon the Rampart 50 foote, which makes that the superficies of the <hi>Profile</hi> of the
said Rampart wilbe 933 1/3. Moreouer, for the <hi>Profile</hi> of the parapet, which is K 99 1/4. the
heigth EC 6 foote, HF, 4. AB for the footbanke a foote and a halfe; AC 3. BD 2.
CG 20. HG 2 1/2. the solidity of the Rampart &amp; the parapet is required.</p>
               </div>
               <div type="subsection">
                  <head>Of the Rampart.</head>
                  <p>THe <hi>Icnographie</hi> sheweth, that CM 10 foote is the talud exteriour, and HN 15
foote the interiour, the angle B is right in the <hi>Dodecagone,</hi> and in the <hi>Polygones</hi>
upon it, ye must remember once for all, that if the <hi>Profile</hi> on all sides hold one &amp; the
same dimensions, to wit in the faces, flanks, &amp; <gap reason="illegible" resp="#TECH" extent="1 word">
                        <desc>〈◊〉</desc>
                     </gap> the angles BAD shalbe cutt
by halues from the lines HB, EA, KD. Also the angle of the <hi>Polygone</hi> being 150, &amp; the
flanked right; the angle flanking interiour wilbe 30 degrees, as it is marked, and the
shoulder 120 degrees, which makes that the triangles right-angles are as followes:
those which haue their angles pointed of 45 degrees, shalbe <hi>Isosceles,</hi> or like angles,
BM, MC upon the basis each of them 10 foote, the lines C 3. 3 G, each 50 foote, BX
&amp; XH, each 75 foote, GN, NH 15 foote, and the like in the triangles hauing their
Hypotenouses at KD. Moreouer in the triangle ORA, in the shoulder RO 10, OA
5, 7735, the line marked 5 A, 43, 30125, therefore takeing the lines BX, and 5 A from
BA 24 rod, or 288 foote, there will remaine HF 169, 69875. Likewise AD 144 foote,
PD, or RV, wilbe 138, 2265, and by adding to it FV. FR will come to 148, 2265, the
line A 12 is equall to A 5. taken from AD, there will remaine 100, 69857 for T 8, to
which add 8 I, 60, TI will come to 160, 69875, and LI, 169, 359, add to the said TI, IZ,
15, ye shall haue EK 175, 69875.</p>
                  <p>The demy-curtaine 13 D, makes 216, then 9 F, 226, also 11 K 291, &amp; 10 I, 276: so
that if ye add CR 272, 2265, RF 148, 2265, and F 9. which is 226, ye shall haue 646,
453 for CFR 9. the circuit exteriour.</p>
                  <p>Ye shall finde also GL 193, 359, &amp; LI, 169, 35904: &amp; 10 I, 276. whereof the summe
for GLI 10, wilbe 638, 718 the circuit interiour, which being added to the exteriour
abouenamed, will amount to 1285, 171, its halfe is 642, 5855, which multiplyed by
G3, the distance of the parallells 50, will come to 32129, 275 for the superficies,
betweene the abouesaid circuits, and then multiply by 15 the heights, ye shall haue
the solidity of the wall, without the taluds 481939, 125. CRF 9. 10. ILGC, which
had bene too short as here followeth.</p>
                  <p>
                     <pb n="41" facs="tcp:1568:24"/>
The Authour hauing made this aboue with so many lines, if from the midst of
LR, he had drawne a perpendicular line upon the face, and cutt af from it 20, 2071
its double substracted from the summe of the abouesaid perpendicular, and from
BA, AD, D 13, which is 683, the remainder wilbe 642, 5856, which multiplyed by 15,
it wilbe the same as aboue.</p>
               </div>
               <div type="subsection">
                  <head>Of the Taluds or slooping vvalls or Ramparts.</head>
                  <p>THe <hi>Taluds</hi> without the <hi>Pyramids,</hi> which are in the angles, shalbe calculated thus,
their <hi>Profile</hi> is a triangle, which multiplyed by the length, or else as <hi>Demy-paralleli<g ref="char:EOLhyphen"/>pedes,</hi>
the <hi>Basis</hi> multiplyed by the heigth, afterward the halfe taken, add to it then
CR 272, 2265, RV 138, 2265, with D 13, which is 216, the summe 626, 453 multiplyed
by MC, 10, the superficiall basis wilbe 6264, 53; likewise HE 169, 69875, EY 160, 69875
&amp; I 10, which is 276, makeing together 606, 3975, which being multiplyed by IY 15,
will make 9095, 9625 for the other superficiall basis, together with the former will
make 15360, 4925 (because they are of a like heigth) by which heigth of 15 being mul<g ref="char:EOLhyphen"/>tiplyed,
then the halfe will come to 115203, 69375 for the taluds, aswell interiour, as
exteriour besides the <hi>Pyramides.</hi>
                  </p>
               </div>
               <div type="subsection">
                  <head>Of Pyramids, and double Pyramids of the Taluds.</head>
                  <p>THere are 3 <hi>Pyramides</hi> in the angles <hi>convexe</hi> B, A, K, and three double <hi>Pyramids</hi> in
the angles <hi>concave,</hi> H, E, D, which I say because <hi>Marolois</hi> makeing no distinction
of them, taketh two things for one: As for exemple, the body upon VFXD is
1000 foot <hi>cubicall,</hi> and he <gap reason="illegible" resp="#TECH" extent="1 span">
                        <desc>〈…〉</desc>
                     </gap> but 500, and so of the two others.</p>
                  <p>The <hi>Superficies</hi> of the triangle BMC, is 50 from ROAP, is the right-angle RO, OA
57, 735, and YIZK 225, and then the double <hi>superficies</hi> of GNH 225 (according to
that as we haue said before touching the Authours fault) ESLT its double <hi>Superfi<g ref="char:EOLhyphen"/>cies</hi>
is 259, 8057, &amp; the double <hi>superficies</hi> VFXC, of 200, whereof the summe is 1071,
5425, which multiplyed by the <hi>tierce</hi> of the common heights, ye shall haue for the
abouesaid fixe bodies 5087, 7125, (whereas <hi>Marolois</hi> hath but 3375, 69375) to which
if ye add, aswell the Taluds 115203, 69375, as the Rampart 481934, 125, the summe
wilbe 602230, 5312, for the soliditie of the Rampart, besides the parapet.</p>
                  <p>Those which will not take the paines to haue it done soe exactly, but are conten<g ref="char:EOLhyphen"/>ted
to come somewhat neere unto it, shall add unto it BAD 13, which is 648, with
HEK 11, being 636, 396, and the halfe of the summe multiplyed by the <hi>profile</hi> of the
Rampart 937 1/2 ye shall haue 602060, which comes the neerest unto 602230, found out
aboue (being onely 170 too litle) for <hi>Marolois</hi> found out but 600518, with much
adoe, hauing 1712 too litle.</p>
               </div>
               <div type="subsection">
                  <head>Of a Parapet.</head>
                  <p>WE haue before sett downe the dimensions of a <hi>Parapet</hi> as ye may see by the letter
K, newly cutt, with its Rampart H, in this plate, &amp; ye must not thinke it strange,
that the Parapet is made upon a greater measure, then that of the Rampart, the
reason is, because there are noe more dissections, or cutting of, and that wee haue
not roome to make that which we would within the some Plate.</p>
                  <p>
                     <pb n="42" facs="tcp:1568:25"/>
Now if ye desire to calculate the <hi>Profile</hi> as the Authour hath done, the whole as
the brevitie of the Rampart showes aboue mentioned, its situation is termined on
the outside by CRF 9. and on the inside by a parallell line, betweene the abouesaid
&amp; GLI 10, distant from the other 20 foote, and for the avoyding of the confusion
which the plurality of lines might cause, we will take for the said paralell, the line
GLI 10, and therefore 3 G, or 7 S, will make 20, or else the line LT; ye shall finde by
the triangles, that TR wilbe 5, 369. add hereunto C 3, which is 20, and the summe of
CR knowne aboue, taken from 272, 2265, there will remaine for GL 246, 8675, then
from RF 148, 2265, substracting the length equall to TR, 5, 359, there will remaine
142, 8675, afterward add thereunto 8 V, or its equall 20, ye shall haue 162, 8675 for
LI; also F 9, being 226, then I 10 wilbe 246; then the summe of CRF 9, (added to
GLI 10) and the halfe taken, ye shall haue for the middle length of the parapett
651, 094.</p>
                  <p>For the <hi>superficies</hi> of the <hi>Profile</hi> of the <hi>Parapet</hi> K, the triangle EIF 17 1/2: and DOE 2 1/4,
the <hi>trapeze,</hi> (or unequally side) IFGC 75; and BOCA 4 1/2, the summe is 99 1/4, for the
<hi>Superficies</hi> of the <hi>Profile,</hi> which multiplyed by the middle length aboue said, ye shall
haue 64621, 0795 for the solidity of the parapet, which is much too much; for it
ought to be as I haue calculated it with its dissections 63976, 9475, to which add
602230, 5312 from the Rampart ye shall haue 666207, 478, for the whole solidity of
the Rampart and Parapet, whereof the double 1332414, 956, wilbe the twelfth part
of the Circuit, which multiply by 12, ye shall haue the totall summe 15988979, 472,
and diuided by 144, ye shall haue 111034, 68 plyntides, or as <hi>Marolois</hi> calls them
Chevilles, peggs or pynnes, for the whole circuit of the <hi>Dodecagone.</hi>
                  </p>
                  <p>Seing then there are 9252, 88 pinnes in the 12 part of this Fortresse <hi>Dodecagonall,</hi>
the Ingenier may conjecture, for how much he may let out the same worke, which
is about 16, 20, 25 or 30 pinnes, according to the situation of the place, the ground
and other considerations, and after that the undertakers shall offer to make it ac<g ref="char:EOLhyphen"/>cording
to the calculation, made thereof, they may take on the said worke upon
condition, that they shall finish it in such a time, &amp; with so many men as is specified
in the contract, and soe at that instant they beginn the worke, &amp; finish it according
to their bargaines and conditions, as the greatnesse of the worke requires, and the
time limited, for which also the undertaker is bound to haue as many worke men
upon it, as shall be found needfull for the finishing of the said worke: &amp; for the better
assurance thereof, it is requisite to know how many pinnes a man may spit, and lay
upon a wheele-barrow in a day: for those that are skilled therein, say that a man if
he works his best, he may dig &amp; lay up 4 1/2 pinnes in a day, but ordinarily men
suppose that one can doe three pinnes euery day, without takeing too much
paines, according to which, one may easely make his calculation how many spad<g ref="char:EOLhyphen"/>men
he must use to make up that worke in such a time prefixed, for men which shall
doe nothing else, but spit and digg up the Earth &amp; the others to carrie it away upon
wheele-barrowes to the Rampart, for ye must haue as many men to carry up the
Earth in the wheel-barrowes, as that the spiters may be continually kept in worke
without any cessation or stay, to the intent the Work-master may finish his worke
within the time limited.</p>
               </div>
               <div type="subsection">
                  <head>Note.</head>
                  <p>WE say here, that a man may in case of necessity spit in a day 4 1/2 pinnes, and
commonly three in a day with leasure, but it is to be understood, this must be in
a good and fast ground, which wilbe beare spiting without falling or breaking; but
when the Earth is leane and sandie, it wilbe impossible for a man to doe so much, &amp;
so by consequence one cannot know any certaine rule.</p>
               </div>
               <div type="subsection">
                  <pb n="43" facs="tcp:1568:25"/>
                  <head>The 1. Maxime.</head>
                  <p>ACcording to which plotts and calculations all other places aswell regular as irre<g ref="char:EOLhyphen"/>gular
may be fortified, and hold this for a maxime, that the place so fortified, as
we haue taught aboue, wilbe better then the others.</p>
               </div>
               <div type="subsection">
                  <head>The 2. Maxime.</head>
                  <p>THat the line of defence which comes from the angle of the flanke to the angle
of the Bulwarke, called the line of <hi>deffence fichant</hi> ought not to be much longer
then 60 rod, because it is as farre as a Musket can well carry, but if ye will defend
the face with Canon, then it may be a 100, or 120 foote longe.</p>
               </div>
               <div type="subsection">
                  <head>The 3. Maxime.</head>
                  <p>THat lesser the angle of the <hi>tenaille</hi> is, it is so much the better, because the faces
looke more directly one upon another, therefore ye may see that in the plots of
the <hi>Dodecagone</hi> aboue said: ye must make the angle of the Bulwarke onely of 90 de<g ref="char:EOLhyphen"/>grees,
that the angle of the <hi>tenaille</hi> may be shutt the closser.</p>
               </div>
               <div type="subsection">
                  <head>The 4. Maxime.</head>
                  <p>BY how much the flanke and the gorge are greater and spacious, by so much they
are the fitter for defence.</p>
               </div>
               <div type="subsection">
                  <head>The 5. Maxime.</head>
                  <p>THe further the defence is made in the curtaine, it is the better, because ye may
bring the more men to giue fire upon it, for the defence of the faces. Therefore
in the plots of the <hi>Dodecagone</hi> abouesaid, ye must see that the angle of the Bulwarke
be made of 90 degrees, to the end ye may giue fire the larger.</p>
               </div>
               <div type="subsection">
                  <head>The 6. Maxime.</head>
                  <p>That the angle flanked ought to be noe lesse then 60, and not aboue 90 degrees.</p>
               </div>
               <div type="subsection">
                  <head>The 7. Maxime.</head>
                  <p>THat the angle of the <hi>Polygone,</hi> which ye intend to fortify, ought not to be lesse
then 90 degrees, but the greater it is, it wilbe so much the better.</p>
               </div>
               <div type="subsection">
                  <head>The 8. Maxime.</head>
                  <p>THat in all Fortresses wee will make the face to be 24 rod, and the curtaine 36,
according to which the lines of the <hi>Polygones</hi> exteriour will make about 60 rod,
and the lines of the <hi>Polygones</hi> interiour 60 rod. In a <hi>Heptagone</hi> and the <hi>Polygones</hi> un<g ref="char:EOLhyphen"/>derneath,
the <hi>Polygones</hi> exteriour wilbe more then 80 rod, and aboue lesse then 80.
The <hi>Polygones</hi> interiour which are beneath the said <hi>Heptagone,</hi> are lesse then 60 rod,
and aboue more then 60, the one encreasing, the other decreasing, untill that the
<pb n="44" facs="tcp:1568:26"/>
angles of the <hi>Polygones</hi> come to be 180 degrees, and then ye haue the <hi>Polygones</hi> exte<g ref="char:EOLhyphen"/>riour,
and interiour equall, and each of them 70 rod, the line of defence fichant in
the whole about 60 rod, &amp; the angle forming the flanke of 40 degrees.</p>
               </div>
               <div type="subsection">
                  <head>The 9 Maxime.</head>
                  <p>THat the angle flanking interiour ought to be noe lesse then 15 degrees, but the
greater the better they are.</p>
               </div>
               <div type="subsection">
                  <head>The 10. Maxime.</head>
                  <p>THat the angle of the flanke be alwayes right, the angle of the shoulder must be
at the least 105 degrees, and the greater the better.</p>
               </div>
               <div type="subsection">
                  <head>The 11. Maxime.</head>
                  <p>IF it be needfull to fortifie any <hi>Polygone,</hi> either regular or irregular, whereof the
sides are lesse then is here spoken of, then ye must proportion out the gorges,
flankes and faces, according to the forme of the angle, as ye shall se in a table follo<g ref="char:EOLhyphen"/>wing.</p>
                  <p>Herewith wee will put an end to our first part of Fortification, and will come now
to the fortifying of places irregular.</p>
                  <trailer>FINIS.</trailer>
               </div>
            </div>
         </div>
         <div type="table">
            <pb facs="tcp:1568:26"/>
            <pb facs="tcp:1568:27"/>
            <head>A
THE DIMENSIONS OF
<gap reason="illegible" resp="#TECH" extent="1 word">
                  <desc>〈◊〉</desc>
               </gap> IN TWO MANNERS.</head>
            <p>
               <table>
                  <row>
                     <cell> </cell>
                     <cell> </cell>
                     <cell> </cell>
                     <cell> </cell>
                     <cell> </cell>
                     <cell>The curtain right.</cell>
                     <cell cols="6">The second manner is, VVhen the angle flancked is tvvo thirds of the Polygone.</cell>
                  </row>
                  <row>
                     <cell>VIII.</cell>
                     <cell>IX.</cell>
                     <cell>X.</cell>
                     <cell>XI</cell>
                     <cell>XII.</cell>
                     <cell> </cell>
                     <cell>IIII.</cell>
                     <cell>V.</cell>
                     <cell>VI.</cell>
                     <cell>VII.</cell>
                     <cell>VIII.</cell>
                  </row>
                  <row>
                     <cell>6.</cell>
                     <cell>36.</cell>
                     <cell>36.</cell>
                     <cell>36.</cell>
                     <cell>36.</cell>
                     <cell>36.</cell>
                     <cell>36.</cell>
                     <cell>36.</cell>
                     <cell>36.</cell>
                     <cell>36.</cell>
                     <cell>36.</cell>
                  </row>
                  <row>
                     <cell>4.</cell>
                     <cell>24.</cell>
                     <cell>24.</cell>
                     <cell>24.</cell>
                     <cell>24.</cell>
                     <cell>24.</cell>
                     <cell>24.</cell>
                     <cell>24.</cell>
                     <cell>24.</cell>
                     <cell>24.</cell>
                     <cell>24.</cell>
                  </row>
                  <row>
                     <cell>1.52</cell>
                     <cell>21.29.</cell>
                     <cell>21.09</cell>
                     <cell>20.93</cell>
                     <cell>20.78</cell>
                     <cell>16.97</cell>
                     <cell>23.18</cell>
                     <cell>22.82</cell>
                     <cell>22.55</cell>
                     <cell>22.34</cell>
                     <cell>22.17</cell>
                  </row>
                  <row>
                     <cell>2.71</cell>
                     <cell>13.22</cell>
                     <cell>13.65</cell>
                     <cell>14.02</cell>
                     <cell>14.34</cell>
                     <cell>16.97</cell>
                     <cell>9.23</cell>
                     <cell>10.83</cell>
                     <cell>12.00</cell>
                     <cell>12.90</cell>
                     <cell>13.63</cell>
                  </row>
                  <row>
                     <cell>3.48</cell>
                     <cell>24.84</cell>
                     <cell>25.96</cell>
                     <cell>26.90</cell>
                     <cell>27.71</cell>
                     <cell>33.94</cell>
                     <cell>13.05</cell>
                     <cell>17.53</cell>
                     <cell>20.78</cell>
                     <cell>23.26</cell>
                     <cell>25.19</cell>
                  </row>
                  <row>
                     <cell>
                        <gap reason="illegible" resp="#TECH" extent="1 letter">
                           <desc>•</desc>
                        </gap>3.03</cell>
                     <cell>23.60</cell>
                     <cell>24.08</cell>
                     <cell>24.50</cell>
                     <cell>24.88</cell>
                     <cell>28.97</cell>
                     <cell>19.73</cell>
                     <cell>20.40</cell>
                     <cell>21.10</cell>
                     <cell>21.75</cell>
                     <cell>22.32</cell>
                  </row>
                  <row>
                     <cell>7.90</cell>
                     <cell>28.12</cell>
                     <cell>28.30</cell>
                     <cell>28.46</cell>
                     <cell>28.60</cell>
                     <cell>28.97</cell>
                     <cell>26.26</cell>
                     <cell>26.77</cell>
                     <cell>27.10</cell>
                     <cell>27.37</cell>
                     <cell>27.53.</cell>
                  </row>
                  <row>
                     <cell>0.66</cell>
                     <cell>11.09</cell>
                     <cell>11.45</cell>
                     <cell>11.76</cell>
                     <cell>12.04</cell>
                     <cell>12.00</cell>
                     <cell>7.74</cell>
                     <cell>9.09</cell>
                     <cell>10.07</cell>
                     <cell>10.83</cell>
                     <cell>11.44</cell>
                  </row>
                  <row>
                     <cell>4.37</cell>
                     <cell>14.69</cell>
                     <cell>14.90</cell>
                     <cell>15.05</cell>
                     <cell>15.15</cell>
                     <cell>24.00</cell>
                     <cell>7.10</cell>
                     <cell>8.03</cell>
                     <cell>8.33</cell>
                     <cell>8.41<gap reason="illegible" resp="#TECH" extent="1 letter">
                           <desc>•</desc>
                        </gap>
                     </cell>
                     <cell>8.39</cell>
                  </row>
                  <row>
                     <cell>0.61</cell>
                     <cell>11.08</cell>
                     <cell>11.45</cell>
                     <cell>11.75</cell>
                     <cell>12.00</cell>
                     <cell>16.97</cell>
                     <cell>6.21</cell>
                     <cell>7.42</cell>
                     <cell>8.21</cell>
                     <cell>8.77</cell>
                     <cell>9.18</cell>
                  </row>
                  <row>
                     <cell>1.33</cell>
                     <cell>61.43</cell>
                     <cell>61.51</cell>
                     <cell>61.59</cell>
                     <cell>16.66</cell>
                     <cell>60.37</cell>
                     <cell>60.80</cell>
                     <cell>61.10</cell>
                     <cell>61.34</cell>
                     <cell>61.54</cell>
                     <cell>61.72</cell>
                  </row>
                  <row>
                     <cell>8.11</cell>
                     <cell>48.02</cell>
                     <cell>48.00</cell>
                     <cell>48.02</cell>
                     <cell>48.07</cell>
                     <cell>40.97</cell>
                     <cell>53.91</cell>
                     <cell>53.41</cell>
                     <cell>53.44</cell>
                     <cell>53.63</cell>
                     <cell>53.89</cell>
                  </row>
                  <row>
                     <cell>9.05</cell>
                     <cell>78.58</cell>
                     <cell>78.18</cell>
                     <cell>77.85</cell>
                     <cell>77.57</cell>
                     <cell>69.94</cell>
                     <cell>82.36</cell>
                     <cell>81.65</cell>
                     <cell>81.10</cell>
                     <cell>80.68</cell>
                     <cell>80.35</cell>
                  </row>
                  <row>
                     <cell>1.42</cell>
                     <cell>62.43</cell>
                     <cell>63.30</cell>
                     <cell>64.04</cell>
                     <cell>64.69</cell>
                     <cell>69.94</cell>
                     <cell>54.45</cell>
                     <cell>57.66</cell>
                     <cell>60.00</cell>
                     <cell>61.81</cell>
                     <cell>63.26</cell>
                  </row>
                  <row>
                     <cell>
                        <gap reason="illegible" resp="#TECH" extent="1 letter">
                           <desc>•</desc>
                        </gap>3.28</cell>
                     <cell>114.87</cell>
                     <cell>126.50</cell>
                     <cell>138.14</cell>
                     <cell>149.85</cell>
                     <cell>Infinite</cell>
                     <cell>58.24</cell>
                     <cell>69.45</cell>
                     <cell>81.10</cell>
                     <cell>92.55</cell>
                     <cell>104.98</cell>
                  </row>
                  <row>
                     <cell>0.25</cell>
                     <cell>91.27</cell>
                     <cell>102.42</cell>
                     <cell>113.63</cell>
                     <cell>124.97</cell>
                     <cell>Infinite</cell>
                     <cell>38.50</cell>
                     <cell>49.05</cell>
                     <cell>60.00</cell>
                     <cell>70.80</cell>
                     <cell>82.66</cell>
                  </row>
                  <row>
                     <cell>1.28</cell>
                     <cell>22.17</cell>
                     <cell>22.90</cell>
                     <cell>23.51</cell>
                     <cell>24.04</cell>
                     <cell>28.97</cell>
                     <cell>13.95</cell>
                     <cell>16.51</cell>
                     <cell>18.28</cell>
                     <cell>19.60</cell>
                     <cell>20.62</cell>
                  </row>
                  <row>
                     <cell> </cell>
                     <cell> </cell>
                     <cell> </cell>
                     <cell> </cell>
                     <cell> </cell>
                     <cell> </cell>
                     <cell> </cell>
                     <cell> </cell>
                     <cell> </cell>
                     <cell>Angles</cell>
                     <cell> </cell>
                  </row>
                  <row>
                     <cell>35.</cell>
                     <cell>140.</cell>
                     <cell>144.</cell>
                     <cell>147.16 4/11</cell>
                     <cell>150.</cell>
                     <cell>180.</cell>
                     <cell>90.</cell>
                     <cell>108.</cell>
                     <cell>120.</cell>
                     <cell>128.34 <gap reason="illegible" resp="#TECH" extent="2 letters">
                           <desc>••</desc>
                        </gap>
                     </cell>
                     <cell>135.</cell>
                  </row>
                  <row>
                     <cell>
                        <gap reason="illegible" resp="#TECH" extent="1 letter">
                           <desc>•</desc>
                        </gap>2.30</cell>
                     <cell>85.</cell>
                     <cell>87.</cell>
                     <cell>88.38 1/11</cell>
                     <cell>90.</cell>
                     <cell>90.</cell>
                     <cell>60.</cell>
                     <cell>72.</cell>
                     <cell>80.</cell>
                     <cell>85.42 6/7</cell>
                     <cell>90.</cell>
                  </row>
                  <row>
                     <cell>6.15</cell>
                     <cell>27.30</cell>
                     <cell>28.30</cell>
                     <cell>29.19 1/11</cell>
                     <cell>30.</cell>
                     <cell>45.</cell>
                     <cell>15.</cell>
                     <cell>18.</cell>
                     <cell>20.</cell>
                     <cell>21.25 1/7</cell>
                     <cell>22.30</cell>
                  </row>
                  <row>
                     <cell>27.30</cell>
                     <cell>125.</cell>
                     <cell>123.</cell>
                     <cell>121.31 9/11</cell>
                     <cell>120.</cell>
                     <cell>90.</cell>
                     <cell>150.</cell>
                     <cell>144.</cell>
                     <cell>140.</cell>
                     <cell>137.8 4/7</cell>
                     <cell>135.</cell>
                  </row>
                  <row>
                     <cell>
                        <gap reason="illegible" resp="#TECH" extent="1 letter">
                           <desc>•</desc>
                        </gap>0.</cell>
                     <cell>40.</cell>
                     <cell>40.</cell>
                     <cell>40.</cell>
                     <cell>40.</cell>
                     <cell>35.16.</cell>
                     <cell>40.</cell>
                     <cell>40.</cell>
                     <cell>40.</cell>
                     <cell>40.</cell>
                     <cell>40.</cell>
                  </row>
               </table>
            </p>
         </div>
         <div n="2" type="part">
            <pb facs="tcp:1568:27"/>
            <head>THE
SECOND PART,
TREATING
OF THE FORTIFICATION
OF
PLACES IRREGVLAR.
BY
SAMVELL MAROLOIS,
Revewed, Corrected, &amp; Augmented
BY
ALBERT GIRARD
SAMIELOIS.</head>
            <p>
               <seg rend="decorInit">T</seg>He Fortification <hi>irregular</hi> being more variable
by an infinite deale then the <hi>regular,</hi> is therefore more difficult and
requireth for this cause much more judgment and discretion, for
the effectuating of it well, and in choosing the best way to make it
then the former. Now to discusse thereof methodically methinks
it will not be amisse to beginn with the Fortification of a triangle <hi>equilaterall,</hi> that
is, of equal sides; which is well co<g ref="char:cmbAbbrStroke">̄</g>tained amonge the regular <hi>Polygones.</hi> And howbeit
that their angles fall so litle and pointed, that they cannot be duely fortified as
they ought: yet notwithstanding, I think it best to beginn with them, as being irre<g ref="char:EOLhyphen"/>gular
places, fortified noe otherwise then with a Wall or a small Moate. But if the
ground cann afford a good rampart, and a large moate; then I am of the opinion
that sometimes it wilbe requisite, yea, and for the most part better, that one forti<g ref="char:EOLhyphen"/>fies
such a place out of the enclossure, then otherwise, as I hope I shall demonstrate
vnto you hereafter.</p>
            <div type="section">
               <pb n="2" facs="tcp:1568:28"/>
               <head>The 18 Plate &amp; 84. Figure.</head>
               <p>LEt then the triangle A, B, C, be Equiangle and Equilaterall, which ye would
fortifie without diminishing of the place in anywise, nor yet enlarging it
much. To doe this, we will divide the sides of the triangle into 3 equall parts
by the points F and D, and from the distance F, D, shalbe made the triangle Equila<g ref="char:EOLhyphen"/>terall
D, F, E: the like must be done with the other triangles vpon the two sides A,
B, A, C, and so ye shall make a body <hi>Hexangular,</hi> built as a <hi>tenaille,</hi> without which ye
maye make a moate of a competent bredth and capable for a place so fortified; and
within the inside, ye maye cast vp a rampart of some 40, or 50 foote, as necessity shall
require, all as appeareth by this prese<g ref="char:cmbAbbrStroke">̄</g>t figure. But if the<g ref="char:cmbAbbrStroke">̄</g> afterward, ye finde that the
matter requires, that the angles exteriour maye be made, and reduced into Bul<g ref="char:EOLhyphen"/>warks,
as then ye must follow our generall rule, giuen for our regular fortification,
noted before in the 10, &amp; 11 Plates, and shall draw the vtmost angles, to wit privie
lines, as from G to A, then having resolued to laye out the proportio<g ref="char:cmbAbbrStroke">̄</g> of the curtaine
to the face, as 4 to 3. ye must vpon G, H, make 3 equall parts, and foure of the same
parts from G tovvards A, as from G to A. from which point A from the distance
of the 3 parts is made an arch towards I, and fro<g ref="char:cmbAbbrStroke">̄</g> H an other arch of 4 parts towards
the same point I. cutting the first at the point I<g ref="char:punc">▪</g> by which the line G. I. being
drawne cutting H, A. at R. we haue AR. for the face, and by this meanes the said
face wilbe in like proportion to the curtaine as 3 is to 4: Now for to know the flanke,
the Capitall line and the line of the gorge ye shall make an angle of 40 degrees
through the line S. M. passing by the point R, and cutting the line <hi>diagonall</hi> that
is, vvhich extends it selfe from one corner to the other) at S. and so AS wilbe the Ca<g ref="char:EOLhyphen"/>pitall
line, S, T the gorge, T, R the flanke of the Bulwarke, and T, V, the curtaine,
which hath the like proportion to A. R, as 4 to 3. And though this plote be not so
well proportioned as is to be desired: neverthelesse the defence thereof will fall out
well, being dravvne from the midst of the curtaine; but because of the smallnesse
of the angles flanked, which are but 60 degrees, the gorge is very narrow, and the
flank litle enoug: so that the said bulwarke will beare noe cutting off; neither can
containe men sufficient to endure an assault: so that this manner of fortification,
hath many imperfections, and ought not to be built in such a sort, when there is a
commodious place to make it otherwise: yea it would be better to alter somewhat
the angles by makeing them more blunt, and open, as in drawing the line Q. P. in
such wise, that the angle R. Q. P be 22 1/2 degrees, and the face Q. R. comes not
without the fortresse; then drawe the line P, R which giueth the length of the face
Q. R, according to the method abouesaid, &amp; the angle being made 40 degrees,
you shall haue the capitall line Q, S, and R, T the flanke S, T the Gorge, &amp; T V, the
curtaine, which proportion is better then the former; because the angle flanked
is more open then the precedent, the Gorge larger, the flanke greater and stronger
and of sufficient strength to resist a furious batterie, so that by this meanes though
the place will beare noe great alterations, yet it is made much better. Whence ap<g ref="char:EOLhyphen"/>peareth
that by a litle change a fortification may be much bettered, without any
great charge and labour, which ought not onely to be vnderstood of this fortifi<g ref="char:EOLhyphen"/>cation;
but also of all others, as wee hope shall appeare by the rest.</p>
            </div>
            <div type="section">
               <pb n="3" facs="tcp:1568:28"/>
               <head>How to fortifie a square fortresse with a Tenaille.</head>
               <div type="subsection">
                  <head>Figure 85.</head>
                  <p>FIrst ye must consider, whither it were more fitting, to fortifie the angles of a
quadrate, the<g ref="char:cmbAbbrStroke">̄</g> to fortifie it with a <hi>tenaille,</hi> which in my opinion ought to be done,
when as the angles of the square are so farre distant, that it is very needfull, to make
a bulwarke in the midst of the curtaine, then in stead of building vpon the angles
of the square pointed Bulwarks, as commonly the quadrate Bulwarks are: I would
make the angles BCD, FGH, KLM, &amp; OPQ, in the midst of the sides of the
squares, so that the lines, which forme the <hi>tenailles</hi> be all alike among themselues;
as A B C D E F G H &amp;c, and the angles also equall one to another, which is
done by drawing the two <hi>diagonal</hi> lines fro<g ref="char:cmbAbbrStroke">̄</g> the quadrate, to wit, A I, N E, which cuts
through each other in the center R. Then the distance A R being taken; and placed
from A to D, from E to B, from E to H, and from I to F, and finally having made
the angles DCB <hi>Isoceles</hi> &amp;c, from the distance D E, ye shall haue the figure <hi>Octoan<g ref="char:EOLhyphen"/>gular</hi>
formed into a <hi>tenaille,</hi> whereof all the angles wilbe right, which afterwards
may be made angles of the Bulwarks, when there is accommodation to make a <hi>fort
royall</hi> thereof, &amp; that the distance fro<g ref="char:cmbAbbrStroke">̄</g> angle to angle, be about 80 rod; for if the right
angles should come much neerer then 40 or 50 rod, this would cause an imperfe<g ref="char:EOLhyphen"/>ction,
and such a fortificatio<g ref="char:cmbAbbrStroke">̄</g> cannot be called a fort royall: so that in such a case one
ought to take advise, and consider well, whither it were not better, to leaue such a
fortification in the former estate; then to alter it, because the circuit of such a place,
will not be worth the time, labour &amp; expe<g ref="char:cmbAbbrStroke">̄</g>ce, in regard the Bulwarks wilbe too litle,
the lines too short, and too weake to worke their effects: but if so be, the distance of
the angles be capable to beare a perfect fortification the<g ref="char:cmbAbbrStroke">̄</g> ye maye make the plott as
followeth. Let the line EG, be drawne, and divided into three equall parts at the
poincts 1, 2. Then 2 of those parts shalbe placed vpon H, G, as here at S. and from
the points S. &amp; I. of the distances I, G, and G, S, shalbe made the arches, which cutt
through one another at the point 4; by vvhich the line G. 4. being drawne, where
the same cutteth the line H, I, at the point 2, wilbe I, 2; the face, or the skirt of the
Bulwarke. For to haue its flanke, the angle XVI must be made of 40 degrees by the
line XV, passing through the point 2, &amp; 5, and cutting the Diagonall G, R, in the
point X, vvhich shalbe the center of the Bulwarke through vvhich point X a para<g ref="char:EOLhyphen"/>lell
line, being drawne to the line I Gas X X, and from the point 2, drawing a per<g ref="char:EOLhyphen"/>pendicular
line vpon it, as Y 2, ye shall haue all the essentiall parts of this fortifica<g ref="char:EOLhyphen"/>tion,
namely, the line I 2. shalbe the face, 2 Y the flanke: Y X the line of the gorge:
YT the curtaine; &amp; ZI the line of defe<g ref="char:cmbAbbrStroke">̄</g>se flanking. According to vvhich the angles
G, E, C, A, &amp;c. being placed, ye haue the distance I. 2. and vpon the distance I, X,
one may make the plot of such a fortification, vvhich was first built into a tenaille,
as appeareth by the two Bulwarks I &amp; G, &amp; nothing altered in all this fortification;
but the lines of the tenailles 2, H. 5 placed vpon ST, TY, &amp; 2 Y, vvhich in all are
but a litle longer then the abouesaid 2, H, &amp; H, 5. Now the Earth vvhich is taken
from the space T 5, H 2, Y, is sufficient to supply that deffect. The moate vvhich
was made before, if it be broad and deepe enough, ye may leaue it as it was with<g ref="char:EOLhyphen"/>out
makeing any alteration in it. And because that in such places, noe false<g ref="char:EOLhyphen"/>brayes
cann be made, but with great expence; in regard they are made on the out<g ref="char:EOLhyphen"/>side
of the ramparts: and therefore one must make on the other side of the moate a
good covert way, according to our former plots, that your men maye giue the bet<g ref="char:EOLhyphen"/>ter
<pb n="4" facs="tcp:1568:29"/>
resistance to the assaillants. Moreover one maye (as appeareth by the figure
87 from 5 to H) make a good parapet, which shall run downe slooping about some
20, or 24 foote thick, and betweene H &amp; 5 some traverses, rising one aboue an
other, to lodge conveniently behinde them your musketiers, which maye giue fire
vpon the passage to the moate, yea, ye maye make these traverses in such a manner
that they maye easely plant two peeces of ordinance vpon them, that with them
one maye beate vpon, and breake the Ennemies gallerie, when he shall offer to putt
it into the moate, as also to defend the breach, when the assaulters shall attempt any
thing vpon one of the Bulwarks, which maye be done not onely with the said pee<g ref="char:EOLhyphen"/>ces:
but also by the continuall shooting of the muskettiers lodged in the said tra<g ref="char:EOLhyphen"/>verses,
which would doe great spoile &amp; could hardly be entred, because the breach,
having noe false bray vnder the bulwarke (as there can be none here) would make it
more vnentrable, then if there were one. For the Earth of the rampart tumbling
downe into the moate (which is deepe, would cause in my judgment the entrance
to be more troublesome, then if there were a false bray; seing an Ennemy should be
forced with great difficulty, danger, and losse of time, to damme and fill vp the said
moate, which is one of the chiefest observations of an Ennemy besieged, to gaine
time, and to hinder and forslow his Ennemies approches, wherevnto me thinkes
one ought most diligently to endeavour.</p>
                  <p>If one finds this manner of cutting off, good, which neverthelesse I will leaue to
the judgment of Captaines experienced in the art militaire: it is manifest, that this
fortification with a <hi>tenaille</hi> will be changed but a very litle, by the addition of Bul<g ref="char:EOLhyphen"/>warks,
and so of lesse expence: for the Ramparts 5. H. 2. ought to be made low, to
the heigth required, and diminished to the thicknesse of 20 or 24 foote: so that all
maye be done without any great losse, &amp; time. But if the moats be so deepe, that
one cannot from the flanke 5 see the botome of them, being dry, or else cannot dis<g ref="char:EOLhyphen"/>couver
the superficies of the water (if there bea<gap reason="illegible" resp="#TECH" extent="2 letters">
                        <desc>••</desc>
                     </gap>y) and that by the hindrance of
the said Earth, or parrapet 5. H, 2. It were in vaine to fortifie it, seing reason re<g ref="char:EOLhyphen"/>quires,
that it should be slighted: otherwise I see noe cause, that it ought to be taken
away. For to beleeue, that the said Earth might giue some advantage to the Be<g ref="char:EOLhyphen"/>siegers,
that being passed over the moate, they might haue the better accesse to
lodge in the said place: the same maye be said aswell of a false braye, which never<g ref="char:EOLhyphen"/>thelesse
is approued of the most expert Captaines; It is not likely then, that the
said Earth can cause any dammage, which might cause this to be left vndone.</p>
               </div>
            </div>
            <div type="section">
               <head>To fortifie a Quadrilatera irregular in the forme
of a trapeze.</head>
               <div type="subsection">
                  <head>Figure. 86.</head>
                  <p>LEt the <hi>Trapezoide</hi> (A fortresse of vnequall sides) be A B C D, where of the
sides A D are 69 rod, D C 45, CB 40, BA, 46: and the angle B 108 degrees
(and consequently C. 109: 10. D 71: 52, and A. 70: 50, and that ye would
fortifie the same into a quadrangle.</p>
                  <p>To doe this, let there be described two Bulwarks vpon the angles B, C, the one
being the angle of the <hi>Pentagone,</hi> and the other C approching, all in proportio<g ref="char:EOLhyphen"/>ning
the gorges, flanks, and faces according to the distance BC, saying by rule of
three, if 56, 88 the <hi>Polygone</hi> interiour in the tables, giues the face 24, what will 40 rod
giue, the side of the <hi>Polygone</hi> given B, C? the like doe with the flanke, gorge and
<pb n="5" facs="tcp:1568:29"/>
second flanke, according to which Dimensions afterward the said bulwarkes
FGHIK, &amp; LMNHE. are described.</p>
                  <p>And as the distance AD is two great, to describe two Bulwarkes vpon the an<g ref="char:EOLhyphen"/>gles
A, D, which may defend themselues, because this distance exceedeth our
rules giuen heretofore, and the angles too litle: ye shall make or ordaine two Bul<g ref="char:EOLhyphen"/>warkes,
as is seene in this figure, to wit, when as the said distance AD is great
enough, otherwise, ye must make but one Bulwarke, as we will shew you hereafter.
But in this exemple, the flankes of the abouesaid Bulwarks 1. 2. 3. 4. shalbe made
perpendicular lines vpon AD. and so farre lengthned from the angles AD, that
there be meanes to defend the said flanks 1. 2. 3. 4. so that indeed the two Bulwarks
abouesaid, are but in effect as Demy-Bulwarks; whereof their angles 1. 3. make 70.
degrees, and are defended from one side of the curtaine, as a <hi>Pentagone</hi> is defended,
and from the other sides, are the flanks of the said Curtaines 2. A &amp; 4. D defended:
so that the flanks 1. 2. &amp; 3. 4. are also sufficient to defend the two lengths A. 2. &amp; 4. D.
&amp; forasmuch as it is to be doubted, that the neerer one approches to the abouesaid
flanks of the said angles A &amp; D. that they wilbe in the most danger to be ruined: It
wilbe good, to draw back these flanks of the said angles, at the least some 400. foote,
that they maye not be beaten downe with Canon; on the otherside, ye must take
heede that the flankes 1. 2. &amp; 3. 4. be not made too great, nor too farre assunder
from the said angles A. &amp; D. that the lines of defence coming out of the curtaine be
made in the same sort, as the defenses of the <hi>Pentagone</hi> are, as is seene vpon the cur<g ref="char:EOLhyphen"/>taine
B. C. And as the distance A. D. is in this exemple but 69 rod makeing there
in 2 Bulwarks: it followeth necessarily, that the distances 2 A: 4. D. also the flanks,
and the faces of the said Bulwarks be much more lesse, then our former plate<g ref="char:EOLhyphen"/>formes,
will beare: in such sort, that the parts A 2 &amp; 4. D. are but 15 rod, &amp; the flanks
2. 1. &amp; 4 3, onely ten rod; because that otherwise the line of defense cannot come
out of the curtaine F. G. as here from the point O, which of necessity must be
made to defend the face K, 3. Afterward the face 3 K. being made 12 rod, the flanks
K. G. and V, F, wilbe about 7 rod, from the side C. D. ye shall draw a paralell of 10
rod, and the instrument being opened of 70 degrees, it must be moued so much,
that the line of defense M. T. maye come a litle out of the curtaine E P: the
flank P Q. being made equall to E H. ye haue the demy Bulwark P. Q. M N. The
like is to be done vpon the side A. B. and so this place wilbe fortifyed, according to
our intention, and in the same manner, as the figure 86 demonstrateth: and though
the Bulwarkes be very small: notwithstanding by this meanes the angles A, &amp; D,
wilbe well preserued; and the one will defend the other directly. And when as the
distances C. D. are but 45 rod: one maye in some wise from the flanke defend the
angle D. But when the flanke is noe more then 6 9/10 rod, one ought rather to make
the <hi>demy Bulvvarke</hi> P. Q. M. N, having the flanke N M. 10 rod, which is more capa<g ref="char:EOLhyphen"/>ble
to defend N. D. then is E. H. yet with this caveat, that the distance N D be not
too litle: for then by reason of the thicknesse of the parapet, it will be impossible
to discouver N D. if the demy-Bulwarke P Q. M. N. be not made lower then the
curtaine C. D. and in so doing such an inconveniency maye be prevented: the
like is to be vnderstood of the Bulwarks placed vpon the curtaine A. D.</p>
               </div>
            </div>
            <div type="section">
               <head>An other way.</head>
               <div type="subsection">
                  <head>The 19. Plate, and 88. Figure.</head>
                  <p>NOw in such a fortification, which hath but one simple defense, the angles of
the <hi>tenaille</hi> maye lightly be taken in, because that in the figure 86 N M. &amp; N.
<pb n="6" facs="tcp:1568:30"/>
D. are so short: It were better in my opinion, to fortifie the said figure in this
forme following.</p>
                  <p>Let there be made vpon the longest side the Bulwarke 1, 2, 3, 4, 5, 6, proportioned
according to the lenght A. 6. the halfe of A. D, and of the nature of the <hi>Dodecagone,</hi>
whereof the gullet (which is the distance from the one flanke to the other) ma<g ref="char:EOLhyphen"/>keth
27. 71. and the capitall line drawne from the angle thereof through its center
perpendicular vpon the said line from flank to flanke, called extended, maketh 28.
59. as appeareth by the table here to fore many times repeated, which is the cause
of the obliquitie of the flanks vpon the said curtaine, A D, for seing that the <hi>Dode<g ref="char:EOLhyphen"/>cagone</hi>
hath the angle in the circumference of 150 degrees, the flanks will fall per<g ref="char:EOLhyphen"/>pendicularly
vpon the sides, and consequently the same flanks will make vpon the
said curtaine A, D, an angle of the halfe of the angle of a <hi>Dodecagone,</hi> which is 150
degrees, makeing for euery angle of the flanke 75 degrees, and as much will the
angles A 12, &amp; 45. D make. The rest of the Bulwarke in noe wise changes the
proportion. To knovv then the Capitall line 6, 3. you shall say by the rule of pro<g ref="char:EOLhyphen"/>portion:
If the curtaine interiour and exteriour, vvhich are here alike contay<g ref="char:EOLhyphen"/>ning
70 rod, in a right curtaine giving 28. 59. rod, for the capitall line extended,
vvhat vvil 34 1/2 rod, the length A. 6. giue? that vvhich it vvill bring forth, to vvith 14.
9, is the capitall line, 6, 3. for the face ye shall say: if 70 the side of the <hi>Polygone</hi> interiour
or exteriour in a right curtaine (which are equall) giueth for the face 24, what vvil
the side of the <hi>Polygone</hi> A. 6. 34 1/2 rod, giue? ye shall haue for the face 11, 83 rod, which
being placed from 3 to 4, &amp; from 3 to 2 (first the angles 6. 3. 4. &amp; 6. 3. 2. being made
of 45 degrees, because the vvhole angle 2. 3. 4 makes 90 degrees by Hypothesis) ye
shall sett the transporter vpo<g ref="char:cmbAbbrStroke">̄</g> 15 degrees, and shall make the lines 1. 2 &amp; 4. 5 of such an
inclinatio<g ref="char:cmbAbbrStroke">̄</g>, that shall forme the flanks, according to the proportion required, and by
the same meanes shall be knowne the gullet 1. 5, which may be found likewise by
the former rule of proportion, in saying: if 70 giueth 1385 (the halfe of 27. 71) vvhat
vvill 34 1/2 rod giue for A. 6? that vvhich this rule vvill produce shalbe for 1. 6. or 6. 5.
After the same manner must ye make vp the Bulvvarks, E, F, G, H, I, &amp; S, T, V, W, X.
dessigned in the midst of the sides A, K, &amp; R, P, according to their length. But be<g ref="char:EOLhyphen"/>fore
they are layd out, the tvvo sides A B, &amp; C, D, ought to be lengthened so farre,
that one maye make the angles B, K, L &amp; C, R, P, of 75 degrees, and that the line of
defense O. K. termineth in the curtaine M. Q. and to knovv the length of the fa<g ref="char:EOLhyphen"/>ces
and flanks, the face shalbe made double in the flanke, which is done if ye place
vpon the perpendicular O N, the halfe of the line of Defense O K. as from O to
N. and from the point K, the privie right line N K, being drawne, cutting through
the line C, B, at M, ye shall dravv the line M, L, paralell to N, O, or perpendicular
vpon C, B, and so the flanke L, M, vvilbe the halfe of the face L, K. And thus vve
haue finished the fortification of the abouesaid <hi>Quadrilatere</hi> irregular, vvhich in
my opinion is a better fortification, then the precedent figure 86. because these
Bulvvarks are more capable to defend the angles A, D, K, R, and the flanks of the
said Bulvvarks being dravvne <hi>obliquely,</hi> as they are here, cannot be made into right
angles: in such sort, that they are the better able to resist against the force, vvhich
maye be vsed against them, and yet make a good defense, as the figure 88 plainely
demonstrates.</p>
               </div>
            </div>
            <div type="section">
               <pb n="7" facs="tcp:1568:30"/>
               <head>An other way to make the fortification of such a
place regular.</head>
               <div type="subsection">
                  <head>The 19. Plate and 89. Figure.</head>
                  <p>FIrst of all vve vvil describe the quadrate E F. G H. after such a manner that the
line E F is paralell to A. D. &amp; of the greatnesse of the <hi>poligone</hi> exteriour; in the
follovving table of lengths: dravving the paralell E, F, so, that its distance A, D,
be equall to the distance of the <hi>Polygons,</hi> asvvel interiour as exteriour, to the intent,
that the side of the <hi>Quadrilatere</hi> A, D, may serue for the curtaine. Then the angles
I, F, E, &amp; I, E, F, being made 15 degrees (because the angle interiour flanking is of
15 degrees in the square) ye shal take vpon a scale 5. equall parts &amp; place them
vpon the line F, E, and foure of the same parts vpon the line F, I. from the extremity
(or vtmost end) vvhereof and with the said distances ye shall make two arches,
that shall cutt through one an other at X, drawing from thence a line to F, cutting
through the line, I E, at G. then E, G, wilbe the face of the Bulwarke, which will
haue the like proportion to the curtaine, as 4 to 5. But wee will here after in all the
kinds of Polygones, ordaine the curtaine to the face in proportion as 3 to 2. that is
<hi>sesquilatera,</hi> finding it best, as we haue said before. Afterwards, to haue your flanks
ye must make two perpendicular lines G N. and H K, vpon the side A. D. in such
manner, that the lines G N and H K, shalbe the flanks, and N K the curtaine, which is
part of the side A D. The like ye shall doe with the three other sides, and so by this
meanes this fortification wilbe made <hi>regular,</hi> and <hi>royall,</hi> which will not cost much
more, then the former irregular fortification abouesaid, the benefit whereof sur<g ref="char:EOLhyphen"/>passeth
the others by farre: so that in such like accidents, I am of the opinion, that
such places ought to be made regular, in case that time, and the situation wil per<g ref="char:EOLhyphen"/>mit
it: As for the moates, ramparts, and parapets, they must be made as wee
haue taught in the places of regular fortifications.</p>
               </div>
            </div>
            <div type="section">
               <head>The fortification of a Pentagone irregular.</head>
               <div type="subsection">
                  <head>The 19. Plate and 90. 91 Figures.</head>
                  <p>LEt the <hi>Pentagone</hi> irregular be A, B, C, D, E, which one would haue fortified in
such sort, that the Bulwarks come againe to the angles of the propounded fi<g ref="char:EOLhyphen"/>gure;
To doe this, ye shall first measure the outsides, and the angles, which I
supposeye shall finde to be as they stand here vnderneath.</p>
                  <list>
                     <head>rod</head>
                     <item>A B 57.</item>
                     <item>B C 50.</item>
                     <item>C D 46.</item>
                     <item>D E 56:</item>
                  </list>
                  <list>
                     <head>degrees</head>
                     <item>A 72.</item>
                     <item>B 135.</item>
                     <item>C 111.</item>
                     <item>D 97.</item>
                     <item>E 125.</item>
                     <item>540.</item>
                  </list>
                  <p>And seing the angle A, is lesser then 90 degrees, reason requireth that the said
angle be not fortified; because it would make an angle flanked, lesser then 60 de<g ref="char:EOLhyphen"/>grees,
and flanking greater then 150 degrees, against our former <hi>maximes,</hi> accor<g ref="char:EOLhyphen"/>ding
<pb n="8" facs="tcp:1568:31"/>
to which ye shall make of the same angle A. an angle of the bulwarke, ma<g ref="char:EOLhyphen"/>keing
the angle of the Polygone F. so that the right lines FG, and FI, come to cutt
through the lines lengthned BC, DE, in the points G and I. Vpon the angles
whereof, and according to the proportion of the sides shalbe described the Bul<g ref="char:EOLhyphen"/>warks,
takeing heede, that the angle of the <hi>Polygone</hi> show what forme of a Bul<g ref="char:EOLhyphen"/>warke
one must built vpon, to wit, a <hi>Quadrate,</hi> a <hi>Pentagonall</hi> or an <hi>exagonall,</hi> pro<g ref="char:EOLhyphen"/>portioning
out the parts of such a Bulwarke, according to the least side of the
two, and then the figure wilbe described, according to this present forme: And
seing the side DE (because it hath ben lengthned) is longer, then the propor<g ref="char:EOLhyphen"/>tion
can beare of our regular figurs precedent: It wilbe necessary, that betweene
the two Bulwarks D &amp; E, a Ravelin be made, which is a loose peece, that maye be
defended at leastvvise from the flanks of the abouesaid tvvo Bulvvarks: according
to vvhich flank, the angle of the Raveline shalbe made a litle more open, or closser
as the curtaine is either longe, or short. The faces vvhereof shalbe made of 18
or 20 rod, some times a litle lesser, as the place and situation of the ground requi<g ref="char:EOLhyphen"/>reth.
And to giue you to vnderstand more clearely my intention touching the
fortification of places irregular, vvhereof the angles are noe lesse then 90 degrees,
which is the angle of a <hi>Quadrate,</hi> and that the sides doe not differ much from those
places vvhich are regular: It must be proportioned thus: Suppose that one giueth
me the angle C to be fortified, of vvhich the magnitude is III degrees, vvhich
comes neere the angle of a <hi>Pentagone,</hi> according to vvhich I take the shortest line
of the tvvo BC; &amp; C, D, makeing therevvith the angle B, C, D, vvhich is C. D.
contayning 46 rod, we wil seeke out then in the table of the lengths of our regular
fortifications, the dimensions of a <hi>Pentagone,</hi> and will say by the rule of proportion,
if a Polygone 56, 88 giu<gap reason="illegible" resp="#TECH" extent="2 letters">
                        <desc>••</desc>
                     </gap> the face 24, vvhat vvill then a Polygone of 46 rod giue? ye
shall haue for the face 19. 41 rod. The like ye shall haue for the flanke, and then the
Gorge, where by ye shal finde the said Bulvvarke C. as also all the other parts of this
fortresse <hi>Pentagonall:</hi> holding this for an infallible rule, that the angles of the <hi>Poly<g ref="char:EOLhyphen"/>gone,</hi>
which you would fortifie ought to be at the least right, and in case there be any
angle that hath a lesse opening, then the right, ye must make thereof the angle of a
Bulwarke or else dravve a line (if you cannot lessen the place) vvhich vvill forme an
angle compete<g ref="char:cmbAbbrStroke">̄</g>t to builde a Bulwarke vpon, as appeareth by the 90 figure in the an<g ref="char:EOLhyphen"/>gle
A. Which line you must so husband, that if it be possible it maye be made equall
to that, vvhich shall come to cutt through it, that so yee maye haue a nevv angle,
vvherevpon ye maye make likevvise an other Bulvvarke, euen as the said figure
F, G, C, D, I, demonstrateth, and if the lines exceede by much the length of the
<hi>Polygones</hi> interiour, then ye shall take them for sides of the <hi>Polygones</hi> exteriour, in
tracing out the said fortresses vvithin them, &amp; that according to the kinde of
euery angle F, G, C, D, I, and in so doing your <hi>Pentagone</hi> vvilbe fortified.</p>
               </div>
            </div>
            <div type="section">
               <head>An other way.</head>
               <div type="subsection">
                  <head>The 19 Plate &amp; 91 Figure.</head>
                  <p>LEt the <hi>Pentagone</hi> be A, B, C, D, E, vvhich you desire to fortifie after an other
manner then aboue: for the effecting of this, ye shall prepare the angles of the
Bulvvarks, according to the scale of the figure, that you vvould haue fortified, such
as before ye haue traced out, all separated one from an other, as they are marked
out in the 21 Plate by the numbres 97, 98, 99, 100, 101, vvhich angles shalbe placed
<pb n="9" facs="tcp:1568:31"/>
vpon the angles ofte figure to be fortified, observing wel by what meanes the
said place maye be best made vp &amp; with the least expenses, according to our former
<hi>Maximes,</hi> and to that end, if it be soe that the place be girt about with a wall or
a rampart, and that ye would make as much vse of it, as possible might bee for the
saving of charges the which (though ye help your self with the old fortification) is
alwaies great enough, at the least ye must labour, that the sides of the <hi>Pentagone</hi>
be accommodated betweene the two Bulwarks, to serue as a curtaine, as we haue
done in the figure 91. where wee haue placed in the angle A (which is lesse then
90 degrees) the angle of a <hi>Pentagone,</hi> or else the Bulwarke of a <hi>Pentagone,</hi> that maye
be removed so long till ye shall finde the buy sinesse, and the disposition of the place
required drawing from the center of the said Bulwarke F, two lines, as F, G, &amp; F, I,
serving for curtaines, and meeting with the other two sides of the <hi>Pentagone</hi>
lengthned in the points G, &amp; I. Vpon which angles G, C, D, I, ye shall forme after
our former rule (to wit, according to the angles and the sides) the Bulwarkes
vpon them, and if ye finde, that the sides are somewhat longer, then our precedent
rules approue of, in the midst thereof we will cast vp a good Raveline as wee haue
done here betweene the two Bulwarkes D &amp; H, and take this for a generall rule,
that your Bulwarks ought not to be any further assunder then some 60 rod, or
thereabouts, to wit, that the line of defense <hi>fichant,</hi> be of this length or neere vpon
it. If it be so, it would not be needefull otherwise to make a Raveling, but when
as the said line exceedeth by much the said measure, then is it wholly necessarie,
that the said Raveline be placed in the midst, betweene the two Bulwarkes aboue<g ref="char:EOLhyphen"/>said,
to supply thereby the defect of the said line, &amp; the better to blinde the flanks
which by that great distance would lye very open.</p>
               </div>
            </div>
            <div type="section">
               <head>An other way.</head>
               <div type="subsection">
                  <head>The 20. Plate &amp; 92. Figure.</head>
                  <p>IF the place permits to alter the angles a litle, then the fortification wilbe the
better, as is seene in the <hi>Pentagone</hi> A, B, C, D, E, which is the same with the for<g ref="char:EOLhyphen"/>mer,
where the angles of the Bulwarks are changed, and some faces of them vne<g ref="char:EOLhyphen"/>quall,
and so by this meanes the Bulwarks will not be too farre distant one from an
other, as this present figure 92 demonstrateth. But in such a case ye are constrai<g ref="char:EOLhyphen"/>ned
that the curtaines comes or runns a litle out of the sides of the <hi>Pentagone,</hi> and
sometimes cuts through them, as the same figure sheweth, and seing it were hard
to trace out this figure so without some direction, ye shall make vse (as vve haue
said before in the 19 Plate) of Bulwarks cutt out in pastboord, marked in the 21
Plate, according to the space of the angle, vvhich ye vvould fortifie as vve haue
done heere; for the angle A being 72 degrees, ye shall make vse thereof, then
comming to B, and finding it to be the angle of an <hi>Exagone;</hi> I take the Bulvvarke
of the <hi>Exagone,</hi> and place it at B, turning and removing it so long, till the line of the
<hi>tenaille</hi> comes to cutt through the line AB, as here at O. makeing A, O, and O, F,
equall, that the defense maye be made thereby alike: for I am of the opinion, that
the tvvo faces, flanks, and lines of defense ought to be equall among themselues,
because they must necessarily defend each other alike: seing the defense cannot
be vnequall vvithout diminishing the force of the one or of the other, vvherevnto
ye must take speciall heede, as much as possibly may be, to hinder such an irregula<g ref="char:EOLhyphen"/>ritie,
that the one receiue noe preiudice by the other, and so the faces F, H, and
<pb n="8" facs="tcp:1568:32"/>
                     <gap reason="duplicate" extent="1 page">
                        <desc>〈1 page duplicate〉</desc>
                     </gap>
                     <pb n="9" facs="tcp:1568:32"/>
                     <gap reason="duplicate" extent="1 page">
                        <desc>〈1 page duplicate〉</desc>
                     </gap>
                     <pb n="10" facs="tcp:1568:33"/>
AL. wilbe equall, but FH, wilbe vnequall with FG. the second face of the bul<g ref="char:EOLhyphen"/>warke
H, F, G, and yet so, that the said inequality causeth noe great hindrance to
its forme, and force. For first the face H, F, cannot be made noe longer; in regard
of the distance A, F, which maye not be much augmented, vnlesse the Curtaine
M, N, comes much out of the line B, C. Also the line A, F, cannot be augmented
vnlesse consequently the line, or distance F, C, be not more and more augmented
so that alwaies the same difficultie remaines, to wit, that the Bulwarks F, &amp; I. wilbe
of a greater distance then the Bulwarks F, &amp; A, and thus the distances differing, will
make also differing faces, curtaines, and flanks: for according as the space is great
betweene F, I. so ye must haue more men to defend it, then if the place were lesser.
Now seing this defense cannot be made more commodionsly, then from the faces
of the Bulwarks: It is most certaine that the faces ought to be augmented more
then the former: Yet never the lesse without passing the limits of the former
plots in our regular fortification, vvhich haue their faces about 24 rod, some more
some lesse: but if they be much longer, then the lines of defense vvilbe of such a
large extent, that it vvilbe almost impossible to make any vse and profite of them.
For vvhich reason I haue thought fitting to make the augmentation of the faces
F, G. &amp; K, I, according to the distance F, I, remayning notwithstanding within the
bounds of regular fortification; and within the compasse of the maximes groun<g ref="char:EOLhyphen"/>ded
therevpon, vvritten before. And ye must note besides, that the interiour an<g ref="char:EOLhyphen"/>gle
flanking F, A, L, or A, F, H, must never be lesse then 15 degrees: and obserue also,
that the more open this angle is, the more closser the angle of the <hi>tenaille</hi> vvilbe,
and consequently the better. But ye ought on the other side to take heede, that
the angle F, A, L, being large and open, the line A, F. be not lenghtned to farr from
the bodie of the figure to be fortified: so that herein ye must vse discretion re<g ref="char:EOLhyphen"/>quisite
in such a case, and so accommodate the said bulvvarks cutt out in past<g ref="char:EOLhyphen"/>boord
that the said angles be tolerable, and that on the other side the curtaines be
not too farre distant from the sides of the <hi>Polygone</hi> as B. C. &amp; C. D, and as this figure
represents it to your eye.</p>
               </div>
            </div>
            <div type="section">
               <head>Yet an other way.</head>
               <div type="subsection">
                  <head>The 20. Plate &amp; 93. Figure.</head>
                  <p>IF you are desirous that the flanks of the Bulvvarks B, &amp; C, fall vpon the side of
the <hi>Polygone</hi> B, C, so that the part G, H, maye serue for a curtaine; you must doe
as follovveth, the angle B, A, F, is made of 15 degrees, because that in makeing it
greater, the line FA vvould runne too farre from the place A, B, C, D, E: the<g ref="char:cmbAbbrStroke">̄</g> ye shall
make the line <hi>paralell,</hi> F, G, distant from the line B, C, as farre as the <hi>Polygone</hi> exteri<g ref="char:EOLhyphen"/>our
is distant from the <hi>Polygone</hi> interiour, in the <hi>Pentagone;</hi> because that the an<g ref="char:EOLhyphen"/>gle
G, ought to be <hi>Pentagonall,</hi> and if the line F, G, is shorter, then the <hi>Polygone</hi> exte<g ref="char:EOLhyphen"/>riour
in our table of lengths; ye shall sinde out a proportionable distance, in say<g ref="char:EOLhyphen"/>ing:
If the side of the <hi>Polygone</hi> exteriour 8125. giueth distance to the <hi>Polygones</hi> 1677
vvhat distance vvill FG, giue, that vvhich this rule wil produce shalbe the distance
of the paralells B, C, &amp; F, G, and so consequently the paralell F, G, being made,
from that distance ye haue the thing required, and before ye beginne vvith the
Bulvvarks, it is your best vvay to make the lines GH, HI, &amp; IA, and as the line B,
C. hath serued for a curtaine, the line C, D, maye serue for the most part thereto,
seing that the line GH, is not ordinarily paralell to the side of the <hi>Polygone</hi> irregu<g ref="char:EOLhyphen"/>lar,
<pb n="11" facs="tcp:1568:33"/>
C, D, but the side E, D, maye be accommodated as before: so that one part
of it vvill serue for a curtaine to the two Bulwarks; which shalbe made in the angles
I. &amp; H. so that if the angle D, had not ben so sharpe, and that the line G, H, might
haue bene paralell to E, D, it is evident, that one could haue made vse of C, D,
for the curtaine of the tvvo Bulvvarks, G &amp; H. Or else if the line F, G, might
haue bene somevvhat augmented, the curtaine would haue falne much neerer to
C. D: But seing in this exemple it could be noe longer, of necessity the said cur<g ref="char:EOLhyphen"/>taine
must fall vvithin the inside of the figure <hi>Pentagonall</hi> irregular. Then having
dravvne these your lines A, F, G, H, I vvith all circumspection requisite, to vvit, that
the angle flanking interiour be at the least 15. degrees: ye shall draw out vpon them
the Bulwarks, flanks, and curtaines, in such sort, that the faces &amp; flanks of the Bul<g ref="char:EOLhyphen"/>warks,
vvhich are vpon the one side of the <hi>Polygone,</hi> be alike amonge themselues,
as those vvhich are noted in the 92. Figure, &amp; according to our former rules giuen
in our regular fortifications.</p>
               </div>
            </div>
            <div type="section">
               <head>A way how to fortifie a right Curtaine.</head>
               <div type="subsection">
                  <head>The 20. Plate &amp; 94. Figure.</head>
                  <p>IF it be needefull to fortifie a right Curtaine, vvhereof the angles of the Bul<g ref="char:EOLhyphen"/>warks
are right, ye must doe as followeth. Let there be taken 70 rod, wanting
6 seconds (that is 69. 64. rod) and putt vpon the said curtaine A, E, as
many times as the said curtaine will beare it, as appeareth here by the
points A, B, C, D, E, from vvhich points shall rise the privie perpendi<g ref="char:EOLhyphen"/>culars
A F, B G, C H, D I, &amp; F K the Capitals of 28, 97. rod, and on
each side of the said points A, B, C, D, E, shalbe placed 16, 97. rod, as from A, to L.
and at M, raysing the perpendiculars L, N, and M, O, 12 rod, the flanks 6, 11: then
the lines NF, and FO, being drawne, vvhich vvill make the faces of the Bulwarks,
ye shall haue that which is necessarie for the description of such a Bulwarke, where<g ref="char:EOLhyphen"/>of
the face is 24, rod, the flanke 12. the line of defense fichant 60, 37, and the line of the gorge L, A, 16. 97, rod. The moate maye be made broader, seing that the an<g ref="char:EOLhyphen"/>gle
of the <hi>Tenaille</hi> Z hindreth, that the angle of the flanke T, cannot discover the
angle flanked F: but if the expence vvere not too much (which hapneth vvhen
one makes the moate very deepe) one might to that end cut the part X, Y, Z, and
so this inconveniencie vvould be remedied. For I finde that such Bulwarks are
farre better, then those that are made vpon an angle; because the gorge is very
large; the flank, the face, and the curtaine of a competent measure, and according
to our former rules, to wit, the line of Defense fichant is 60 rod, or thereabouts, the
Curtaine 36, the flank 12, the face 24, and the gorge wel nigh 17, rod, which is much
better, and larger, then in the Bulwarks, that are made vpon some angle. So that
such Bulwarks ought to be preferred before the others, were it not for some other
reason, which makes one change his minde, as for to haue more place, or otherwise.
Novv touching the distance of Bulwarks, or a <hi>Polygone</hi> interiour mentioned of 70
rod vvanting 6 seconds, these 6 seconds are of noe great moment: neverthelesse
one must obserue the dimention as neere as possible maye be: Otherwise one
might say, that the <hi>face</hi> being 24, the curtaine 36, the <hi>flank</hi> 12, rod, and the <hi>angle
flanked</hi> right, that then the <hi>Capitall</hi> wilbe wel nigh 29, <hi>the gorge</hi> 17, the <hi>defense flanking</hi>
41. <hi>the line</hi> of the <hi>Poligone</hi> interiour, or exteriour 70. rod, the formed-flanked is 35
degrees, and 16 minutes.</p>
               </div>
            </div>
            <div type="section">
               <pb n="12" facs="tcp:1568:34"/>
               <head>How to fortifie a Hexagone irregular.</head>
               <div type="subsection">
                  <head>The 21. Plate, &amp; 95, 96. Figure.</head>
                  <p>LEt the figure <hi>Hexagonall</hi> to be fortified, be A, B, C, D, E, F, vvhereof the length
of euery side maketh as many rod, as they are marked out, to vvit AB. 70: BC.
132: CD, 114: DE. 80: EF, 124: &amp; FA, 176 rod. To doe this, ye must take
notice of the angles thereof, and as their greatnesse is ye shall order the angles of
the Bulvvarks, according to their formes. And for as much as the angles A &amp; F,
are but 108, &amp; 110½ degrees, vvhich are the angles of a <hi>Pentagone,</hi> it vvilbe good to
make there the angles of demy bulvvarks, to haue the angles more open, and the
angle of the Tenaille more closser, and consequently better. Vpon the curtaine
FA, shalbe placed tvvo Bulwarks G &amp; H, of a competent greatnesse to the cur<g ref="char:EOLhyphen"/>taines,
proportioning out the <hi>Capitall lines,</hi> the <hi>gorge, flanks</hi> and <hi>faces,</hi> according to
the greatnesse of the<g ref="char:cmbAbbrStroke">̄</g>, &amp; as we haue said before in saying: If 70, (which is the dista<g ref="char:cmbAbbrStroke">̄</g>ce
of each angle, or the center of the Bulvvarks, giues for the Capitall line 28, 97. what
will the distances of the centers of the bulvvarks giue? that vvhich this rule will
produce vvilbe the <hi>Capitall line,</hi> and in the like manner shall ye finde the line of the
<hi>gorge, the flank,</hi> and <hi>the face</hi> of the Bulvvarks H, &amp;, G, the Bulwarke I shalbe made
in the midst of the curtaine M, N. or in the midst of the line E, F, and for asmuch
as the angle E, is of 112. degrees, vvhich comes neere vpon the angle of a <hi>Pentagone</hi>
ye shalbe vpon the foresaid angle E describe the angle of a <hi>Pentagone,</hi> and seing that
the line E, D makes 80 rod, vve vvill make the angles flanking interiour of the
forme of a <hi>Pentagone,</hi> to the end, tha the skirts E, L. and D, O. be equall, as we haue
said before: for seing the Ennemies force betvveene E &amp; D is equall, reason requi<g ref="char:EOLhyphen"/>reth
that the defense thereof be likewise made equall, that by this meanes, ye
maye take away all occasion from an Ennemie to attempt any further place the
most advantagious for him. Now in regard that the distance D. C. exceedeth the
measure, vvhich wee haue spoken of before, to wit, of 114 ½ rod, it vvilbe necessarry
to make the Raveline K, betweene the said angles D, &amp; C, to supply the defect of
the defense: the like maye be made betweene C, B, and the angles of the Bulwarks,
and B, the rest shall be made according to their formes &amp; <hi>the faces, flanks</hi> and <hi>Cur<g ref="char:EOLhyphen"/>taines</hi>
in that forme, as vvee haue said aboue, euen as this figure Hexagonall 95. de<g ref="char:EOLhyphen"/>monstrateth.</p>
               </div>
               <div type="subsection">
                  <head>The 96. Figure.</head>
                  <p>HErein it is requisite to note, that vvhen one is bound to fortifie precisely the
angles of the figure, either interiourly, or exteriourly, ye meete many times
vvith difficulties: to vvit, here are some angles or sides too small, and others too
great; in so much, that this irregularitie maye cause many great defects. Which
maye greatly be remedied, vvhen ye maye haue libertie, to change a litle the an<g ref="char:EOLhyphen"/>gles
of the figure, euen as wee haue done in this 96. figure, in such sort, that the
angle E, being but 112. degrees, which is the angle of a <hi>Pentagone,</hi> makes the angle
of the bulwark S, E, T too much pointed, as when ye would make it on the inside of
the angle E. Therefore, see that ye make the face E, S, vpo<g ref="char:cmbAbbrStroke">̄</g> the side ED, that by this
meanes, ye maye haue the angle S, E, T, broader and more open, drawing the line
E O so, that it be equall to ED, and that the angle O, E, D, be 20 degrees, so that
the curtaine Q. P. comes not too farre into the figure, and that the line of defense
ER, maye come a part of it out thereof, if it be possible, as here to R: for the more
the said line commeth out of the curtaine, it is so much the better, which is, when
the angle O, E, D, is broad and open. But this exemple if this had bene observed
<pb n="13" facs="tcp:1568:34"/>
the Bulwarke L, had bene a great distance from the curtaine C, D, and would haue
made it much longer then it is at this present; Then vpon the point O, shalbe
made the second face of the Bulwarke, W, O, V, &amp; so made that O, W, and O, V,
and ES, are of an equall greatnes, &amp; that the line D, X, be drawne in such a manner,
that the angle Y, Z, 5, be capable to receiue the Bulwark of an <hi>Exagone,</hi> and for the
better attayning to such a structure, ye shall make first vpon the line C, B, the flanke
noted by 4, 5, and the face Z, 5, to the end that CB maye serue for a curtaine,
and so fitted, that it maye almost be equall to the curtaine D. C. Then vpon CB,
ye shall make the Bulwarke I. according to the greatnesse of 4, B. answerable
to the Bulwarks G. H. and seing the angles A &amp; Bare sharpe: ye shall make
these two Demy-Bulwarks, according to our method mentioned in the 18 Plate
and so ye haue finished the thing required.</p>
               </div>
               <div type="subsection">
                  <head>Note.</head>
                  <p>AS we haue fortified this figure on the inside: so ye maye doe the like on the
outside in case the ground will afford it, but we suppose here, that it would be
necessaire to make it in such a sort: in regard that the lengths of the sides require
more the interiour fortification, then the exteriour; whence appeareth, that there
are many vvayes to fortifie places irregular, yea, an infinite number, yet bounded
with these limits, to wit, that the angles of the Bulwarks ought not to be noe fur<g ref="char:EOLhyphen"/>ther
assunder then 80 rod, at least 60. that the angles flanked must not be lesse then
60. degrees. That your line of defense ought not to exceede much aboue 60 rod
for by how much the Bulwarkes haue a second flanke, by so much they are the
better; &amp; the more spacious and larger the flanks and gorg<gap reason="illegible" resp="#TECH" extent="2 letters">
                        <desc>••</desc>
                     </gap> 
                     <gap reason="illegible" resp="#TECH" extent="1 word">
                        <desc>〈◊〉</desc>
                     </gap>, the Bulwarks are
the better for them, according to our former <hi>Maxims</hi> set downe in the end of the
first part, according to which an expert and skillfull Ingenier, will be sure as much
as possibly maye be, to haue all these advantages abouesaid. And for the better
facilitating of what is said aboue, wee haue made here the figures 97, 98, 99, 100,
101, which must be cutt out vpon a pastboord &amp; drawne out vpon the same mea<g ref="char:EOLhyphen"/>sure,
as the plott of the place requireth which is to be fortified, and to fitt them
to the places of the figure, with the greater consideration that possible maye bee,
that he maye follow the rules abouesaid as neere as may be, where vnto these fi<g ref="char:EOLhyphen"/>gures
(in my opinion) are of very great vse: for he may turne, and remoue
them on what side soeuer he will, and after he hath found the most convenient
place then he maye joyne &amp; fasten them together with a litle waxe, that after<g ref="char:EOLhyphen"/>wards
he maye overcast the advantages, and disadvantages, which he is to expect.</p>
               </div>
            </div>
            <div type="section">
               <head>How to fortifie an Irregular place lying vpon
the side of a river.</head>
               <div type="subsection">
                  <head>The 22. Plate &amp; 102. Figure.</head>
                  <p>LEt the forme irregular, which ye would haue<g ref="char:punc">▪</g> be the plate of <hi>Hardervvijck,</hi>
noted by the numbers 1, 2, 3, 4, 5, 6, 7, 8, whereof the extremities (or vtmost
ends) are 1 &amp; 6. touching the Dike A, B, and C, D, which ye desire to fortifie.
To doe this ye must first overweigh, how many bulwarks the circuit, of the same
place will take vp, husbanding them so, that ye must make as few as maye be, be<g ref="char:EOLhyphen"/>cause
they are parts of a fortification, which will cost much, and yet so, that you
must not place them so farre assunder, but that the one bulwark must helpe to de<g ref="char:EOLhyphen"/>fend
the other: for this reason we haue made the line of defense about 60. rod,
<pb n="14" facs="tcp:1568:35"/>
which is a longer distance then is giuen when one is to defend them with the Mus<g ref="char:EOLhyphen"/>kett,
or caliver. The others that must be defended with the Cano<g ref="char:cmbAbbrStroke">̄</g>, maye be 1000 foot
distant one from an other, or there abouts: because at the least, it will carry so farr
over, that of<gap reason="illegible" resp="#TECH" extent="1 letter">
                        <desc>•</desc>
                     </gap>entimes a Canon will carry much further then to the vtmost end of
the line of defense; so that they may hinder the batteries, which are made to beate
downe the flank of the angle: from whence the line of defense is drawne, also ye
make it so that the distance of the said angle vnto the angle of the Bulwark be not
so farre as a Canon beares, but rather shorter: for which reason we haue made it
1000, or a 1200 foote at the most. Now experience hath taught vs, of what litle vse
such a defense is, seing a Canon cannot be vsed with that agility as a musket, and
for some other inconveniences, which happens to ordinance, when they shoote
from aboue downeward. It is in noe wise advisable, to make the Bulwarks so farre
from one an other, and it were better to encrease the charge, then to lett them be
so farre assunder. For to pretend that when the said Bulwarks lye so farr distant,
one from an other one hindreth the spoyling of the Flanks, me thinks this reason is
too weake to take place, seing the continuall defense made with muskettiers hin<g ref="char:EOLhyphen"/>ders
much more Besiegers dessignes then that which is made by Canon shott, be<g ref="char:EOLhyphen"/>cause
that in the interim, while they are a chargeing and makeing readie, the Besie<g ref="char:EOLhyphen"/>gers
may advance much, and at last gett into the moate, the bottome whereof
being filled with fagotts and earth cast into it, makes the way accessible, and being
ones gott ouer, they come presently to make a mine in the bulwarke &amp;, to blow it
vp: but if the Besieged haue good store of ordinance so that they may play conti<g ref="char:EOLhyphen"/>nually
vpon them; then it will foreslow, and hinder them much. But if these
places be so built before, that store of Canon cannot be planted vpon them &amp; that
it is vncertaine, vvhither the time, the lord of the tovvne, and other accidents vvill
permit, to furnish them with so many ordinance, and other necessaries belonging
to Bulwarks: vvhich if they vvere, yet the charge of the said peeces vvould at last
grow so excessiue, that the benefit which one receiue by it, would finally come to
nothing: if the Besiegers should take in that place, considering the losse of their
ordinance, would often times be of a greater value, then the place it selfe; so that
this neede not be obserued; but in cases of great necessitie, and where it concernes
the conservation, or the ruine of a kingdome, or a countrie, and that ye are sure
to be assaulted by a mighty ennemy: which must be beaten off and resisted with
an number of ordinance, muskettiers, and small shott, as the Great <hi>Sultan,</hi> who
commonly comes into the field with two or three hundred thousand men caring
not much for the losse of the liues of this men, in such sort that the space, which is
betweene two Bulwarks, maye be easier taken in, when it is small, then being great,
for the more the said Bulwarks are distant one from an other, the more men ye
must haue to man the space vvhich is betwixt them, which would be a disadvan<g ref="char:EOLhyphen"/>tage
to the Besiegers: But on the other side, these Bulwarks ought not to be so
farre assunder, but that the one maye defend the other, and in such a case I find
it fitting that there be made two, or three <hi>Casemates</hi> in the flanks, vvhich ye may
when as the curtaines are so longe, that they may be made there great and wide
enough, to haue the more places of defense which cannot be so soone ruinated by
a large space, as by a small.</p>
                  <p>According then to these considerations, let vs come now to the fortification of
such a place irregular, situated (as we haue said aboue) vpon the edge of a riuer, and
obserue, that commonly, such places are more longe, then broade, or deepe: be<g ref="char:EOLhyphen"/>cause the greatest part of the Inhabitants seeke to haue the accommodation of
the river, and as ordinarily townes are made after a good part of the house are
<pb n="15" facs="tcp:1568:35"/>
built, by the water side, whence it appeareth manifestly, that such townes are
alwaies more long, then large. Which is the reason that the sides 1, 2, 3, 4, 5. 6. are
more difficult to be fortified, then the others parts thereof, seing the angles 2. &amp; 5
are much lesse, then the others, as ye maye conceiue by this present plott, and
when ye will not goe farre out of the circuit: It is wholly necessarie, that about
the angle 5. ye make a bulwark which being pointed, the angle of the Bulvvark
must be so likewise, as appeareth by the angles of the Bulwarck D, &amp; I. whereof the
faces are about 20 rod, and the flanks 8 rod, accommodating them soe, that asmuch
as possibly maye be the face, or the skirt of them, as O, P, or Q, R, looks directly
towards the dike C, D, to the end, that the said face may haue the more force
against the said dike CD: the like is to be vnderstood also of the Bulwark A, or E: the
other Bulwarks shalbe made as the exigencie of the cause requireth, as is here noted
by the Bulwarks B, C, D, and F, G, H, I, whereof in all this circuit ye finde not one
Bulwarke lesse then the other; But as on the one side the charge is somewhat
lesse, so on the other side the Bulwarks are so farre distant one from an other, that
the defense, which is made from the one bulwark to the other, either with musket,
or calliver, wilbe almost in vaine: in such sort, that the discommodity, vvhich
one shall reape on the one side, wilbe much greater, then the husbanding of it so as
to saue the fortification of an other Bulwarke: Therefore the best way is to make
one Bulwarck more, then to depriue it of its best defense, vvhich maye be made
from the flanks, and so we maye say, that the fortification which is accommodated
vpon the said irregular place, marked with E, F, G, H, &amp; I. is better, then that which
is marked with the letters A, B, C, D, because that the lines of defense in this are
much more greater: for which one ought to take diligent advise that he giues him<g ref="char:EOLhyphen"/>selfe
noe disadvantage, for an Ennemy vvho vvill employ all his knowledge &amp;
industrie thereto vvill giue him enough to doe, so that he needs not giue himselfe
any: in such sorte, that this observation is absolutely necessarie. The Bulvvarks then
ought to be so large and capable, as that they maye lodge vvithin them a suffi<g ref="char:EOLhyphen"/>cient
number of Muskettiers, to defend the space, betvveene the tvvo Bul<g ref="char:EOLhyphen"/>warks.
For if the said Bulwarks be too farre assunder, ye must then defend a large
space with as many men, as you would doe a litle, which notwithstanding is
against the order of defense; whereby it appeareth, how requisite it is to obserue
therein a good proportion, to the end, that the expence, time, and labour maye be
answerable to the benefit and profit which one ought to receiue from it. More<g ref="char:EOLhyphen"/>over
the said Bulwarke ought to be made so large, that they maye the better resist
(with a body of pikes and muskettiers lodged in the said Bulwark) at that time,
when as an Ennemie shall giue an Assault vpon it, and seeks to take it in, and by
that meanes such Bulwarks maye be better cutt off, then those that are small, as
wee shall discourse more at large hereafter when wee come to treate of <hi>cuttingh
off:</hi> as well in generall as in particular and so reserue this discourse to its due place;
to the end, wee maye speake more particularly of the fortification of this place
irregular, which I rather choose (to make the Bulwark, I, the stronger) that the
side of the <hi>Polygone</hi> were drawne towards the point C. for the preventing of the
smalnesse of the angle, 5. which causeth the smallnesse of the angles P &amp; R. for with<g ref="char:EOLhyphen"/>out
all question it is better to draw the said line, then to leaue the plate, as it is at
this present, to the intent, the inconveniency abouesaid maye be avoyded; but
ere ye doe this, ye must consider, if the line so drawne, be capable to defend well
the face of the Bulwarke Q. R. which then would fall back almost vpon the an<g ref="char:EOLhyphen"/>gle,
5. so that one might thereby gaine a Bulwark, and the defense would be much
better then before: for otherwise, it were better that the Bulwark should remaine,
<pb n="16" facs="tcp:1568:36"/>
as litle as it is, then to make it large, and open without defence. Moreouer if
the Dike C, D, haue any passable way without it towards the riuer side, it vvere
dangerous to make the said rampart against it, and much better to leaue the vvall
5, 6, as it was, and to make the fortification according to this draught, then to make
it as is abouesaid: vnlesse ye intend to take away the dike, and in stead thereof make
a sufficient wall to resist the vvater, as the vvall S, T, extending the same from T to D.
But seing experience hath showne, vvhat danger there is to take avvay an ancient,
solid, and a setled dike, almost grovvne permanent, to build in the place thereof a
heape of stones or bricks of sufficient strenght to stop the violence of the vvater,
one ought to consider maturely, vvhither it vvere not better to fortifie the plaine,
vvhich is here our question, according to our former rules, then to hazard the
drovvning of all the Countrie, to the dishonour of the Ingenier, vvho gaue his ad<g ref="char:EOLhyphen"/>vise
for such a change, to the dammage and hurt of the Inhabitants, asvvel of the
tovvne it selfe as of the countrie, yea, by endangering the subversion of many hou<g ref="char:EOLhyphen"/>ses,
villages, together vvith the ruine of man and beast. Which an Ingenier of a
sound judgment ought wel to consider &amp; not lightly giue consent to such an
alteration, vnlesse it be in a case of extremity, or else in consideration of a very great
advantage, vvhich one might receiue thereby.</p>
                  <p>If the vvall ST be much raised, as it often hapneth there vvere the countrie lies
lowe, and the rivers flovve high, that one cannot well defend from the curtaine the
face R. It were good to make the Bulwarck H, Y, Z which is 9. &amp; 10. 11. A, and the
Demy V, X, <gap reason="illegible" resp="#TECH" extent="1 letter">
                        <desc>•</desc>
                     </gap>, which would lessen somewhat the circuit of the towne; but would
hinder much the former inconveniency, and the charge would be lesser: for as
then there would be but foure Bulwarcks, vvhich vvould haue the lines of defense
capable, and able to defend the same Bulwarks, and so the Bulwark O, P, or Q. R,
would not come so neere the Dike C, D, which being wholly commaunded by the
said Dike, the force vvilbe lesser: for the small distance betvveene Q, and C, or
from T, to R, vvould cause the Besiegers to make that Bulwarke continually in<g ref="char:EOLhyphen"/>effectuall,
as vvell by Canon as Muskets, as by casting in of firevvorks into it,
vvhich could not be done, if this bulvvark stood backvvard as here H, Y, &amp; Z
doe, and yet is neere enough to defend well the face X, <gap reason="illegible" resp="#TECH" extent="1 letter">
                        <desc>•</desc>
                     </gap>, as also the moate: euen
as this forme demonstrateth, marked vvith the double blinde lines, 12, 9, 10, 11, A.</p>
                  <p>That vvhich we haue spoken of the side 5. 6 maye be said also of the side 1, 2. But
if the defense of the Bulvvarck E, be better then of the Bulvvark F, reason requi<g ref="char:EOLhyphen"/>reth,
that it be left so, vvithout altering the said Bulvvark E, by takeing diligent
heede, of the advantages, and disadvantages, vvhich the site of the place maye
bring to such accidents as may fall out, according to which ye must order &amp; acco<g ref="char:cmbAbbrStroke">̄</g>
                     <g ref="char:EOLhyphen"/>modate
the Bulvvark: for most often the seate is that part, vvhich ought most of
all to be had in consideration, not onely in this figure, but also in all others vvhat<g ref="char:EOLhyphen"/>soeuer
they bee, either regular, or irregular.</p>
               </div>
               <div type="subsection">
                  <head>Note.</head>
                  <p>THat in maritimate places, such as are situated by a riuer side, where the banks,
or d<gap reason="illegible" resp="#TECH" extent="1 letter">
                        <desc>•</desc>
                     </gap>kes, come to touch, ye must drawe them in such a manner that the skirt
S, 6. maye be as farre distant as possibly maye be from the extremity, or vtmost end
6, that the said space S. 6, maye help to defend the furthest part of the said Dike.
D, C.</p>
               </div>
            </div>
            <div type="section">
               <pb n="17" facs="tcp:1568:36"/>
               <head>How to fortifie a place situated by a river side, where it is necessarie
to make also some fortification on the other side of the
water opposite to it.</head>
               <div type="subsection">
                  <head>The 23. Plate, &amp; 103. Figure.</head>
                  <p>LEt the tovvne irregular be A, B, C, D, E, F, G, &amp; H, having many other oblique
cornes, as well interiour as exteriour, situated vpon the side of a large river,
about some 200, or 300, foote broad &amp; that the side M, N, ofte said towne (as it is
ordinary) is in noe vvise fortified; vvhich place you are desirous to make stronge,
and capable of resistance. To doe this ye must first dravve the lines FE, DB. so
that they fall not into the old moate, but that there be left space enough to make a
rampart therevpon, on the outside vvhereof ye shall trace out your Bulvvarks, ac<g ref="char:EOLhyphen"/>cording
to our precedent rules: so that the lines of defense doe not much exceede
aboue 60 rod, vvhich is within a musket short (as vve haue often times said) to the
end, that the one Bulvvarke maye helpe to defend the other, as the art of defense
requireth, vvithout makeing many angles, or sides, as much as possibly may bee, to
saue charges: because it is certaine, that the Bulvvarks, vvhich are made vpon a
right curtaine, are stronger then those that are made vpon angles: for seing (as
vvee haue said at the first) that the figures of many sides are better to be fortified,
then those vvhich haue fevver: for as the quantity of the sides diminish, so also
the greatnesse of their angles diminish, vvhich aftervvard cause the greatnesse of
the angles of the <hi>tenailles,</hi> or Flankers: and the more the same angle flanking is
open, the lesse is it capable of flanking; contrarievvise, the more the said angle of
the <hi>tenaille</hi> is pointed, it hath alvvaies bene found the better: so that this is without
all dispute. According to vvhich; seing that the greatnesse of the angle of the
<hi>Polygone</hi> begetteth the smallnesse of the angle flanking, &amp; that the, more open the
angle is the neerer it comes to a 180. degrees (vvhich make tvvo right angles) it is
manifest then, that Bulvvarks made vpon tvvo right angles (makeing a continued
line) are better, then those vvhich are made vpon some angle lesser then the tvvo
right angles are, and hereby vvee haue sufficiently proued the goodnesse of those
Bulwarks, vvhich are made vpon right lines, which is the cause (as I beleeue) that
a great Mathematician consumed his time wholly in this point, by maintayning
that all fortifications, aswell great as small ought to be made in a square-forme: but
seing that the Bulwarks towards the 4 angles by this meanes become lesse forcible
then the others, as the figures A and B, demonstrate in the 23, Plate: me thinks,
this ought to be taken into consideration. Whither it were not better, to make a
Fortresse, whereof the Bulwarks and the lines of defense be of a like force, then to
make them as aboue. For it is impossible, that one should make a fortresse stronger
in one place, but ye must diminish the strength thereof in an other place, to wit,
as the common proverb is, one ought to cutt his coate according to his cloath; But
when the situation of the place, and the <hi>avenues</hi> thereof be such, that one maye be
assured of the resistance, which maye be made better here then there, reason then
requireth that in such a case, one must make such an <hi>avenue</hi> stronger, by dimi<g ref="char:EOLhyphen"/>nishing
the strength of an other, which is not so subject to be attempted as the
former is: For the site of a place sometimes will require this irregularity. But when
as it falls out in a plaine field, it is reason that the strength thereof be also regular, so
then in such a case one cannot take any advantage in one place more then a<gap reason="illegible" resp="#TECH" extent="1 letter">
                        <desc>•</desc>
                     </gap>
other,
without hurting, and weakning of an other, which one ought maturely to
<pb n="18" facs="tcp:1568:37"/>
consider, and not yeeld easely therevnto vvithout good and pregnant reasons.
And seing these Countries, which lye lowe, and are subject to invndations &amp; over<g ref="char:EOLhyphen"/>flowings,
the rivers are commonly bounded in vvith Banks and Dikes, for the pre<g ref="char:EOLhyphen"/>venting
of such inconveniencies and the preservation of the Inhabitants from an
vtter subversion. These dikes coming to touch both the one and the other part
of the said tovvnes (as here in the points H, &amp; A.) vvhich sometimes are separa<g ref="char:EOLhyphen"/>ted
from the said towne by a vvall, vvhich goes from A, to N. and from M, to H,
vvhich in the Figure C is called a <hi>Doudan</hi> made in the forme of an Asses back, nar<g ref="char:EOLhyphen"/>row
in the midst, and bending downwards on both sides, vvhich is made ouer a
moate (to stop the vvater, vvhich othervvise vvould breake into the land) is
called by those of these countries a <hi>Beer</hi> that is, a Beare; in regard of the strength,
vvhich makes it almost inviolable. Therefore the <hi>Basis,</hi> or foundation of such a
worke, is layd first with a grate of beames of timber, locked one into an other with
squared beames bound fast together; vpon vvhich the vvall is built: these beames
and piles vvhich are driuen in and layd in this groundvvorke are some 8, 10, or 12,
foote long: according to the depth of the riuer; and about 7, 8, 9, or 10, ynches
thick, lying tvvo or three foote distance one from an other, vvhich also ought to
be in length answerable to the depth of the vvater. Sometimes these <hi>Beares</hi> are
made vvholly of timber, and are lyned vvith huge thick oaken plancks, betvveene
them closse together, and are much longer then the former; because the vpper
ends must stand of much aboue the vvater, as ye thinke the vvater can rise in win<g ref="char:EOLhyphen"/>ter,
and on both sides of these piles, you shall laye tvvo great beames or bands of
timber, the one at the endes of the piles, and the other in the midst, betvveene the
bottome, and the vpper end of them, fastned together vvith yron bolts (vvhich
are as thick as these piles) and passing through these piles, and then ye shall line
them with good stronge oaken boords, in joyning them as closse together as possi<g ref="char:EOLhyphen"/>ble
maye bee, that they maye keepe out the water the better, and last the longer.
Now if ye resolue to make noe such separation, but to let the banck or dike stand;
then it wilbe good to cutt and pare it as narrow as you can, to keepe an Ennemy
from coming vpo<g ref="char:cmbAbbrStroke">̄</g> it with many men in front, or to hinder his approches the better
on that side. I am of the opinion also, that ye ought to make the line C, B. &amp; F,
G. about 300, foote longe, that one might giue the more fire vpon an Ennemy,
both at his falling on, and going off; but when there is noe fortification made on
the other side of the riuer, it were much better that the dike did not stand against
the point A; but that it were made neerer to the inside of the towne, that one
might the better offend the approches made on the outside thereof, to wit, to<g ref="char:EOLhyphen"/>wards
the river, as is showne in the former Figure and 22 Plate: but if the other
side of the riner lying opposite to the towne, ought to be fortified, (for the reasons
abouesaid) then it matters not greatly: seing one maye sufficiently offend the
Approches on that side: and because the cutting off would be chargeable, if it be
made in a <hi>circular forme</hi> (me thinks) the best course is to draw the right line, O, P
and the two others O, Y, and P. K: so that O Y, and P. K. maye be of the length of
one of the sides of an <hi>Octogone,</hi> or thereabouts, that the Bulwarks, O &amp; P. maye be
well defended from the curtaines, and that the Bulwarke also on the other side,
maye likewise helpe to defend the curtaines: then betweene O and P. according
to their distance maye be made the Bulwarks Q. and R, but seing the distances E,
F. and B, D. are too longe to be defended from the Bulwarks D, &amp; E. ye must
make the two Bulwarks S, T. whereof the faces are 16 rod, the flanks 8 rod, &amp; the
faces of the other Bulwarks are each of them 20 rod, or thereabouts: which distance
is capable to lodge men enough in it, to defend it, and if neede requires, to make
<pb n="19" facs="tcp:1568:37"/>
also therein some speciall cuttings off, as wee shall declare vnto you hereafter.</p>
                  <p>Note that if the lines D, B, F, &amp; E, be too short to make the Bulwarks vpon
them, marked S, &amp; T: it is apparant ye maye then lengthen the sides so farre, that
the said Bulwarks maye (with conveniency) be made vpon them, then ye must
drawe a line paralell to D, E. but if the distance D, B. and E, F. be so, that the angles
B &amp; F maye be defended well from the Bulwarks E and D. as then you neede not
make the said Bulwarks S. and T: seing that from the others, namely. E &amp; D, they
maye be sufficiently defended. And for asmuch as I finde these fortifications to
be best, which come neerest to the demensions giuen before in our regular forti<g ref="char:EOLhyphen"/>fications,
termed <hi>Royall,</hi> whereof the faces, flankes, defences, and gorges (which are
the principall parts of a fortification) are all capable to worke well their effects:
one ought to haue a speciall care aboue all things, to fitt the sides of places to be
fortified, that they maye be almost of the length of <hi>Polygones,</hi> which ye shall finde
in the table of our demensions, described hereafter, euen as wee haue done here in
lengthning the sides B, D, and F, E. till that X, Z be equall to the lengthened sides
B, X. and F, Z. Vpon which, and in the very midst of them, ye shall make three
Bulwarks and vpon the angles X, and Z, the two Bulwarks X, and Z, which are
the Bulwarks of an <hi>Hexagone,</hi> because the angels X, and Z, make each of them 120
degrees, which are (indeed) the angles of an <hi>Hexagone</hi> as appeareth by the said
table, in which are taken all the demensions belonging to an <hi>Hexagone,</hi> aswell the
gorges, flanks, as the faces: and from them, ye maye drawe out your Bulwarkes X
and Z, abouesaid, which wilbe more <hi>royall,</hi> then the two Bulwarks D, and E, yea or
of the others likewise: so that this fortification will not cost much more then the
former, makeing the place more spacious, the circuit almost alike, and the Bul<g ref="char:EOLhyphen"/>warks
much better: and in my opinion, this forme of fortification ought to be
preferred farre aboue the other, considering what advantages one maye gett
thereby. But if one were tyed to the forme B, D, E, F, whereof the two sides B, D.
and F, E, are longer then 90 rod, which is a distance too farre for the Bulwarks D,
&amp; E. to help to defend the angles F and B, one should be driuen to make the two
Bulwarks S. T. lesser then the former, whereof the faces would make but 16, rod,
which notwithstanding wilbe capable to defend the abouesaid Angles F, and B.</p>
                  <p>Note that if the place requires, that ye must lengthen the line O, P. as farr as the
riue side I, K. lyeth, then ye maye drawe from the furthest end of the Bul<g ref="char:EOLhyphen"/>warks
O, and P. right lines to I, and K, and then ye maye make two Bulwarks vpon
the said lines, one vpon the right curtaine, by which ye shall make your fortifi<g ref="char:EOLhyphen"/>cation
the stronger, because the angles of the Bulwarks O, P. wilbe so much the
larger, and the defense of the other Bulwarks vpon the said lines the better.</p>
               </div>
            </div>
            <div type="section">
               <head>How to fortifie a place situated by the sea-side, and to make
therevnto a commodious Haven.</head>
               <div type="subsection">
                  <head>The 23 &amp; 24. Plates, and the 103. &amp; 104. Figures.</head>
                  <p>PLaces lying by the sea-side, haue oftentimes neede of a good hauen, aswell to
harbour such shipping, as maye daylie come into them, as also to keepe them
safe from an Ennemy, and from the violence of stormes and tempests: And for
asmuch as these places must resist the injuries of winde, weather, and the raging
billowes of the sea, as is said, they ought to be soundly fortified and kept: and be<g ref="char:EOLhyphen"/>cause
Earth alone will not be sufficient to withstand the beating of the sea vpon
them in regard of the fragility thereof, which would be washed away, such places
<pb n="20" facs="tcp:1568:38"/>
ought to be made with <hi>free-stone,</hi> or at least wise with good brick, with driving in
on the outside of the wall next the sea-side many stronge piles, by clasping them
together in this manner following:</p>
                  <p>FIrst some 300. foote, or thereabouts from the wall A, B. (marked figure 104)
ye must driue in a rowe of piles a foote thick in <hi>diameter,</hi> and some 8. or 10. foote
longe, as the 24, Plate, and the 104, &amp; 105, Figures demonstrate. These must be
pointed with yron, and sharpned well, that they maye enter the better into the
ground, and must be driven in with an Engine called in Dutch a <hi>Hye,</hi> hauing a block
plated with yron of some 1000, or 1200; pound weight, which falls downe vpon
the heads of these piles, and is drawne vp with a pullie, with some 40. men, euen as
one should ring at a Bell, foure or fiue of them guiding the <hi>Hye,</hi> that the logg maye
fall downe perpendicular just vpon the head of the pile, that they driue in, and
shall driue it in so deepe, till the head thereof be but three, or foure foote aboue the
ground.</p>
                  <p>After ye haue driuen in the first row, some sixe or seuen foote distance from it, ye
must driue in the second rovv, whereof the vpper ends must be aboue the ground,
more then the first row by a foote and a halfe, or at the most two foote: so that
your second row ought to be foure foote and a half, or at the most sixe foote. Then
about sixe foote neerer the towne, ye must driue in a third row of piles, the heads
being a foote or two foote aboue the second row, as the site and the necessity of
the place shall require, continuing so till you come to the very wall of the towne
against which you shall laye bedds made of Bundles of brush (as the figures 106.
and 107. showes) wherevpon ye shall lay heauie stones 3, or 4, <hi>cubicall</hi> foote thick,
to make them lye firme and fast betweene the rowes, which are also driven in with
stakes, or sparrs as the figure 105, &amp; 106, demonstrate. All these rowes must be so
ordered by a masons line, that they may lye euen from the one side to the other,
and to keepe them closse together, ye must haue long sparrs sawne in two, through
which you must boore holes, and driue yron, or wooden pinnes through the said
rowes, and clinch them well, and (as is said) remember, that the piles of the second
row are longer then the first, and the third rovv longer then the second, and so
consequently the rest must bee. Then euery ninth foote, ye must laye crosse sparrs
of the same weight as the first, or thereabouts, which ye joyne to euery row by
driving great yron bolts through the piles and the other sparrs, vvhich lye crosse
the other rowes, makeing through them <hi>quadrangular chambers,</hi> vvhich you lay
bundles of brush into in makeing them lye fast together by diving in of stakes and
in laying first a bedd of brush, and then a row of flint stones vpon it, and your brush
must be hedged, and wreathed together, to make it lye the faster and firmer, that
it maye not be loosened, and driven away, with the violence of the vvater, as ye
maye see in the 24. Plate, and the 106. &amp; 107. Figures.</p>
                  <p>This being done, then ye shall laye the <hi>Basis</hi> of the wall first by driving in piles into
the Earth and foundation, if it be moorish, as the 108. figure sheweth. But if your
foundation be good and firme, then ye shall make (as it were) but a <hi>Gridiron</hi> of
wood vpon it, as the figure 109 noteth, these sparrs vvherewith you make it, must
be some 8, 10, or 12, foote longe (according to the ponderosity of the wall, and as
your foundation shall require) and some 10, or 12, ynches thick. Vpon this you
shall beginn to lay your wall about 10, or 12, foote thick, allowing to euery foote of
<hi>t<gap reason="illegible" resp="#TECH" extent="1 letter">
                           <desc>•</desc>
                        </gap>lude,</hi> two foote of height, laying within it spurrs of wood from 16, to 20, foote, and
foure or fiue foote longe, making them lye levell with the wall (as the art of <hi>Masonrie</hi>
teacheth) and some sixe foote distant one from an other: then by this meanes, ye
<pb n="21" facs="tcp:1568:38"/>
shall binde the vaults one to an other, and the two vaults shalbe comprehended by
the third, to make them last the longer, and wilbe the better able to resist the waues
of the sea, when the winde makes them beate against the vvall, filling the vaults,
vvhich are betvveene the spurrs vvith good Earth, stamped and beaten in wel, that
there be noe holes, or hollovvnesse betvveene them: In doeing so ye make your
hauen as the greatnesse of the place vvill beare it, and according to the number of
ships, vvhich you meane to harbour in it. The mouth or entrance into the hauen
being some 20, 24, or 30, foote broade, according to the greatnesse or smallnesse of
the ships that are to come into it. Ye maye make the hauen, either of a round
forme, ovall, square, or (a <hi>paralellogramma</hi>) vvith a right angle, as the site of the place
and the accommodation of the Inhabitants shall require. On the outside of the
mouth, ye shall driue in the breath of 100, or 150. foote rovves of piles, from one end
to the other, as abouesaid, which maye serue for the comming in, and going out, to
make the entrance of the ships the more easie, as appeareth by the 104, figure: in
vvhich the paralell lines AB, CE, EF, FG, GH, HR, are rovves of piles filled and
stuffed vvith bundles of brush, and stones vpon them, as vvee haue noted in the
106. figure, where ye must obserue, that the vvall of the figure 106, vvhich ye see
on the outside, is the same as the figure 110 is, vvhich ye see on the inside. The
rest of the tovvne, asvvell that part of it vvhich lies next the sea, as the other side
maye be fortified in that forme as the plate of <hi>Ostend</hi> demonstrates, vvhich is the
next follovving, makeing your fortification soe, that the faces of the Bulvvarks
maye be about 100 foote or more, to hinder the better the approches, vvhich an
Ennemie maye make on that side, seing those places wilbe the weakest, in regard of
the banks, and shelues of sand noted Z, which are commonly in such places: There<g ref="char:EOLhyphen"/>fore
one is constrained to raise the ramparts higher in such places, then the order
of fortifying vvel requireth, that one maye lye the safer vnder couvert from an en<g ref="char:EOLhyphen"/>nemies
batterie. If the vtmost ends A, and B, be of a rock, ye must cutt them off
as much as possible maye be, both in the height, and in the bredth, as the commo<g ref="char:EOLhyphen"/>diousnesse
and the site of the place vvill afford: if it be sandie it vvilbe safer to
deepen the moate euen vp to ones neck, in case the countrie circumjacent vvil
permit it, as ye maye see here in the 25. Plate of Ostend &amp; the Figure 112, in vvhich
towne hath bin practized &amp; found out as many inventions to make it invincible as
in any tovvne of our age, and noe lesse inventions tryed on the ennemies part to
gaine it, vvhich they did at last after three yeares, three months and odd daies
siege, vsing all manner of industrie, in makeing their the approches, galleries, mines,
and other inventions, which the art of man could invent them. Neither was there
lesse art vsed on the defensiue part to make them get it by ynches meale as appea<g ref="char:EOLhyphen"/>red
by the generall, and particular cuttings off, counter mines, counter-batteries,
and other vvorkes vvhich vvere made in such sort, that this place vvas as it vvere a
schoole, and a studdie of euells, to bring men to thier ends, vvhere nothing vvas
either omitted, or forgotten, but many strange engines invented, aswell to stop
the mouths of the channels and hauens, as for the approches towards the tovvne,
as this 25. Plate demonstrateth, where ye shall see the approches made with ga<g ref="char:EOLhyphen"/>bions,
or great Bassketts filled with Earth &amp; woolsacks to stop the water breaches
and at other times sand-baggs: for the reason why they made vse rather of these
things, then to advance their workes and by approches &amp; sapps (whereof we in<g ref="char:EOLhyphen"/>tend
to treate hereafter) was because the countrie lay low, and was sometimes
overflowne with water, in regard of the ebbing and flowing of the sea, entring in,
and going out betweene the mouths A &amp; B.</p>
               </div>
            </div>
            <div type="section">
               <pb n="22" facs="tcp:1568:39"/>
               <head>Of some loose Peeces in regular fortresses.</head>
               <div type="subsection">
                  <head>The 23. Plate &amp; 111. Figure.</head>
                  <p>MAny men are of the opinion, that in places of great importance to
forslow and hinder an ennemy the more, one ought on the outside of a
place regular to make diverse works separated from the bodie of it, by that
meanes to giue the Assaillant the more worke, that he cannot come to advance his
dessigne. And though I dare not approue much of them; in regard of the great
expence which they will cost, and the number of men necessary to keepe and
defend them: yet I will giue here some instruction to those, that are desirous to
make such works, Let AB then be the side of a <hi>Decagone,</hi> vpon which ye shall make
by the helpe of our former table the Bulwarks Q, T, Y, Z, S, R, then ye shall drawe
the paralell lines G, I, H, and HP, for the faces of the Bulwarks of the distance of
some 10, or 12, rod, for the bredth of the moate, and for to finde the angle L, M, N,
ye shall draw the angle of the shoulder passing through the angle of the Bulwarke
R. the line RM, the like ye shall doe vvith the line Q, M, then ye shall make the
faces LM, MN, of 24 rod, from whence ye shall dravv the flanks LK, &amp; NO,
equall to the flanks TY, or SZ, and finally the lines IK, &amp; OP, ansvvering to
the points Q, and R. &amp; for the better keeping of them ye shall make the Ravelins
VWX, vvhereof the angle W comes noe further from the center of the fortresse
then the angle M, dravving from the angle of the flanke O, a line vnto the point
W, and the face V, W, of the length M N. Ye maye make likewise the flanks 3, 4,
&amp; V 6, but then the defenses of the Bulvvarks vvilbe of noe vse, because they blinde
the faces LM, &amp; MN, on the outside of these loose vvorks, ye maye make a good
moate vvith a couvert vvay, and a parapet, as the figure 111 demonstrateth. These
vvorks vvill cost much, and ye must haue a great many men to guard them: so that
one ought to be vvell advised ere he vndertakes the makeing of them: and to see
if the meanes of the Lord of the place, his forces, and time will permitt it: more
ouer he ought to consider that the entrances in and commings out of the said
loose peeces, are dangerous and difficult, and therefore hardly to be relieued.</p>
               </div>
            </div>
            <div type="section">
               <head>How to make a fortresse, where two great riuers are not aboue 15,
or 18, rod assunder one from an other, or thereabouts.</head>
               <div type="subsection">
                  <head>The 26. Plate &amp; 113. Figure.</head>
                  <p>THat you maye the better vnderstand my intention and meaning I haue
thought good to make vse of the Plate of S. Andrews Fort made by the <hi>Admi<g ref="char:EOLhyphen"/>rant
of Arragon,</hi> that yeare as he withdrew his army from the siege of <hi>Bommel,</hi> which
is a Fort situated in <hi>Bommelsvvard,</hi> betweene these two great rivers called the <hi>Mase,</hi>
and the <hi>VVhale,</hi> haueing noe great distance betweene A &amp; C, then some 80, rod,
being the narrovvst place of the whole Iland, and consequently stronge by nature
and situation, having but two <hi>avenues,</hi> or passages to come to it, to wit, one vpon
the left side from <hi>Rossems</hi> field, and the other on the right side from <hi>Hervverden</hi>
situated at the vtmost end of <hi>Bommelsvvard,</hi> opposite against the <hi>Vorne,</hi> or <hi>Nassaus
Fort,</hi> which is a fortresse, with fiue Bulwarks, and well made. Now to ordaine
the said place, ye must first resolue if ye intend to make a Covert-Way vvith a
<pb n="23" facs="tcp:1568:39"/>
parapet round about the place, and with all suppose that the circuit interiour
(though litle enough) is able to lodge in it as many men, as ye meane to leaue there
in garnison, according to which ye shall first make the angles of the <hi>Tenailles</hi> A, B, C,
and according to the course of the sides of both the rivers ye shall make the tvvo
angles of the Tenailles A, I, H, &amp; C, R, D, and finally the other two D, E, F, &amp; F, G, H,
&amp;c. which angles, because the sides of the rivers runs somewhat slanting towards
one of the sides, they cannot be equall, which causeth the inequality of the sides of
the Tenailles, and consequently of this fortresse <hi>Pentagonall:</hi> then ye shall make of
the distance of some 6, or 7 rod, paralell lines to the lines A, B, C, R, D, which vvill
forme the bredth of the parapet for the covert way: then on the inside ye shall
make a paralell of some 18 foote for the bredth of the covert way, the bredth of
the moate about some 7 rod, which lines of the moate towards the interiour side,
make the angles M, N, O, P, Q, which shalbe the angles of the Bulwarks, the faces,
flanks, and curtaines whereof often ye shall finde rules giuen in our former rules
of the 10 Plate, and so ye shall haue the thing required. The Heads K, and L, are
made to breake the course of the water, which otherwise would spoile the fortifi<g ref="char:EOLhyphen"/>cation
and especially the angles D, &amp; H, of the parapet of the covert vvay, vvhich
having a good moate of some 12 rod, as this Plate sheweth, it wil make a great
resistance.</p>
               </div>
               <div type="subsection">
                  <head>Note.</head>
                  <p>THat this figure for want of takeing heede, is turnd the wrong way: so that the
angle F ought to be with all that which lies on that side on the left hand; and
the angles A, B, C, with all that is on the left hand towards the right hand, the cause
is, because they cutt the Plate as the Figure was marked.</p>
               </div>
            </div>
            <div type="section">
               <head>How a Generall shall come to besiege a Towne.</head>
               <p>WE haue for a time bene minded to describe the order, which an Army
ought to keepe in marching towards the place, which one intends to besiege,
where it is necessarie to treate of militarie motions, of the order of the march,
vvhich every souldier ought to obserue in particular, as also of the Companies,
Regiments, and of the vvhole Army, but seing I haue noe leisure to doe it at this
present, I will reserue that for the next Edition to make this and other things in
some places more compleate. And now vvee vvill beginn to treate of quarters,
and lodgings of euery companie, then of euery regiment, and finally of the whole
army, as also of their entrenchments, and the things vvhich depends thereon, that
we maye afterward come to the approches, sapps, mines, galleries and interiour
cuttings off, as followeth.</p>
               <div type="subsection">
                  <head>The 27, 28, Plates, and 114, &amp; 115. Figures.</head>
                  <p>WHen as an Armie is come within 3, or 4, miles of the place, where it shall
quarter. The Quartermaster Generall goes out before with some 50, 80, or
100 horse, that he maye the better view the ground &amp; place where the army shall
encampe, before they come thither, which ought (if it be possible) to be neere
vnto some river side, nor farre from a good wood, and where there is good store of
forrage, asvvell for horse as stravv &amp; wood for hutting and makeing of paillasses.
The said Quartermaster Generall then having viewed all the grounds &amp; chosen
the best, shall drawe a draught of it, and show it to the Generall of the Army, which
<pb n="24" facs="tcp:1568:40"/>
being done and resolued, he shall then goe in all diligence with all the other parti<g ref="char:EOLhyphen"/>cular
Quartermasters of the Regiments, to giue them their ground and quarter:
which shalbe 300 foote deepe, and the bredth according to the number of the
Companies and the greatnesse of the Regiments. After this the particular Quar<g ref="char:EOLhyphen"/>termasters
shall line &amp; draw out their quarters to distribute them according to the
number and qualities of the companies, giuing to euery companie, which is about
110 or 120, two rowes of Hutts, to these which are 150, 3, rowes, &amp; to 200, foure
rowes, and all running downe in right lines from the front, so that the said rowes
are all paralels one to another, each row being 200 foote deepe, and 8 broad<g ref="char:punc">▪</g> The
Sutlars Hutts must be 20 foote deepe, and 60, foote is allowed for the Captaines
Hutt, and enbowring, and the streete betweene the Hutts, and the said lodging are
100 foote, which with the 200 foote for the souldiers Hutts, makes in all 300 foote,
which is the depth, that a regiment must haue, either for Horse, or foote, &amp; other
quarters: and the rowes betweene them, which make the streets &amp; back streets,
shall be likewise &amp; must be 8 foote: which rowes in their depth shalbe divided into 25
parts<g ref="char:punc">▪</g> so that euery of them make 8 foote for the depth of the said Hutts, and the
bredth being likewise 8 foote, each hutt will containe 64 foote square, for euery
two souldiers, that they maye the better lye together and help each other, as well
in makeing vp their Hutts as before and afterward. And for the better accom<g ref="char:EOLhyphen"/>modation
of the Army the Quartermaster Generall ought to take care, that the
Quarter (as is said) be neere vnto some river, wood, and fourrage, and to labour
that the said Quarter be provided with all things necessarie, and quartred as neere
the Towne besieged, as possibly maye bee, to the end the trenches and approches
maye be relieued, as soone as maye be in case of necessity: And seing oftentimes
there happenssome mischiefe amonge the Hutts, which joyne closse together,
when as fire takes them, so that one row, a whole streete, yea sometimes the vvhole
Quarter is burnt before any order can be taken, they shall build them I, <gap reason="illegible" resp="#TECH" extent="1 letter">
                        <desc>•</desc>
                     </gap>, or 3, foote
assunder one from another, to the end one maye pull them downe quickly without
endangering the other, and so by this meanes maye be kept from fyring. From the
front of the Hutts, ye shall Kitspit 10, foote, where ye shall se<gap reason="illegible" resp="#TECH" extent="1 letter">
                        <desc>•</desc>
                     </gap>t vp your crutches for
your piks and armes, and beyond them some 16, or 10, foote further is the distance
betweene the Captaines lodging and the armes being 28, 30, or 32, foote deepe, and
24, or 28, broad in the front. But when the streets betweene the Hutts, and the
Captaines lodging are but 20 foote, then the said lodging is to be 40 foote deepe.
Beyond the Captaines Hutts there is a place of 200, or 250, foote or thereabouts
called the Alarm place to drawe in armes, at the end whereof the line of entrench<g ref="char:EOLhyphen"/>ment
for the Campe runneth, to wit, haueing a ditch some 6, 7, or 8, foote broade,
5, or 6, foote deepe, and the parapet of the same bredth and height, to wit, the basis
of 8, foote, and 4, or 5, foote high: but when it is 6 foote high, then ye must make a
foote banke which must be a foote high, and 2, or 3, foote broad, that ye maye
the better discouver the fields about ye. Behinde the Regiment are the sutlars
Hutts or tents, leaving a street betweene them and the souldiers Hutts of 20 foote
and the bredth of their hutts are likewise 20, foote. Betweene the sutlars and the
other Regiments there is a streete, or a separation made betweene regiment and
regiment about 40, 50, yea 100, foote as the ground will afford it, and the great<g ref="char:EOLhyphen"/>nesse
of the said Regiments. And the better to accommodate euery Regiment,
the Quartermaster Generall ought to know the greatnesse, and the number of the
companies of them. And so, as is said, ye haue the depth of a regiment, which is 300,
foote, in which are contained the Captaines, and the sutlars lodgings with their
streets, and the distances betweene them and the souldiers.</p>
                  <p>
                     <pb n="25" facs="tcp:1568:40"/>
The Colonell is lodged in the midst of his regiment leaving a streete of 80 foote,
as the Figures 114 &amp; 115 demonstrate, to lodge therein his traine and the officers
of his Regiment, as the Quartermaster, the Marshall, Chirurgian, &amp; others. In the
midst of the quarter the Generall of the Armie is lodged some 600 foote, or more
from the entrenchment, according to the greatnesse of the Campe, and the ac<g ref="char:EOLhyphen"/>commodation
of the place, having a front of some 700 foote more or lesse, as his
traine is either great or small, being 300 foote deepe (as all the other quarters are)
having in the midst, where they sett his pavillions, an overture of 400 foote broad,
for to discouver by sight the place where they drawe vp in armes. Behinde him
the master of the ordinance is quartered, having his quarter 300 foote deepe, and
700 foote in front more or lesse according as his traine is great. For in case that
the carrages and victualls must be lodged within the compasse of the Campe, it is
very necessarie the said place be larger, that it maye containe them all, and as then
ye maye separate the traine of victuals from the traine of the ordinance. Upon
the right hand are lodged sometimes the other Officers belonging to the armie,
leaving betweene them and the rest, a streete of some 40, 50, or 60, foote, that they
maye freely passe through it with the ammunition of warre, to the place where
they are to be vsed: and then round about it are the foote lodged, according to
the former order, being as is said) 300 foote deepe with the Captaines tents, and
the sutlars hutts, and the bredth of the front according to the greatnesse of the re<g ref="char:EOLhyphen"/>giment,
euery companie of 100 men takeing vp 32 foote with the streets, which
are betweene the hutts, and before them is the place of Armes 200, or 250 foote,
to draw vp by companies into their divisions and battallions, to wit, euery compa<g ref="char:EOLhyphen"/>nie
directly before his Captaines lodging &amp; their to draw vp in parado &amp; to
receiue the commaunds of the Generall of the Army. In the front of the hutts
the Lieutenants and Ensignes are lodged, and the Sergants &amp; Gentlemen of the
armes in the reere next the <gap reason="illegible" resp="#TECH" extent="1 word">
                        <desc>〈◊〉</desc>
                     </gap>, they maye presently prevent any disorders
which might fall out. And for the more easie vnderstanding of what is said aboue
in the 27 Plate, &amp; 114 Figure, wee haue here represented the quarter of an English
Regiment consisting of 20 Companies, as they were quartered (as I remember) be<g ref="char:EOLhyphen"/>fore
<hi>Gulick</hi> whereof the Plate K, L, M, N, O, P, is the Colonels lodging, Q, R, S, T,
his Kitchin &amp; Stable, H, I, the Captaines lodgings 24 foote broad, and 30, or 32,
foote deepe. G, the crutches or the forks against which the Pikes and Muskets
stand. CA, the souldiers Hutts, whereof euery file containeth 25, and 8 foote in
depth and bredth, the goings out are betweene the two files; but the foure vtmost
hutts of euery companie haue their goings out towards the streets, CH, &amp; AE,
which is the Sutlars streete, E F, are the Sutlars Hutts, which are made either large
or straight, as euery ones occasion shall require, leaving a litle space betvveene
them, for their more freedome, and for the danger of fyring. The scale which is
herevnto annexed will shew you the true measures.</p>
               </div>
               <div type="subsection">
                  <head>The 28, Plate, and 115. Figure.</head>
                  <p>THe 28, Plate is the draught of a Colonels lodging, in a larger forme, that one
may the better vnderstant the order, which is here to be obserued. 9, is his
tent, &amp; his gallerie to goe into his tent, 5, 6, is his sleeping tent, where it maye be
so ordered, which would not be amisse, that there be a gallery from 5, to 6, to goe in
and out prively from one tent to an other, 7, is a hutt for the Colonels servants: 11
his Kitchin, 10 &amp; 12 are also Hutts, 13 in his Stable, 14 and 15 are the officers Hutts of
the Regiment, and all other officers, which are not ranged vnder any Companie,
<pb n="26" facs="tcp:1568:41"/>
are lodged in this streete, behinde the Colonell. 2, &amp; 3, are the Captaines tents, 16,
&amp; 17, the places where they draw vp in armes, 4, 4, 4, 4. are the souldiers Hutts, the
side KL, from the colonels lodging is a right line with the Captaines lodgings,
not to hinder the sight of the front of the Hutts. But as for mee I thinke it were
more convenient that the front of the Captaines lodgings, were made in a right
line euen with the front of the Colonell, to wit, that 2 &amp; 3, and M, &amp; N, maye be in a
right line, whereby the alarme place should be of an equall bredth.</p>
               </div>
               <div type="subsection">
                  <head>The 29. Plate &amp; 121. Figure.</head>
                  <p>IF necessitie requires to quarter the Horse vvith the foote within the circuit of
one line, which is vsually done when one feares an Ennemie to fall on vpon many
sides, and that there is noe other accommodation for the horse without the campe,
otherwise it were much better to lodge the Horse out of the foote quarter, for the
avoyding of many inconveniences, which the foote might receiue by them, and
which the Horsemen might receiue from the foote, leaving betweene the Sutlars
Hutts of the foote and them, a streete of 40, 50, yea sometimes of 100 foote accor<g ref="char:EOLhyphen"/>ding
as the place will afford it, having their front towards the place of armes, &amp;
euery regiment quartred together, being commonly 8 troupes in a regiment allo<g ref="char:EOLhyphen"/>wing
to euery hutt 10 foote in length: betweene them and their Horse there is a
space, or a streete giuen them of 5, or 6, foote broad, to lay in their fourrage: then
betweene the same 5 foote, &amp; the great streetes (which are ordinarily 20 foote) is
made a space of 10 foote for their horse, allowing to euery horse 4 foote in bredth.
The great streets are made as is said of 20 foote, the narrow of 8, or 12, foote, that
they maye the better come one to an other, and to joyne together in case of neces<g ref="char:EOLhyphen"/>sity,
and for other considerations, in such wise that in one row, which is 200, foote
in depth, there are three such streetes of 8 or 12 foote: For otherwise the rowes,
because of the great spaces, which such Hutts will take vp, makes the entrance into
them vneasie, and thus the lodging of a troupe of horse of 70 foote, to wit, the lod<g ref="char:EOLhyphen"/>ging
of the Horsmen 110 foote &amp; 2 small streets 5 foote, the streete betweene the
Horse 20 foote, and twise 10 foote for their horses, which makes in all 70 foote: and
when as the streets betweene the Horse-heads and the Hutts shalbe sixe foote,
the front wilbe 72 foote, of which bredth the Captaines lodging is made, leaving
betweene him and his souldiers Hutts a streete of 18 or 20 foote, and the depth 40,
or 42, foote, and seing the depth of the Horsemens Hutts is 200 foote, as the Hutts
of the foote are and 40 the Captaines, with the streete of 20 foote, makes 60, foote
and 40 for the Sutlars streete, it is manifest then that the quarter for the Horse (as
is said) wilbe 300 foote deepe. Then betweene the companies there is a streete of
20 foote, which if necessity requires maye be made narrower. And seing the Cap<g ref="char:EOLhyphen"/>taine
which commandeth a Regiment of 4 or eight troupes, hath noe greater
traine then an other horse Captaine hath, he is lodged noe otherwise then they are;
neither takes vp any more ground, onely the honorablest place is giuen him, be<g ref="char:EOLhyphen"/>cause
he commandeth for that time: but the army being in garnison, hath noe com<g ref="char:EOLhyphen"/>maund
ouer them.</p>
                  <p>In the front of these Hutts are lodged the Lieutenants and Corners, and next
vnto the sutlars streete are the Hutts of the Corporals and Quartermaster, that
they maye vpon any occasion be ready to prevent any disorders that maye
happen. Beseides the ordinary Sutlars, which vse to follow the Regiments, there
are a great number of other Sutlars and Tradsmen, which follow the Armie, as
Drapers, Marchants and others, which are all lodged in a quarter by themselues a
<pb n="27" facs="tcp:1568:41"/>
part; to the end that those which haue neede of any thing, maye goe presently thi<g ref="char:EOLhyphen"/>ther
and buy it. And this is the reason why all of one profession are lodged in a
streete, or two rowes, leaving a large streete betweene the principall Tradsmen of
some 200 foote or there abouts, which shall serue as a Markett-place, vvhere all
things necessary aswell for the sustentation of man as other wares are daylie sould,
which are brought thither by the Countrie men, and others. The other rowes
which are of an other profession, haue their streetes more narrow as 15, 18, or 20,
foote. Those which are of a contrarie profession haue a streete of some 30, or 40,
foote, as the place will afford it, and the quality of the marchants. The Butchers
quarter is ordinarily made in one of the furthest corners of the Campe, because of
the garbages, and panches of the Beasts they kill, which they are toburie without
the quarter in a hole or a ditch digged for that purpose some 200 foote without
the entrenchment, that noe euill sent or filthy stinke maye cause the infection of
the aire. If the Campe be quartered by a riuer-side (which one must seeke to doe
if it be possible) it will not onely be able to furnish the souldiers with water for their
accommodation, and to preserue them on that side from an ennemie, but also
wilbe good for the shipping, which maye bring the<g ref="char:cmbAbbrStroke">̄</g> all manner of victuals and com<g ref="char:EOLhyphen"/>modities
as experience hath showne in diverse sieges, which if it so fals out then the
market place is made by the river side in the same place where they should draw
in armes being 300 foote broad or there abouts, without having any Hutts in all
this plaine, that they maye not hinder the entrances in, and going out of the shipps,
from whence they fetch all things necessarie, aswell for amunition, as for victuals,
and the Marchants, Sutlars, and Mercers and others following the army are lodged
on this side, and separated by streetes some 12, 15, or 18, foote, according to the site
and commodiousnesse of the place, as wee haue said aboue.</p>
                  <p>In the quarter of the Master of the ordinance is <gap reason="illegible" resp="#TECH" extent="1 word">
                        <desc>〈◊〉</desc>
                     </gap> lodged the Commissarie
of the Victuals, and his Conductours, as wee haue said before, and that when as his
magazine is not very great in respect of the place, as also all the other officers, over
which the said master of the ordinance commandeth, as the Commissarie of the
ordinance, his Conductours, the Maister gunner, and Gentlemen of the ordinance
and the ordinary Gunners. The Commissarie of the Amunition<g ref="char:punc">▪</g> with his traine,
as Carpenters, Smiths, Watermen, Pioniers, Miners, and others, all of them being
lodged by themselues, that one maye finde their lodgings the better. The Master
of the ordinance hath commonly the gentlemen of the ordinance lodged within
his circuit, that they maye be ready vpon any occasion to receiue his commaunds,
and to execute them as the Generall of the Armie shall thinke good, as appeareth
by the Figure 122: In which A is the place ordayned for the master of the ordi<g ref="char:EOLhyphen"/>nance:
B, the quarter of the Inginiers, the Commis and his conductours, C, the
quarter of the Carpenters, belonging to the Armie. D, The quarter of the Car<g ref="char:EOLhyphen"/>penters
which attends vpon the ordinance: E, the quarter of the saylours follo<g ref="char:EOLhyphen"/>wing
the traine of the ordinance. F, G. the Pioniers quarter. I, is the master Gun<g ref="char:EOLhyphen"/>ners
haueing 100, or 150. Canoniers vnder him, and the Provost marshall of ordi<g ref="char:EOLhyphen"/>nance.
H, The Miners quarter. L, the Magazine for the amunition, and his Com<g ref="char:EOLhyphen"/>mis:
E, the Magazine for the ordinance; with his Commis, M, N, the Magazine for
the Victuals, and O, a place where the waggons stand: but when they feare noe
ennemie then this place is appointed without the Campe some 200, 300, or 400,
footewithout the entrenchme<g ref="char:cmbAbbrStroke">̄</g>t. But when there is any doubt, or that the waggons
maye giue any hindrance being sett without, they appoint them ordinarily to stand
on that side by the master of the ordinance his quarter, where also the Waggon
master is lodged, with his lieutenant and their conductours, the better to keepe all
<pb n="28" facs="tcp:1568:42"/>
things in good order, and that they maye presently be employed vpon any occa<g ref="char:EOLhyphen"/>sion,
when the waggon-master shall call for them, and for the better vnderstanding
hereof wee haue made here a draught of it, as appeareth by the Figure 122.</p>
               </div>
               <div type="subsection">
                  <head>Figure 123.</head>
                  <p>HAving described the particular lodgings, and quarters of euery companie of a
Regiment as well of foote as of Horse and other officers, it will be requisite
to represent them together in a Generall quarter. And because exemples are of
great vse: I will take first this Figure 123, which was his Excel<g ref="char:punc">▪</g> quarter before Gulick
in the yeare 1611, G is then the quarter and tents of the Generall: I the quarter of
the Master of the; ordinance K the officers of the Armie; L the market place, where
all the tradsmen and marchants stand, which followes the Armie, as we haue said
before. F &amp; H are the French Regiments, namely F, Monsieur Chastillon his Regi<g ref="char:EOLhyphen"/>ment,
H, Monsieur Bethunes. A, the Regiment of Count Ernest of Nassou: B
English companies commaunded by Monsieur Medkercke Lieut. Colonell to Ge<g ref="char:EOLhyphen"/>nerall
Horatius Vere. Care 8, companies of Frizes. E, are 6 Germanie companies.
D the 4 companies of the gards, to which quarters are added the number, which
shew the length, and the bredth of euery quarter in particular, also the length of
the streets, &amp; the greatnesse of the whole quarter in Generall.</p>
               </div>
               <div type="subsection">
                  <head>Figure 124. &amp; 125.</head>
                  <p>ANd because commonly the Captaines, after their souldiers are hutted, build
Hutts in the place, where their tents stood, being warmer, &amp; cooler against
the sunne, and more durable. I thought it not amisse to represent the forme of
them: A, then is the Captaines Hutt, B his Kitchin. C, his stable, D. the place
where his fourrage lies. E, is the streete betweene the Captaines lodging, which is
8 foote. the scale noted by the numbers 124 and 125 will shew the depth and bredth
of the said lodgings, and the largnesse of the streets.</p>
               </div>
               <div type="subsection">
                  <head>Figure 126.</head>
                  <p>THe Figure 126, is a quarter of Horse and foote, whereof A, is the Generalls
lodging. I, the lodging of the master of the ordinance. G, L, F, H, are foure Regi<g ref="char:EOLhyphen"/>ments
of Horse. B, C, D, E, M, N, O, P, are 8 regiments of foote. K the Market place
for the Sutlars; the Halfe squares 1. 2. 3. 4. 5. 6. 7. 8. 9. &amp; 10. are the places of defense,
to hinder the giving on of an Ennemie, whereof euerie face is about 100 foote (as
also in the Figure 123. are the exteriour angles 3, &amp; 4) to the intent that one maye
lodge more men in them to defend the skirt AB, the Overtures 13, 14, 15, &amp; 16, are
the avenues, passages and entrances into the generall quarter: whence it is necessa<g ref="char:EOLhyphen"/>rie,
that a Quartermaster Generall ought to haue true notice of the number and
qualitie of the Regiments &amp; companies, that he maye dispose of them according
as the place and the nature of the ground will afford, and for the better effectua<g ref="char:EOLhyphen"/>ting
of what is said before, it would be good, to draw out a draught of the great<g ref="char:EOLhyphen"/>nesse
of euery Regiment in paper, and aboue it to put the colonels names, to alter
and change them according to the accommodation of the place &amp; the number
and greatnesse of the Regiments, setting them downe in two, three or foure rowes,
or in length if the Entrenchment be by a river-side, lodging the Nations which
cannot agree well together as farre assunder as possibly may be one from an other,
<pb n="29" facs="tcp:1568:42"/>
to prevent mischiefs, quarrels, and other disorders, which maye happen betweene
them. If he quarters the Horse with the foote, the Generall of them, ought to
haue his quarter in the same front as the Generall of the Campe hath, or betweene
the troupes of Horse, being not farre distant from the said Generall, and his front,
and there must be, if it be possible, an overture made of 300. or 400, foote, that one
maye haue the perfect sight of the Generals quarter towards the place of armes,
for to draw in and out. The sutlars and marchants, which follow the Armie ought
to be quartered behinde the Generals quarter, on that side where the master of
the ordinance lies: but the Butchers shambles, as is said before, in one of the cor<g ref="char:EOLhyphen"/>ners
of the campe, or if they be within, to be stricktly commaunded to carry out
their offald and filth out of the Campe, or els to digg vp great holes to cast them
in to them, that by such noysome smells the aire maye not be infected.</p>
               </div>
               <div type="subsection">
                  <head>The 29 Plate, Figures 116, 117, 118, 119, &amp; 120.</head>
                  <p>AT the ende of the said 200, or 250, foote, the entrenchment is kilspitted made
by the souldiers for nothing, euery companie against his owne quarter, if it so
falls out, which entrenchements are (as we haue said some 6, 7, or 8, foote more or
lesse, as necessitie requires. For when one feares an Ennemie, it is needfull that the
entrenchements be made stronger, and greater, them when there is no appearance
to be attempted: in the midst of these entrenchments there maye be made spurrs,
&amp; redoubts on euery side of some 4, 5, or 6, rod, for the better defending of the said
trenches: for from them they maye bed scouvered all alonge, and so by night or
otherwise they maye hinder an vnexpected attempt, being distant one from an
other some 40, or 50 rod, according to the greatnesse of the skirts of the trenches.
The reason why one maketh these square redoubts is, because others cannot be so
soone made, otherwise I should be of the opinion that one ought to make great
flanks, and large skirts, to draw the more men to flancker the<g ref="char:cmbAbbrStroke">̄</g>, and not to entrench
the inside (to wit in the entrenchments of the campe) as appeareth by the en<g ref="char:EOLhyphen"/>trenchment
A B C, Figure 116, which would make a better defense, if one should
assault the squares D, E, F, G. It is true, that when one hath passed the entrench<g ref="char:EOLhyphen"/>ment,
that the space A &amp; C, being open, would be sooner taken in then the square:
but I leaue this to your consideratio<g ref="char:cmbAbbrStroke">̄</g>, if when ye haue lost your trenches, the square
redoubts maye be kept, in regard of their smallnesse and the fewnesse of men that
mans them, to wit, some 25, 30, or 40, men at the most: now for the better preven<g ref="char:EOLhyphen"/>ting
of such a danger, ye maye make the lines, and entrenchments D, F, leaving
onely a gapp open of some 3, or 4, foote, for an entrance in and out vvith a draw<g ref="char:EOLhyphen"/>bridge,
and so this would be as difficult to be taken in as the whole squares; so that
I should rather resolue to make the entrenchment of a Campe with skirts of demy<g ref="char:EOLhyphen"/>squares:
so much the greater on the outside (as is said) without makeing whole
squares, or redoubts. For in so doing the defense would be much better, and the
comming to defend it more commodious and easie. Those which finde the other
manner better maye make vse of it, for my owne part I rather approue of these
Demy-squares. The Entrenchments which are made without the enclossure of
the Campe, as those which enclosse a towne, or for to cutt of the passage of an En<g ref="char:EOLhyphen"/>nemie,
to hinder their Victuals &amp; such like things ought to be made with strongh
redoubts as Prince Maurice did at the siege of the Grave, where the Ennemies
army lay closse by his campe, not daring once to attempt the passage: because of
the strongh entrenchment, which he had made by the said square-redoubts, being
not further distant one from an other then some 50, or 60, rod, and about as much
<pb n="30" facs="tcp:1568:43"/>
also vpon the Entrenchment, which were made (as I haue said) in the forme of
Bulwarks, and within them were the said squares, which in my opinion are excee<g ref="char:EOLhyphen"/>ding
good in such entrenchments, which are made without the circuit of the quar<g ref="char:EOLhyphen"/>ter,
especially, vpon the Avenues that they maye lodge in them some 25, or 30 men
to gard them, &amp; to hinder an Ennemies passage, but when one is not resolued to
make the said entrenchments like Bulvvarks, there ought to be made at the least
such square vvorks as the Figures 116, &amp; 117, demonstrate, because they are wholly
enclossed, having but one entrance as narrovv as possibly maye be, being advanta<g ref="char:EOLhyphen"/>gious
asvvell vvithout as vvithin. For as long as the Approches are not much
advanced before, and about the towne, they maye send men vnto them, and occa<g ref="char:EOLhyphen"/>sion
many hindrances, if they be not vvell entrenched: The Figure 117, will giue
vs clearely to vnderstand, that vvhich wee come to speake off, the square D, E, F, G,
being the same of the squares of the Figure 116, which is an entrenchment running
round about the tovvne, vvhich is besieged, and is as farre distant from it at the
least as a muskett can vvell beare, beginning and ending at the entrenchment of
the quarter; DE, is the outside of the Redoubt contayning 4, rod, or 48, foote; the
space marked I, is the talud of the parapet; 2, the superficies thereof; 13, the foot<g ref="char:EOLhyphen"/>banck;
5, the ditch eight foote broade, and 6 foote deepe, as ye maye more plainely
vnderstand by the Figure 118, which is the Profile of the said entrenchment, where<g ref="char:EOLhyphen"/>of
the height, and the bredth are noted here, the bottome of the ditch being 2,
foote vvide, and consequently euery side of the talud is the halfe of the height, or
depth, the foote banke in the basis 3 foote, a foote high, and aboue 2<gap reason="illegible" resp="#TECH" extent="1 letter">
                        <desc>•</desc>
                     </gap> foote. And
there ought to be one the outside of the parapet an edge of some 2, foote, vvhich
vvas forgotten in this Figure 118, but ye maye see it marked in the 120, A, T. And
seing the said squares or Redoubts are chiefly made vpon the <hi>Advenues</hi> and passa<g ref="char:EOLhyphen"/>ges,
to hinder thereby the attempts of an Ennemie, vvhich secks as much as possi<g ref="char:EOLhyphen"/>bly
maye be to keepe a free passage, and entrance into the towne besieged: It is
sometime (for ones better assurance) necessarie to vse the greatest care &amp; perfe<g ref="char:EOLhyphen"/>ction
to hinder him; so that those squares be made like litle Bulwarks, as appeareth
by the Figure 119, and then the sides of these square workes are greater then those
aboue, according to the qualitie of the passage, their curtaines being at the least of
those provisionall Forts some 4, rod, according to vvhich the other parts being
proportioned as the table of our dimensions shevves, the faces F, C, &amp; D, E, 3 2/5 rod,
the flank C, A, 103, rod, and the line of the gorge 1. 22, rod, the Rampartas almost
all other provisionall vvorks are onely made of 6, foote high at the least, and at the
highest 9, or 10 foote, makeing the basis of 14, or 15, foote, and 3, or 4, foote of
height vvith the ordinary taluds, vpon vvhich is made a parapett of 7, or 8, foote
broade, &amp; 5, or 6, foote high, with a footebanke some 3 foote with the taluds, accor<g ref="char:EOLhyphen"/>ding
to the quality of the ground, to wit, sometimes but a foote high, and asmuch
Talude, and otherwhiles but halfe a foote onely, then one supputes hovv vvide the
ditch vvilbe according to the said Rampart, being eueryvvhere 6 foote deepe or
thereabouts: And vvhen one raises the rampart aboue 6 foote, vvhich is vsually
made in provisionall fortresses, vvhereof the curtaine is 5, rod or more; I thinke it
vvere not amisse, to make in the ditch a foote banke afect the fashion of a counter<g ref="char:EOLhyphen"/>scharfe
some; foote, that if neede be the muskettiers maye runn along it, raysing
the parapet thereof aboue the plaine field, as much as the said rampart exceedeth
6 foote in heigth, or somevvhat lesse, as the draught shewes, which vve haue made
thereof marked vvith the number 120, vvhere vve haue raised the parapet 2 foote
higher then the field, as likevvise the edge of the ditch, and cutting the Talud of
the ditch tovvards the same place some 3 foote, makeing together 5, foote, vvith
<pb n="31" facs="tcp:1568:43"/>
the allowance of a litle Talud, as commonly one giues to parapets, to serue as a
parapet to the ditch, and there to be vnder covert, and seing there rests yet three
foote, before ye come to the bottome of the ditch, ye maye make a second foot<g ref="char:EOLhyphen"/>banke,
a foote and a halfe high, that ye maye the better descend from the other to
charge &amp; discharg your muskett, while the other are a giving fire, and for to knovv
the greatnesse of the parapets, and hovv vvide the ditch must be ansvverable to it,
vve vvill make here this calculation thereof follovving.</p>
                  <p>Before vvee come to the supputation of the said profile (Figure 120) vve must
set dovvne 6, in the place of a 5, for the line S, R. To marke out 10, for M, K, &amp; an
O omitted at the interfection of F, H, and of a paralell through E, to B, C.</p>
               </div>
            </div>
            <div type="section">
               <head>A B C D.</head>
               <p>A D, makeing 14. foote, BC, 9 1/2, the summe being multiplyed by C, G, 3, the halfe
vvilbe 35 1/4 for the superficies A B C D.</p>
            </div>
            <div type="section">
               <head>B E F I.</head>
               <p>F, H, 5, being multiplyed by I, H, 1/<gap reason="illegible" resp="#TECH" extent="1 letter">
                     <desc>•</desc>
                  </gap> the halfe of the product vvilbe 1 1/4 for the
triangle F, H, <gap reason="illegible" resp="#TECH" extent="1 letter">
                     <desc>•</desc>
                  </gap>, then F, O, I, multiplying the halfe of O, E, ye shall haue 2, for the
triangle F, O, E. Finally, the summe of O, E, 4. &amp; H, B, 6, multiplyed by 2, the halfe
of O, H, ye shall haue 20, to vvhich add 3 1/4 for the tvvo triangles abouesaid, ye
shall haue 23 1/4 for the superficies of B E F I.</p>
            </div>
            <div type="section">
               <head>L M K, and all the rasing.</head>
               <p>The halfe of 1/4 LM, being multiplyed by M, K, 10, ye shall haue 10, for the triangle
LM, K: to vvhich add A B C D 35 1/4 &amp; B, E, F, I, 23 1/4 there vvill come for all the
rasing 68 1/2, vvhich ought to be equall to that vvhich is voyd, M N O P Q R S T,
but to the end we maye resolue this by the Trapeze M, T, S, R, we will substract
from the Summe abouesaid the two Triangles M N O, 4 1/2, &amp; O P Q, 1 1/<gap reason="illegible" resp="#TECH" extent="1 letter">
                     <desc>•</desc>
                  </gap>, vvhich
make 5 1/<gap reason="illegible" resp="#TECH" extent="1 letter">
                     <desc>•</desc>
                  </gap>, and vvill remayne 62 7/<gap reason="illegible" resp="#TECH" extent="1 letter">
                     <desc>•</desc>
                  </gap> for the trapeze M, T, S, R, which diuided by the
depth which is 6, it will giue 10 23/4<gap reason="illegible" resp="#TECH" extent="1 letter">
                     <desc>•</desc>
                  </gap> the Talud exteriour 6, with the interiour 3, makes
9, the halfe is 4 1/2, vvhich added to 10 23/48 ye shall haue 14 47/48 for T, M, which is very
neere 15 foote, and likewise 4 1/2 substracted from 10 48/23 ye shall haue 5 47/48 for S, R,
(makeing very neere 6) the proofe is that the superficies of M N O P Q R S T,
is 68 1/2 equall to the superficies of the vvhole rasing, the like ye maye doe with all
provisionall fortifications.</p>
               <div type="subsection">
                  <head>The 33 Plate, and 140. Figure.</head>
                  <p>ABout the entrenchment of a Campe, there are made some gapps, avenues,
and passages for men, and waggons to goe out, and in, which haue noe ditches,
or ramparts, some being 6, 7, or 8, foote vvide, as occasion serues, shutt in vvith a
vvodden gate, or Turnepikes made of sparrs some tvvo ynches and a halfe thick in
diameter, and about fiue or six foote high, plated with yron heads at the points, and
having tvvo great Iron nailes driuen through them eight or nine ynches long,
and blund headed on the other side of the thicknesse of an ynch, halfe an ynch,
or thereabouts; they are pointed to driue them in the better into the ground in
two places, to stopp vp the passage, as the 33 Plate, and the 140 Figure shevveth,
<pb n="32" facs="tcp:1568:44"/>
which pikes three or foure rowes of them, must be driven in closse one to another
as high as a mans girdle, vvhich is about 3 foote, or three foote and a halfe, the first
and vtmost rovv must be driven into the ground deeper then the other, and so
the one aboue the other rovv, that they maye not be pulled vp. These are of good
vse also to be driuen in vpon the topp of a breach (as S<hi rend="sup">r</hi>. <hi>Francis Vere</hi> did in <hi>Ostend</hi>)
vvhen an Ennemy is ready to giue an assault, and that one hath not time enough,
to cast vp a breast of Earth vpon it. These and an other Instrument called in
Dutch a <hi>frize Ruyter,</hi> and by vs a <hi>turnepike</hi> (as also your <hi>quadrangular</hi> tanternailes
cast dovvne vpon a breach) are of singular vse, to barrocadoe, and stopp vp places<g ref="char:punc">▪</g>
A Turne-pike is made in this manner follovving:</p>
               </div>
               <div type="subsection">
                  <head>The 33 Plate &amp; 141 Figure.</head>
                  <p>TO make a turne-pike, ye must take a round sparre some 12 or 15 foote longe,
and about 5, or 6, ynches in <hi>diameter,</hi> and boore holes through it in many
places: so that these holes meete not one vvith an other, being boored right one
vnder another, about an ynch in a <hi>sexangular</hi> forme, that the circuit maye be divi<g ref="char:EOLhyphen"/>ded
into three equall parts, and in euery part, ye must boore a hole as is said one vn<g ref="char:EOLhyphen"/>der
an other, that the <hi>demypikes</hi> of sixe foote length, vvell sharpned with yron
heads at both ends, about an ynch or an ynch and a halfe, maye be putt crossvvise
fast through the holes of the sparres 3 or 4, ynches one from an other, euen as the
Figure 141 demonstrateth.</p>
                  <p>These <hi>turne-pikes</hi> are of a very good defense against horsemen, to stopp a passage
into the Campe, to stand at the entrance into a worke, or vpon the gapp of a worke:
They maye be made so that yee maye runne them vpon wheeles, to remoue them
from one place to an other and joyne their <hi>axeltrees</hi> together with pinnes of yron,
so that on a sudden ye maye shutt in the passages vnto an army, and being so joyned
ye cannot remoue the one without the other, so that these turnepikes joyned to<g ref="char:EOLhyphen"/>gether
giues the longer and better resistance. There are other inventions to keepe
out an Ennemie, but having noe leisure now at this time to treate of them,
wee will passe them over, and come to handle of the Approches.</p>
               </div>
            </div>
            <div type="section">
               <head>OF APPROCHES.</head>
               <div type="subsection">
                  <head>The 31, &amp; 32 Plates, and 127. 128. 129. 130. 131. 132. 133. 134. Figures.</head>
                  <p>FOr asmuch as in approches (whereof we intend annon to speake) one must
of necessity vse showels, spades, fire-rakes, pickaxses, mattocks, hatches, bils, and
axses, to giue the more lustre to our buysinesse I haue thought good to describe
them here. And seing <hi>Monsieur Doncker</hi> in his life time Controuler of the fortifi<g ref="char:EOLhyphen"/>cations
in the vnited provinces, and besides at the siege of Gulick Controuler of
the princes of <hi>Brandenburgh</hi> and of <hi>Nieuburgh</hi> their ordinance, a man being very
skillfull in makeing these materials, gaue me the modell of them in that true forme
as ye shall see them represented here to your view in the 31, and 32 Plates, by the
numbers 127, 128. 129. 130. 131. 132. 133. 134. 135. 136. 137. 138. and 139.</p>
                  <p>The Figure 127 is an ammunition spade, whereof the part A B, is a foote high
and A, C, two foote, being in all three foote longe: the point A B, is platted with a
sharpe edge of yron some sixe ynches broad, that ye maye spitt a foote into the
Earth with it.</p>
                  <p>
                     <pb n="33" facs="tcp:1568:44"/>
The 128 Figure is a showell, made more hollow, and some what greater, then a
spade, which cannot be vsed with that nimblenesse, as the former: because of the
great quantity of Earth, which it will take: so that for ordinary vse I should rather
advise one to vse the spade, for those that are not able, and stronge men.</p>
                  <p>The showel 129, hath a plate of yron onely, being fitt to levell, and plaine the
ground, and for this reason (in my opinion) ought to be made longer, then the
other, because it must be vsed with as much strength as the other.</p>
                  <p>The Figure 130 is a pickaxe, well knowne to workemen, vvherewith ye digg vp
a stonie &amp; hard ground, into which a spade or a showell will not enter.</p>
                  <p>The 131 Figure is a Mattock, the head whereof is like an axe made bending, which
is also well knowne, and vsed to digg vp hard and stonie grounds.</p>
                  <p>The 132 Figure is a hatchet, to be vsed with one hand.</p>
                  <p>The 133 Figure is an Axe, to be vsed with both hand:</p>
                  <p>The 134 is a lesse kinde of axe, vsed with both hands not vsuall in these parts.</p>
                  <p>The Figure 135 demonstrated in the 32 Plate, is an amunition wheele-barrow,
which will hold a foote of Earth deepe, and if it be well loaded a foote and a halfe,
which wheele-barrow, as the Figure 136 sheweth, is made of an <hi>i<gap reason="illegible" resp="#TECH" extent="1 letter">
                           <desc>•</desc>
                        </gap>nographick</hi> forme,
contayning 16 ynches in length, and 14, or 15, ynches in bredth, and 7, ynches high,
the boords being made for lightnesse of firre wood; saving the axeltree, and the
handles, which are of other wood some 17, ynches long, but the shorter they are,
the better they are, and that for diverse reasons.</p>
                  <p>The Figure 137 is a bill, to cutt brush and braunches with all, and vsefull for the
makeing of Bavins, and bundles of brush, Gabions, and for other necessary occa<g ref="char:EOLhyphen"/>sions,
aswell in hutting, as to be vsed in trenches &amp; works.</p>
                  <p>The 138 Figure is a kind of a crooked bill, serving for the same vse.</p>
                  <p>The Figure 139 is a longe showel, or a rake for the casting vp of Earth out of
galleries, to fill vp a moate, and in other dangerous places. And the forme A, in
the 31 Plate, is good also to plaine the Earth vvhich is cast vpon a gallerie, to
keepe it from fyring, which otherwise might happen to a gallerie.</p>
               </div>
               <div type="subsection">
                  <head>The 33 Plate &amp; 144. 145. Figures.</head>
                  <p>BEfore wee come to speake of Approches, it is very necessarie, that one should
gett an exact draught, as well of the interiour, as of the exteriour part of that
towne, of fortresse, which one resolues to approach vnto, with all the markes, and
observations, as namely, of hedges, wayes, hills, valleys, and the like, that ye maye
know the better how to order and runne your approches. Ye ought not to break
ground noe neerer at the first the<g ref="char:cmbAbbrStroke">̄</g> within a muskett shott, or at the furthest as farre
as a harquebusse a Crock can reach, and (as I say) ye ought to beginne your tren<g ref="char:EOLhyphen"/>ches,
somewhat further off from the towne; if there be a commodious accesse
from the quarter to the trenches, that when neede requires ye maye the sooner
relieue, and second your men in the approches, if the Ennemie shall sallie, or fall out
vpon them. For, when the place where you first breake ground is a great vvay
from the quarter, it vvilbe disadvantagious vnto you, because ye must allwaies
keepe in them a stronge gard, to repulse an Ennemy, and to beate them back when
they shall fa<gap reason="illegible" resp="#TECH" extent="1 letter">
                        <desc>•</desc>
                     </gap>lout, and while your men are a makeing ready, and coming from the
quarter, many good occasions maye be lost, before they cann be at hand. There<g ref="char:EOLhyphen"/>fore
you must haue a great care, and circumspection, where your trenches are to
beginn, and where your quarter must be made, as neere to and as covertly from the
towne as possibly maye bee, considering well, whither it were not better to quarter
<pb n="34" facs="tcp:1568:45"/>
sometimes the more incommodiously, that ye maye beginn your approches in a
place of most advantage, neere vnto the towne, or place, which ye are resolved to
take in: then to choose a place more commodious for your quarter, that would be
a hindrance to your dessigne, by reason of the great distance betweene that and
the approches, or which maye lie too open to Canon shott, all which in my judge<g ref="char:EOLhyphen"/>ment
ought to be maturely considered, that your dessigne maye not be hindred
or fore-slowed.</p>
                  <p>The next thing is for you, to knowe the weakest part, and side of the towne, or
place, vvhere you maye beginn your approches, and which place you intend to
gaine. For, it is a great helpe, especially in places regular, to choose out the most
advantagious place. If you should make a breach in a curtaine, betvveene tvvo
bulwarks, ye shall finde it to be the retyredst place, the best to be defended, soonest
cutt off, and the hardest for you to approch vnto, therefore would advise you, not
to beginn there. And if it hath a <hi>tenaille,</hi> then ye haue lesse reason to make any
attempt vpon that place, having a retyred angle, and so consequently the cutting
of wilbe according to their vvish. But to approch to the angles of a Bulvvarke,
vvhich are angles shooting out, being the exteriour parts of a tovvne, or fortresse
wilbe the easiest for you to come vnto, and the hardest for them within to cutt off:
seing the place is litle, and that the ramparts themselues maye giue some hin<g ref="char:EOLhyphen"/>drance
there vnto.</p>
                  <p>The place the<g ref="char:cmbAbbrStroke">̄</g> being resolued on, a certaine nu<g ref="char:cmbAbbrStroke">̄</g>ber of souldiers (or Commaunded
men) are choosen out of euery Regiment, and Companie to the number of 4, or
500 men, more or lesse, to goe downe in the night to breake ground, and to be<g ref="char:EOLhyphen"/>ginn
the approches. Also there must be placed a competent number of horse, and
foote, to helpe to guard and defend these workemen, if an ennemy should sallie out
vpon them. These commaunded men haue each of them ten stivers a night, or
more as the danger of the worke shall require: they having men (as is said) in armes
lying round about them, to defend them as appeareth by the numbers 20. 20: in
the 145 figure. Then the Ingenier, who hath the ordering of the approches, setts
these men out in a right (or a crooked) line placing three or foure men vpon every
rod, and all in a file, in as right a line as possibly maye bee, takeing special care, that
his men maye stand as much out of daunger of shott as is possible, vvhich is done
also by the helpe of these gates, which lies about them in keeping their marches
closse, that they maye not be discouvered by those of the towne. More ouer, they
must laye out <hi>Sentinell perdues,</hi> before and round about them, which if they heare,
or see any thing, maye giue the alarme silently before an Ennemie can fall vpon
the workemen: For the alarme being once giuen, these gards are to draw vp, and
helpe to defend the Workemen. But if they see that the Ennemie sallies out to
stronge for them, these gards then maye drawe into these <hi>Corps de garde</hi> made pur<g ref="char:EOLhyphen"/>posely
for them, and withall the commaunded men must quitt their worke for that
time, and bringe off their armes, spades, showells, and mattocks; but is hast and
necessity constraines them, to defend themselues; then they must betake them<g ref="char:EOLhyphen"/>selues
to their armes, and cast away their materials, retyring softly (with the gards
abouesaid) if they cannot make the place good, to the <hi>Corps de garde</hi> made first for
their retreate. These workes ought to be stronge, and able to repulse and keepe
out an ennemie, yea it often hapneth, that they vpon a disorderly retreate, into the
towne maye be followed, and beaten back with the losse of many men, even to their
very moate side, and that the Besiegers maye discouver the strength, or weaknesse
of their vvorks, and spie out some advantages for them. The Ennemie being bea<g ref="char:EOLhyphen"/>ten
back, the commaunded men maye fall instantly to their vvorke againe, and
<pb n="35" facs="tcp:1568:45"/>
being gott some 3 foote deepe, and casting vp the Earth towards the tovvne, they
maye worke with the more safetie, and out of daunger. And for this reason euery
souldier will make as much hast as possibly he can to gett into the ground for his
owne preservation, and the Earth being cast vp thus out of holes, they maye after<g ref="char:EOLhyphen"/>wards
repaire it, and make thereof a large trench, and ditch, namely, (as is said) 3
foote broade, and 3 foote high, casting the Earth vpon the edg of the trench, and
the next day maye make it 6 foote broad, and six foote high: for the larger the
trench is, the higher ought the parapet to be; because othervvise, they might be
discouvered by those of the towne, and so your men maye be the better vnder
covert, and lie safer in the said approches. And because this cannot be done so
exactly by night, fresh commaunded men are sent downe in the morning from the
quarter to repaire, and enlarge the trenches, and if the trenches be so large, and so
high, that one cannot well discover the fields round about them, then ye must
make a foot-banke or two, for the muskettiers to come to the topp of the trench to
giue fire over the<g ref="char:cmbAbbrStroke">̄</g> through muskett baskets, which is done mosttimes when a sapp
is begunn: At the first entrance into the trenches, or approches, ye make a square
worke, or two, called Redoubts, or a <hi>Corps de garde</hi> being distant one from an other
some 40, or 50, rod, that in them ye maye keepe a stronge gard the daye following,
and the Ingenier, who hath the mannaging of the approaches; maye so order &amp;
encourage his men, that the said <hi>Corps de garde</hi> maye be in defense before daye, to
the end, that if the Ennemie should sallie out vpo<g ref="char:cmbAbbrStroke">̄</g> the trenches, that from the same
<hi>Corps de garde</hi> they maye be beaten back: the bredth of euerie side ought to be some
4, or 5, or at the most 6 rod, and the ditch broad &amp; deepe as necessitie shall require.
They ought to be made in my opinion in such a manner, that the two opposite an<g ref="char:EOLhyphen"/>gles
doe enfile the said thrench as appeareth by the Figure 117, Plate 29, and by the
<hi>Corps de garde</hi> D E F, Figure 145. For then the said trenches will not onely lie open
vnto it, but also one maye discouver the fields round about it. But if it be not found
good to make them so, then the best way in my judgment vvere to make them out
of the Trenches a rod and a halfe, or at most two rods distant from them: so that
the said trenches ought to be betweene the towne, and the said <hi>Corps de garde:</hi> one of
the sides must be paralell to the said trench that ye maye march by it in the night,
both with men and waggons, and to draw vp the ordinance betvveene the said
<hi>Corps de garde,</hi> and the Trench, and so the said <hi>Corps de garde</hi> will flanke the said
trenches on that side where they lie most open as ye maye note by the <hi>Corps de garde</hi>
in the 4, Figure, 145 &amp; 33 Plate.</p>
                  <p>After your commaunded men haue vvrought almost to the breake of the day,
then they must be drawne off (without beating of a drumme) by a Sergant or the
Quartermaster of a Regiment, and being returned to their quarter the Sergant shall
deliver the note of the number of his men to the Quartermaster of his regiment,
and the Quartermaster to the controuler of the works, vvho to that end comes to
v<gap reason="illegible" resp="#TECH" extent="1 letter">
                        <desc>•</desc>
                     </gap>site the said worke and to see if there were as many men as was appointed, least
there should be any fraude committed therein. Then the Controuler is to giue
the Quartermaster his attestation for the worke men, or in his absence the Ingenier
giues the said Certificate, and the Quartermaster brings it to the States, who giues
an ordinance vpon it to the Treasurer, and so the Quartermaster receiues money
for the workemen of euery companie, to wit, ten stivers, giues it to the Sergants &amp;
the Sergants to the souldiers of every company.</p>
                  <p>The reparing of the trenches are made by the vndertakers (as wee haue said) for
so much, or so much the rod, according as one desires to haue them large and spa<g ref="char:EOLhyphen"/>tious,
as some times 6, 8, foote, or more, as necessity requires. For oftentimes they
<pb n="36" facs="tcp:1568:46"/>
must be so broad, that a waggon loaden vvith fagotts, Brush, or Gabions maye goe
in them. The wages of euery souldier is then augmented some times to 15, 20, or 30.
stivers a day, when there is evident daunger, as there is commonly, at last before
one beginns to sapp: for the muskettiers playing continually vpo<g ref="char:cmbAbbrStroke">̄</g> the points of the
Trenches, where they imagine that the approches will run, kils many men: yea so
that sometimes they are forced to giue ouer the worke, because many men are not
able to worke in it, and being too hott, they putt in a resolute man or two, into
the vvorke, promising to giue them more then ordinarie if they vvill hasten the
worke, and this is considerable, whither this extraordinary expence be not profi<g ref="char:EOLhyphen"/>table
for the advancing of the approches, and gayning of time, then to spare a litle
money and foreslow them: For experience hath many times taught vs: that expe<g ref="char:EOLhyphen"/>dition
in such cases hath wrought many great effects.</p>
                  <p>When you are approched so neere your Ennemie, that by reason of their con<g ref="char:EOLhyphen"/>tinuall
shooting vpon your points ye cannot advance your trenches any further;
then you must beginn your sapp, which ye shall runne, if it be possible, directly vpo<g ref="char:cmbAbbrStroke">̄</g>
the point or side of the Bulwarke, which ye intend to take in, as the point, I, &amp; K,
Figure 145, demonstrate. And because tvvo men at the most can but vvorke in
them, these sapps are ordinarily taken on by some resolute souldiers for some 7, 8,
yea or 12, gilders a rod, as the danger requireth: they first make the sap some 3 foote
broad, and about 3. 4. 5. or 6 foote deepe according as the ground is, either high or
lovve, then these vndertakers or others are to repaire the Sapps, and receiue for
their paines 6. 7. or 8, gilders a rod, and so make it 6 foote broad, or thereabouts
casting vp the Earth on both sides, that they maye be the better vnder covert, and
the safer from the Ennemies shott.</p>
                  <p>According to which we haue made the Figure 144, whereof P, Q, are two Bul<g ref="char:EOLhyphen"/>warks.
A is the beginning of the Approches, A, B, the first trench or line vvhere
the workemen breake ground, carryed in such a manner towards the angle R. (in
case the same line be lengthned and comes out of the <hi>Corps</hi> of the Fortresse) in
the angle B is made a <hi>Corps de garde</hi> for the assurance of those, vvhich garde the
trenches, as appeareth by the Figure 145 to the letter B. At C is made a line towards
the angle S, which must be drawne in such a sorte, that if it be lengthned, it vvill
fall on the outside of the Corps of the fortresse Q. vvhich is continued (as the
said Figure demonstrated) to I, the parapet of the covert vvay, vvhere
one beginns a mine to blowe vp the counterscharfe, that ye maye come to
the brinke of the moate. From D, is drawne the line E, K, to assure one the better of
the enclossure K, E, I, betweene K, E, &amp; I, E (before ye come to peerce through with
your sapp) ye ought to make the lines L, O, &amp; F, M: that from these lines you maye
giue fire vpon the Ennemies Muskettiers, setting along vpon these lines muskett
basketts that ye maye play continually vpon the besieged, that vnder the favour
thereof, you maye advance your sapps towards the faces R, T, &amp; V, S, as the said
Figures 144, &amp; 145. shewes. If the <hi>Corps de garde</hi> be in some eminent places as they
ought to be (if it be possibly) after ye are advanced to them, ye make a batterie vpon
them, but if there be one peece of ground higher then another, that is more com<g ref="char:EOLhyphen"/>modious,
which ye may choose for your batteries, as wee haue done here in the
Figures G, H, P, O, X, Z, Y, Figure 145.</p>
               </div>
               <div type="subsection">
                  <head>Figure 142. 143.</head>
                  <p>WHen ye beginn your trenches of Approche, ye commonly make some
batterie, that vnder the favour thereof your men maye worke forward with
<pb n="37" facs="tcp:1568:46"/>
the more safety, and hinder the Ennemies from falling out, vvhich vvould much
foreslow your works. Your Batteries then are made first in such a manner that they
maye beate vpon the Parapet of the ramparts &amp; Bulwarks of the towne, to dismount
the ennemies ordinance, and for this reason you must raise your Batteries high
according to the height of the ramparts, so that your Canon maye play freely
about two foote lower, then the topp of the parapet, according to which, and in
consideration of the distance, ye must raise your said batteries, takeing heed that
your Canon be planted vpon a plaine superficies, and elevated some 13, degrees,
when the distance is farre off: ye must not raise them so high as when the batteries
are neere vnto the place: so that ye must either raise, or sinke them, as neede shall
require. Ye make your batteries, and platformes according to the greatnesse, and
number of your peeces: for a <hi>Demy-Canon,</hi> being shorter then a whole, of necessity
the platforme of the one, must be longer, and deeper then the other, and seing a
Canon being mounted vpon its Carriage, is some 16 or 18 foote longe; it is evident,
that the batteries ought to be made for recoyling at the least 10, or 12 foote longer
makeing together 28, or 30 foote: 12, or 15 of the first foote tovvards the parapet,
must be vnderlayd with thick &amp; stronge oken plancks and the other with hurdles,
when ye haue not plancks enough: vpon the said batteries ye make a parapet 12, 16,
or 20 foote thick or thereabouts, with port-holes for your canon as the Figure
143 demontrateth. Sometimes ye sett vp Gabions 6 foote high and 3 foote broad
filled with Earth, for your ordinance to play out of, leaving a little space betvveene
them, to putt out the mouth of your Canon, which space so soone as the Canon is
discharged is presently stopped and blinded vvith a bundle of brush full of leaues,
that the ennemie maye not discouver the port-holes, but when you make your
batteries vpon the Counterscharfe, or vpon the brinke of the moate, then the
port-holes assoone as your Cannon is sho<gap reason="illegible" resp="#TECH" extent="2 letters">
                        <desc>••</desc>
                     </gap> off, are shutt with doores of thick oken
planks musket proofe, that the said port-holes maye not be seene. Sometimes ye
sett onely Gabions vpon the parapets of Batteries which containe 7 foote in Dia<g ref="char:EOLhyphen"/>meter,
and 10 in heigth, yea oftentimes sett 3 rovves of them vpon he said parapet,
which make in all 21 foote thick as appeareth by the Figure 149, &amp; the 34, Plate,
There are vsually made three sorts of Gabions, to wit, the ordinary of 6 foote high
&amp; 3 foote wide: the middle sized 7 foote high, and 5 wide, and the double Gabions
10 foote high, and seuen foote wide in the mouths, as appeareth by the Figures
146. 147. &amp; 148. the platforme or bed, is a foote higher behinde then before, or by
the parapet to the end the peeces maye not recoyle too farre, as also that with the
more ease they maye be drawne vp towards their port-holes, and seing euery peece
is broad at the Axeltree some 7 foote, ye must allow 5, or 6 foote for a space be<g ref="char:EOLhyphen"/>tweene
the Axeltrees of each peece one both sides &amp; so haueing 4, 5, or 7. foote
distance betweene them one maye the better come to the mouths of the peeces
to lade them, for it is necessary to haue roome enough vnto both sides to come to
them readily, that being discharged ye may draw them vp againe into their places.</p>
                  <p>If the sides lye open, they must be blinded vvith a parapet of Earth or vvith
Gabions; at the furthest ende of the batterie, ye must make a cellar or a place for
your powder bullets &amp; match and other necessaries, for the Conductour, which
shall giue out the pouder, the bullets, with a gentleman of the ordinance, who
shall giue order to the Canoniers, when and how often they shall shoote, and
without whose knowledge, and Commaund they shall doe nothing: the amunition
which is there must be covered, with horse skinns and haire cloth to prevent the
danger of fyring, and to that end this hole is made in the Earth. The circuit of
the batterie is oftentimes trenched about as the others in the approches are, but
<pb n="38" facs="tcp:1568:47"/>
otherwise, vvhen an ennemie is not to be feared, onely is compassed about with
match bound vp with stakes, that noe man vnwares or without leaue maye come
within the compasse thereof. The entrance into the said batterie is made slooping,
that one maye the better come vp, and goe downe, and chiefly that ye maye with
the more ease draw vp the Canon into them. The Batteries must not be farre
from the trenches, but that vpon all occasions they maye be seconded.</p>
                  <p>According to which directions ye shall easely make all sorts of batteries, as for
exemple: The Generall would haue you to make a batterie for foure peeces of
Canon, ye must take for euerie peece at least 12 foote, in length: so that for the
foure peeces ye must haue 48 foote, and then for the two vtmost peeces each 5
foote makes 10 foote, which with the 48 make in all 58 foote, vvhich shalbe the
bredth of the said batterie for 4 peeces, excepting the Parapets &amp; Taluds, vvhich
oftentimes haue as much Talud, as heith, and sometimes the halfe, and for the
depth, ye must take 28, or 30 foote, or thereabouts besides the Parapets and Ta<g ref="char:EOLhyphen"/>luds,
the first 12, or 15 foote are layd with Oaken plancks, and the other vvith
hurdles, for whole Canon, (as we haue said) vvhich carrye a bullet of 48 pound
weight, but some two foote lesse for the halfe Canon, and for other peeces accor<g ref="char:EOLhyphen"/>dingly;
The said plancks must be layd both at length and sidelings, and the hur<g ref="char:EOLhyphen"/>dles
along the peeces, as appeareth by the Figure 143, in which H is the ditch, G
the edge, F the Talud, E the parapet, B the bedding of the plancks, C the Talud.
The Figure 142 is the profile of the said batterie 8. 12 is the cellar, where the powder
stands, which ought to be somewhat neerer the batterie then is marked here, and
was made in the same time as the battery was, and the Earth which is cast vp out of
it, is vsed to raize the said batterie: when ye haue not earth enough to make vp
the batterie with all, then ye must digg round about it, as we haue said in this ex<g ref="char:EOLhyphen"/>emple
143. But for a batterie, which is made vpon the brinke of a moate, it is not
commonly so high, nor taketh vp such a great space, as this present batterie doth;
because the ground will not afford it, and that they cannot soo well cover such
places: so that one is constrained to entrench them more narrowly, vvithin the
place to be the more secure vnder convert from the short of the besieged, which for<g ref="char:EOLhyphen"/>beares
not to offend, yee aswell by hand granadoes as otherwise.</p>
               </div>
            </div>
            <div type="section">
               <head>How to pierce through a Counterscharfe, and to make a
Gallerie over a moate.</head>
               <div type="subsection">
                  <head>The 34 Plate, and 150. 151. 152. &amp; 153, Figures.</head>
                  <p>WHen you are come with your sapp to the parapet of the covert way, then you
must make batteries to beate dovvne the flancks, and the other places of
defense of the Fortresse or towne, and vvithall ye beginn then to pierce into their
counterscharfe: and for the better effectuating thereof, if it be high ye must make
an entrance into it through a mine, so that your discent into the moate maye be
made leuell with the Superficies of the water of the moate, which discent must goe
downe slanting as F, L, &amp; the Figure 150, G, H, I, K, is the furthest end of the mine,
or the discent into the moate F, G, the height of the mine, being 6 foote or aboue,
and some 5 foote broade, or some what more, that the Earth vvhich is taken out of
it maye the more commodiously be carryed away, and that the more men maye
march in front in it. Before ye gett in the ground at the entrance ye must vnder<g ref="char:EOLhyphen"/>prop
it with posts as the former F, G, H, shewes, vntill such time as ye are gott so
deepe, that ye are vnder the Earth, and then for keeping the earth from falling
<pb n="39" facs="tcp:1568:47"/>
downe, ye must driue in posts on both sides, and laye oaken plancks (which are not
very broade crosse vpon them, continuing so as you advance your mine in keeping
the Earth from tumbling downe: these posts and plancks must stand and joyne
closse one to another as ye see represented by the Figures 150, &amp; 153, Plate 34. In
which F, G, H, is the entrance into the mine to descend into the moate. The 3
first posts (because ye are not yet entred much into the ground) are made in that
manner as the Figure 152 demonstrates, the rest are sett in that forme, as the Figure
150 showes, in such sort that I, K, is the entrance into the Counterscharfe. If the
ground lye lowe, and that ye cannot gett into the counterscharfe after the manner
abouesaid, then ye must continue your sapp, to the brinke of the moate, and that ye
maye keepe it from fyring, ye must cover it ouer with fyrre plancks and cast earth
vpon it, that your men maye worke with the more safety and that ye maye hinder
the besieged from casting in of granadoes, and other fire works, ye must place mus<g ref="char:EOLhyphen"/>kettiers
round about the approches, which if they perceiue the ennemie cast any
fire workes from the rampart vpon it, they maye giue fire presently vpon them.</p>
                  <p>Being gotten through the Counterscharfe and come to the edge of the moate:
ye presently cast abundance of fagots, brush &amp; earth into it, to fill it vp, and one or
two of your resolutest men leaps into the moate to lay them right vpon the face
of the Bulwarke, that as you fill vp the moate to come to the skirt of the Bulwarke
so ye maye advance your gallery till you are over in setting your posts forward,
and laying plancks over it and casting Earth vpon the gallerie, which must be 7 or
8 foote high, and 6, 7, or 8 foote broade for the larger it is so much the better and
the more men maye march in Front in it: the posts, or supporters maye be sett
some 5, or 6 foote distance one from an other, vvhich maye be plancked on the in
side, and on the outside with oake<g ref="char:cmbAbbrStroke">̄</g> planks, and the posts being some 6 ynches thick,
the gapps, or spaces betweene then, are filled with Earth, to resist the force or vio<g ref="char:EOLhyphen"/>lence
of canon, and aboue the gall<gap reason="illegible" resp="#TECH" extent="1 letter">
                        <desc>•</desc>
                     </gap>rie, as is said, ye cast vpon it a foote or halfe a
foote of earth thick, and then spread it abroad with a fire-rake to keepe it from fy<g ref="char:EOLhyphen"/>ring,
which fire-rake is described in the 31 Plate, by the Figure A.</p>
               </div>
               <div type="subsection">
                  <head>The 151 Figure.</head>
                  <p>WHen you haue putt over your gallerie (as we haue said) then you must be<g ref="char:EOLhyphen"/>ginn
to mine, as the place, and as the Assaillants shall finde it best, either vpon
your right, or left hand, high or low, if the water hinder you not mining &amp; wor<g ref="char:EOLhyphen"/>keing
in this manner following: The Earth which you digg out of the mine, must
be carryed away in wheelebarrows through the gallerie whither you will. If you
please you maye cast it into the water towards the angle of the Bulwarke, and so
fill vp the moate with it, if it be not incommodious for you to carry it through the
gallerie: But on the other side, ye must marke well the turnings of your mine,
which maye occasion the Besieged to counter-mine, and so to hinder the dessigne
of the Besiegers. For if they haue once discouvered, or mett with the mine of the
Assailants, they must be forced to stopp it vp &amp; to abandon it, and so beginn an<g ref="char:EOLhyphen"/>other.
The Countermines which are made in ramparts, or Bulvvarks vvhen a
fortresse is new made, being some 5, or 6 foote high, and 3, or 4 foote broad, are of
singular vse, which doe encircle the place, and from them ye maye heare the least
noise that is made on the outside, and which way one workes, and by that meanes
maye hinder them the better from myning.</p>
                  <p>These mines are commonly made in the forme of a <hi>paralellograme</hi> or a long
square, to wit, the chamber in which the pouder is layd, must be 4 or 5 foote high,
<pb n="40" facs="tcp:1568:48"/>
and 3 or 4 foote broad, and in length answerable to the ponderosity or weight of
the rampart, and according to the breach, which ye intend to make. If ye vvould
blowe vp the rampart on the inside, you must peerce into it some 6, or 8 foote, and
then ye must make your chamber, but onely 4 foote high, some 3 or 4 foote broad,
and some 6 foote longe, according to the number of the barrells of pouder, which
you meane to laye in it, and the greatnesse of the wall, vvhich you intend to blovv
vp. The reason why the chamber is made here but onely 4 foote high, is to the
end that the exhalation finding the least resistance towards the inside, forces it
with the more violence and makes therein a greater shaking and breach to the ter<g ref="char:EOLhyphen"/>rour,
and hurt of the besieged: when ye would blow vp the vpper part of the ram<g ref="char:EOLhyphen"/>part,
the<g ref="char:cmbAbbrStroke">̄</g> you make your mine some what ascending vpwards: if the moate be very
deepe, that your dessigne be not frustrate by reason of the water, for your better
assurance, ye must make your chamber some 5, 6, or 7 foote high, to the intent that
the exhalation maye breake vpwards according to the intention of the Master<g ref="char:EOLhyphen"/>miner.
But the entrance into the said chamber, as we haue said aboue, must be
onely 4 foote high and 3 broad, to the end one maye the better stopp it, and hinder
the exhalatio<g ref="char:cmbAbbrStroke">̄</g> from breaking out backward, towards the gallerie, which one ought
deligently to prevent, in shunning those inconveniences and mischiefs, which of<g ref="char:EOLhyphen"/>tentimes
by such casualities haue hapned heretofore.</p>
                  <p>Then having chambred your pouder, and noted well, that those within haue
not discouvered it: you must stopp, and shutt vp your mine exceeding firme that
it maye take the better effect. To doe this, the best way wilbe to stopp it at E, with
two hughe plancks, just at the said entrance at E with great sparts of timber, and
driving them into the Earth, as firmely as possibly may be. The chamber F G H I
is 4 foote broad, and F G, &amp; F, I, is sixe foote in length: Oftentimes the bredth is
but 3 foote, that one maye be the better assured of the resistance of the posts and
plancks. In one of the plancks, which stoppeth vp the entrance E into the mine,
ye make a hole in it, to putt your traine through which runns from E, to B,
that through it ye maye giue fire to the pouder in the said chamber: After these
plancks ye damme vp your mine with good Earth, from E, to B: the turnings C D E,
are made to delude the besieged, that they maye not finde out your mine by coun<g ref="char:EOLhyphen"/>ter
myning; but most often it runns right forward, or somewhat winding. The
length of the chamber F, I, (which is here but sixe foote) is made as longe as neces<g ref="char:EOLhyphen"/>sity
requireth, but the bredth F G, is ordinarily noe more then 3, or 4, foote at the
most: and to weaken the more the place which you intend to blow vp; me thinkes it
would be good before ye spring your mine to digg some Holes in some corners
that the exhalation may haue the better vent, and easie bursting out. Some are of
the opinion that a barrell of pouder will blowe vp 12 foote of Earth, according to
which ye may make the said chamber, and lay in as many barrils of pouder as you
please, to the end you maye make your breach the larger &amp; more spatious. But
seing this is yet vnresolved, I will leaue the judgment thereof to those which
haue more experience therein then my selfe.</p>
               </div>
            </div>
            <div type="section">
               <head>How one must be prepared against a Siege.</head>
               <div type="subsection">
                  <head>The 35 Plate and 154 &amp; 155. Figures.</head>
                  <p>HAving succinctly spoken of Approches, Sapps, the descent into a moate, gal<g ref="char:EOLhyphen"/>leries
and mines: me thinks it will not be amisse now to treate of the prepara<g ref="char:EOLhyphen"/>tions
which must be made against a seige.</p>
                  <p>
                     <pb n="41" facs="tcp:1568:48"/>
If then one should be suddenly surprized: so that there is noe time to make any
outworks, halfe moones, Horne works or other peeces of fortifications as well
loose, as joyning to the wall, or place: one ought in my opinion (besides the care
that ought to be take<g ref="char:cmbAbbrStroke">̄</g> for materials, amunition, and victualls (whereof I doe not in<g ref="char:EOLhyphen"/>tend
here to speake) one is to take speciall heede vpon what side of the towne or
Fortresse the Ennemie will beginn and runne his approches, towards what Bulwark
he makes them, on which side I would make some works to hinder an ennemie, as
we shall declare in the 38 Plate &amp; Figure 159. But if one be advertized of the Siege
some time before, or that ye imagine, it wilbe good to provide such necessaries and
to fortifie those places with a more capable defe<g ref="char:cmbAbbrStroke">̄</g>se, which we inte<g ref="char:cmbAbbrStroke">̄</g>d to speake of here<g ref="char:EOLhyphen"/>after
(according as ye shall finde the weaknesse of the place to require, &amp; as time
will permit you to doe it before ye be besieged) as well without the towne as within,
to make good entrenchments &amp; to provide munition, victualls, and men sufficient
to defend that place, without the Towne, you must make Horneworks invented of
late yeares, Halfmoones, traverses, and other works, all tending to hinder the Be<g ref="char:EOLhyphen"/>siegers
from getting into your moate, and to prolonge the siege with hopes of re<g ref="char:EOLhyphen"/>liefe,
seing experience hath taught vs, that when an Ennemy comes once to enter
your moate, and to putt over his gallerie, that towne or place cannot long hould
out: if you haue not made stronge workes, entrenchments, and cuttings off without
(to giue an Ennemie his handfull, and to make them gaine your work<gap reason="illegible" resp="#TECH" extent="1 letter">
                        <desc>•</desc>
                     </gap> ynch by
ynch) which notwithstanding are not of so good a resistance, as is your settled,
firme, and solid rampart. These workes ought to be drawne out according to the
greatnesse of the place, and the men which ye haue to man them. For, if ye haue
many of those works, they will require a great many men to defend them so that if
ye haue not men enough to keepe them, that labour and expence will be in vaine,
and so an Ennemie maye soone become master of them. And seing in all obser<g ref="char:EOLhyphen"/>vations,
exemples are of great efficacie I haue thought good, and profitable to
make you vnderstand my intention by representing vnto you the Plate of <hi>Gulich</hi>
prepared against that siege, whereof the Bulwarks of the towne are marked by the
numbers 2, 3, 4, 5, the Castle, which is quadrangular by the Ciphers 6, 7, 8, 9. And
seing the towne stands vpon a low ground, and the Castle vpon the side 6, 9, 8, vpon
a higher ground: in all likelyhood the approches was to be begun on this side, as
the Besiegers did in the yeare 1611, for which reason, and to hinder the Approches
on that side, they made the angles 9. 8. and betweene them the Horneworks c, d,
f, the Ravelins c, g, h, b, being not further assunder one from an other, but that
from the curtaine one might defend the vtmost hornes c, d, f. But seing c, and f,
are very narrow, to wit, onely some 24 rod, and shoote out farre from the bodie of
the Fortresse: in my opinion they ought rather and it had beene much better to
haue made the angles in the forme of the Raveline c, &amp; f, and so haue quitted the
said horne-works, because (as we haue said) they were too straight, and narrow, and
to haue made them at g, or vpon the curtaine 6, 9, the Horneworks 1, and (also
whither the Raveline b, could not haue defended the Raveline c, in the place of
the angle of the Bulwark 8) and to haue made the hornworke q. vpon the cur<g ref="char:EOLhyphen"/>taine
<gap reason="illegible" resp="#TECH" extent="1 letter">
                        <desc>•</desc>
                     </gap>, 8, and so might haue saved the Raveline a. And betweene the two Bulwarks
of the towne 4, &amp; 5, the Raveline r, &amp; o, betweene 3, &amp; 4, and so haue saved the en<g ref="char:EOLhyphen"/>trenchment
n, which runs out farre fro<g ref="char:cmbAbbrStroke">̄</g> the angle 3, and is of noe great defense. The
Raveline k, is made betweene the Bulwarks 2, &amp; 3, to take away the entrenchment
m, made in a Tenaille, but the sides being of a very small distance, &amp; for this consi<g ref="char:EOLhyphen"/>deratio<g ref="char:cmbAbbrStroke">̄</g>
of litle vse, yea many times hurtfull as experience hath showne oftentimes.
The reason why I make of the angles 8, and 9, the Ravelins, c, and f, in stead of the
<pb n="42" facs="tcp:1568:49"/>
Horneworks, is, that the Horneworkes d, &amp; i, might be the better defended, which
wilbe reciprocaly defended from the said Horneworks, and will not be so farre
distant from the body of the said fortresse. Those which are of an other opinion,
maye follow their owne intention and experience, against whome I will not con<g ref="char:EOLhyphen"/>tend
acknowledging that experience strikes a great stroake in all occurrence,
saving that I am onely permitted to giue advise therevpon.</p>
                  <p>The said Horne works are made in bredth, and height as necessity requires and
as they maye resist the forces of an Ennemie, and according to the time they haue
to make them. For the first one makes a Rampart, or a parapet, some 12, 16, or 20,
foote broade, 6 foote high, and a ditch of the same bredth of 12, 16, or 20 foote, and
some 6 foote deepe. If one cares not for the expence and hath time, ye maye add
to the former bredth 6, 8, 10, or 12 foote more, in enlarging also to so much the
bredth of the ditch, and then the Rampart is made some 3. 4. 5. or 6 foote high, and
vpon it also ye shall make a parapett of 6 foote high, with a foot-banck some 3 foote
broad, and a foote high, the ditch is enlarged and deepned, according to the great<g ref="char:EOLhyphen"/>nesse
of the Rampart, and as wee haue taught in the Plates of our regular fortifi<g ref="char:EOLhyphen"/>cation
before: and the higher the Ramparts be, the entrenchments are the better
covered: one maye make them the further from the place, to wit within a musket
shott, so that there wilbe a better meanes for entrenching, and cuttings off, and to
fors<gap reason="illegible" resp="#TECH" extent="1 letter">
                        <desc>•</desc>
                     </gap>ow and hinder an Ennemy from advancing his approches.</p>
               </div>
               <div type="subsection">
                  <head>The 38 Plate &amp; 159 Figure.</head>
                  <p>IF one hath not time to make these workes abouesaid, as when an Ennemy is
neerer at hand, then one did expect: After ye haue observed well the place
towards which the Assaillant makes his account to beginn his approches, as to<g ref="char:EOLhyphen"/>wards
these two Bulwarks, one might make litle ditches without them as A B C
D, which are in the extention of the Capitals beginning in the Angles A, C, of the
length of 600 foote, or thereabouts (to wit, that the vtmost end B, D, be not out
of muskett shott) of the bredth of some 6 foote at the most, and 5 foote deepe
without the parapet, the Earth being playned from the one part to the other, to
the end that you maye not hinder the sight of the muskettiers, which you shall
lodg in them, and in stead thereof vpon the edg of these shalbe sett small mus<g ref="char:EOLhyphen"/>kett
basketts filled with Earth, easie to be removed from one place to an other: It
wilbe good for ones better security to hold there a <hi>Corps de garde,</hi> that if the enne<g ref="char:EOLhyphen"/>mie
seeke to beate them from thence, they maye be the more able to discharge
their duties, whereby (in my opinion) the approches of the Besiegers maye be much
hindred, &amp; being so puzled they wilbe constrayned euery time to alter thier des<g ref="char:EOLhyphen"/>signes
and so to beginn their approches againe a good way further off, and more
crookedly, as towards B, D, to which being come they can gett noe advantage,
seing they are enfiled with the angles of the Bulwarks: If they had time to make
chests in them, or to make them in such a sort, that the Besiegers could not driue
them out of them, it would be much better.</p>
               </div>
            </div>
            <div type="section">
               <head>Of Cuttings off, aswell generall, as particular.</head>
               <div type="subsection">
                  <head>The 36 Plate &amp; 156 Figure.</head>
                  <p>IF an Ennemie be gott into the skirt of the Bulwarke g, h, and that one hath not
time to cutt it off royally, &amp; yet you are resolued to make him gayne the place
<pb n="43" facs="tcp:1568:49"/>
foote by foote, you must make the cuttings off f, l, m, whereof n, o, p, is the
ditch, makeing the angle of the Tenaille l, as much pointed as possible maye be,
that the lines f, l, and l, m, maye be the better seene from one an other, carrying
the outward edg of the ditch n, o, &amp; p, as neere the skirt g, h as possibly maye be,
that ye maye haue the ditch as large as maye be, to hinder the takeing away of the
tenaille l. If the whole face be not ruined, but onely the angle of the Bulwarke
r, one shall make the angle t, from the Tenaille s, t, u, (which in regard of the
smallnesse of it wilbe better then the former) so that on the inside of the cutting
off x, y, z, one maye haue space there to make the ditch as great and as deepe as
maye bee: the entrance ought to be in the angle of the tenaille t. But seing that
fortification is better, which hath two flancked, and flanking angles, ye must
make the entrances in and out also double, to haue the same the more easie, and if
time &amp; occasion would permit, they may make in the angle t, two issues, which in
my opinion might be made vpon the two sides s, t, and t, u, as neere the angle t, as
one can: and ye must note by the waye, that the Bulwarke against our intention is
made massie, and not hollow.</p>
               </div>
               <div type="subsection">
                  <head>The 38 Plate &amp; 159 Figure.</head>
                  <p>IF the two faces be wholly spoyld, as the Figure 159. demonstrateth, then I should
thinke it good, to make the angles a, b, c, contayning the angle of the <hi>tenaille</hi> b,
as litle as maye bee to gaine the better place of defense in makeing the ditch, as
large and as deepe as is possible, as it is here marked out by the lines d, g, &amp; e.</p>
                  <p>When the Bulwark hath a Catt noted B, and that its angle h, is ruined, then one
might so order the cuttings off l, m, n, o, &amp; the ditch p. q. r. s<g ref="char:punc">▪</g> t, that the besiegers
should be compelled to vndermine the Catt, and to passe the ditch, which the lines
p, q, r, s, t, represents vpon the edge exteriour.</p>
                  <p>But if the whole Bulwarke be ruined, you shall drawe from the midst of the
curtaine of the Bulwarke ruined a privie line marked by the letters h, I, vpon the
inside whereof, ye shall make the two skirts of the bulwarks, according to our ge<g ref="char:EOLhyphen"/>nerall
method giuen in our regular fortifications, and the other cuttings off h, k, l,
m, n, i, shall haue: the other Bulwark B, being also ruined, one maye draw the privie
line s, h, &amp; make within it two other skirts, as h, o, p, q, r, s, and so o, h, k, p, l, wilbe a
perfect bulwark, having flancks, gorges, faces and curtaines of the same propor<g ref="char:EOLhyphen"/>tion,
as the two Bulwarks had which were ruined, and by this meanes euerie place
aswell regular as irregular maye be cutt off. Many other sorts of cuttings off might
be described, according to the situation of the place, and the manner of attemp<g ref="char:EOLhyphen"/>ting,
by the industrie of the lngenier, which hath the ordering of such cuttings off:
But seing the like inventions were abundantly practized in the Towne of Ostend,
the Lovers thereof maye peruse the 25 Plate of this bocke, and see what cuttings
off was vsed there, the ennemy having possessed halfe the towne, before he gayned
the whole.</p>
               </div>
            </div>
            <div type="section">
               <head>How one ought to carrie him selfe vpon an Assault.</head>
               <div type="subsection">
                  <head>The 36, &amp; 38 Plates, &amp; 156, &amp; 159, Figures.</head>
                  <p>IF the ennemie prepares to giue you an assault, and that his breach be great
enough, those within must labour by all meanes and seeke to stopp it &amp; to defend
<pb n="44" facs="tcp:1568:50"/>
them selues in the best manner they are able, and aboue all if it be possible to driue
in some strong piles vpon the top of the breach, which we before haue called <hi>pali<g ref="char:EOLhyphen"/>sadoes,</hi>
for an assault, described in the 33 Plate and Figure 140, each palissadoe having
2 yron pinnes some 10 ynches longe, driven through them, as we haue said that by
this meanes one may keepe them from comming vp and entring the rampart or
breach. Now seing the breach ought to be defended by able men, furnished with
armes fitting to such an end, ye must make choise of your best ablest, and most cou<g ref="char:EOLhyphen"/>ragious
men, which must stand vnder the breach to second those which helps to
defend it, and shall fall on, when they see their fellow-souldiers repulsed back. On
the inside of the cutting off you shall place some other troupes of a stronger body
then the former, to the end, that if those men, which defends the breach, should be
forced to retreate into the ditch, that the others at that very instant maye show
themselues vpon the top of the rampart of the new cutting off, and if there be any
meanes to plant a peece of ordinance or two vpon it (which maye be blinded till
the Besiegers falls on) it will greatly offend them. The entrances, and sallies to the
said breach, ought in my opinion (if the cutting off be in the <hi>tenaille</hi> of the angles
t. l. Figure 156, &amp; b, 159) of an easie accesse, being raised as litle as possibly may be,
whereof the one maye serue for an entrance, &amp; the other for a comming out, choo<g ref="char:EOLhyphen"/>sing
the one or the other for the most commodious, according to the situation of
the place. And seing the cuttings off (as we haue said before) are esteemed the
best, which haue two angles flanking, ye must at the first make the cutting off, h,
k, l, m, n, i: Figure 159, to be raised euen with the height of the rampart, or according
to the height of the Bulwarks, if they be a litle lower, then the curtaine, if that the
batteries doe not commaund them. For in such a case, you must raise it much
higher, that from thence (with the more vivacity, and courage) ye maye repulse
the Assaillants. But seing this cutting off is of a better defense, and is much more
labour, then the cutting off, a, b, c, ye must consider well, it time will giue you leaue
to doe it, if not ye maye make vse of the cutting off a, b, c, for oftentimes necessity
hath noe lawe.</p>
                  <p>And seing experience hath taught vs too much what difficulties, one shall meete
with all in such cutting off: the onely way is in my minde to hinder (as much as
possibly maye be) the Ennemies descent into the moate: which besides other in<g ref="char:EOLhyphen"/>ventions
that are in vse, maye be done by the meanes of the cuttings off, at the lines
a, b, &amp; c, d, Figure 159, which are made here right opposite to the angles of the Bul<g ref="char:EOLhyphen"/>warkes
from one part to an other, besett with small muskett baskets &amp; filled with
Earth as we haue said before.</p>
               </div>
            </div>
            <div type="section">
               <head>Of Casemates.</head>
               <div type="subsection">
                  <head>The 37 Plate &amp; 157, &amp; 158, Figures.</head>
                  <p>FOr asmuch as we haue seene the difficulties, which Casemates haue caused to
the besieged, and the small benefit they haue receiued by them, which not
withstanding haue bene made with all the industrie that possibly might be, there<g ref="char:EOLhyphen"/>by
to hinder an Ennemie from putting ouer a moate and makeing his batteries
vpon the brinke of the moate, to beate downe the flanks, and to dismount the
peeces of ordinance, planted in the said Casemates, to wit, that besides the expence,
the gorges are made by this meanes lesser, the Orillon or pillow being noe more
<pb n="45" facs="tcp:1568:50"/>
then the 2/3 of the flanck, and is of litle resistance, and on the other side giues but litle
advantage, being soone stopt, as we haue seene in time past: I was minded not to
haue spoken of them at all, though I esteeme them good, if they were made in such
a sort, that there mouths might not be stopped vp, and the peeces within them
dismounted: which hath not bene done hitherto to my remembrance. For<gap reason="illegible" resp="#TECH" extent="1 letter">
                        <desc>•</desc>
                     </gap>f<gap reason="illegible" resp="#TECH" extent="1 letter">
                        <desc>•</desc>
                     </gap>hese
Casemates be made of brick batts, when the Besiegers shall play vpon them with
there ordinance, the bricks flying into the port-holes will doe more hurt to the Ca<g ref="char:EOLhyphen"/>noniers,
and other men, then the Ennemies bullets themselues, and by this meanes
the portholes wilbe easely filled, and stopped vp, as wee haue seene in diverse
places. If your Casemate be made of Earth, ye must giue it a great Talude (that is
much slooping) which maketh the gorge so narrow, namely in those Fortresses,
which are vnder an <hi>Hexagone,</hi> that oftentimes there wilbe hardly any entrance into
the bulwark, which we call the gullet, the Orillon, and the flanke very litle, and
consequently wilbe of litle resistance, wherein they finde so many difficulties, that
many great Captaines haue resolued wholly, to leaue them vnmade. If one could
not preserue them otherwise then they haue done to this present: I should ap<g ref="char:EOLhyphen"/>proue
of them: But seing I cannot resolue of a thing, which I dare not wholly ap<g ref="char:EOLhyphen"/>proue
off, because experience, and many men slaine in the warres haue not found
it good, this is my opinion also. In the Figures 157, &amp; 158, of the Plate 37, a, b, is
the vtmost end of the shoulder, the double of p, a, Figure 157, the mouth, or port<g ref="char:EOLhyphen"/>hole
of the Casemate, and as b, p, maketh 150, foote, so p, a, will make 50 foote, p, t,
equall to p, a, wilbe likewise 50 foote, t, v, is 36 foote, from <hi>a</hi> ye shall draw a line to <hi>u,</hi>
that ye maye the better discouver the exteriour brinke of the moate, and the said
t, u, shall containe three portholes for three peeces of Canon, which shalbe vauted
ouer from d, e, to, t, u, with steps as the Figure 158 demonstrats, marked betweene
t, v, and e, d, in such sort that the first Vault on the side of e, d, is closse by the super<g ref="char:EOLhyphen"/>ficies
of the water enlarging or raising the said Vaults more and more, vntill that
the last vault towards t, v, be raised aboue the superficies l, f, g, k, which is the plate<g ref="char:EOLhyphen"/>forme
of the Casemate, some 3 foote, or thereabouts, and seing that t, e, &amp; d, v, are
about 20 foote, ye shall advance as farre as possibly ye can the parapet t, f, and g, v,
as much as the canon, and the place will permit you, to giue the better soliditie &amp;
firmenesse to the parapet of the Casemates. Then vpon the topp of the basis f,
g, e, d, the said parapet shalbe so raised that the inside f, g, shalbe lined with a wall,
that it maye prevent the falling downe of such a heigth, &amp; so that the ennemie
maye not discover the vpper part of your vault, h, i, k, l, and firmely joyned asvvel
to the wall, as to the Orillon and on the outside with hard Earth, as strong as possi<g ref="char:EOLhyphen"/>bly
maye, going downe sloopingly, that it maye not be subject to tumble downe
into the moate, and this will hinder the Ennemie greatly from entring into the
moate and putting his gallerie ouer. For by this meanes they must be driuen first
to beate downe the shoulder, and make it to fall into the moate at the space p, a, e, d,
which for this reason must be made as deepe, as possibly ye can, to the end, that
the portholes 3, 4, &amp; 5, be not easely stopt, the place l, k, f, g, is about 20 foote vnco<g ref="char:EOLhyphen"/>vered,
and the vault i, h, l, k, also 20 foote broade. The line h, i, is about some 54,
foote: the Colomne is made in the midst of l, k, to make the vaults crosswise: be<g ref="char:EOLhyphen"/>cause
the distance betweene l, k, is too great, to make there a single vault, which
maye serue to make vpon it the parapet of the superiour place, to gayne more
place for the gorge, and to lodge the Canoniers, and there amunition dry.</p>
                  <p>The entrance into the <hi>Casemate</hi> must be in that place, where m, n, is, vnder the
rampart, and must be vaulted from m, to i, &amp; from n, to o, being some 10 or 12 foote
broad, or thereabouts, that ye maye the better draw in your ordinance &amp; all what
<pb n="46" facs="tcp:1568:51"/>
ye haue neede of into the Casemate, and make it as high as necessity requires: The
orillon a, v, y, b, is al together massie, that it maye giue the greater resistance. And
because ye maye the better vnderstand our intention, we haue added herevnto
the Figure 158, which raised worke is represented in perspectiue: in which ye may
see the parapet of the false bray, the port-holes of the Casemate, and other things,
which we haue thought necessarie to make knowne.</p>
               </div>
               <div type="subsection">
                  <head>The 38, Plate &amp; 160, Figure.</head>
                  <p>A Fortresse being thus provided with good false-brayes, aswell vnder the Bul<g ref="char:EOLhyphen"/>warkes,
as along the curtaines, broad according to our former plots: I could
wish that a Casemate weere made in that forme which wee shall now describe, and
that the curtaines, were drawne in as the farre as the bredth of the falsebray with the
parapet containes, to wit, that the false brayes vnder the Bulwarks might end on the
outside of the foundamentall lines a, b, and the like: and contrariewise, that in the
curtaines the said falsebrayes maye end within the said fundamentall line c, d, so
that the space i, f, g, maye be accommodated, as the Figure 160, representeth, to
plant therein two peeces of ordinance, which will worke noe small effect: &amp; by
this meanes the Casemates, wilbe better preserued then otherwise, because ye
neede not feare the flying of brick-batts about your eares, seing that the flanck e,
will serue as a stay and a covert therevnto: so that in stead of one shoulder ye shall
haue two, to wit, b, p, and c, e.</p>
                  <p>The descent into the false-bray, which goes round about the Bulwarke ought to
be made at m, and to come out at y, and seing one makes sometimes some privie
sallies, betweene A and p, one might also make the entrance into the Casemate in
this place, makeing a vault from m, to y, to wit, in the vnderpart of the Case<g ref="char:EOLhyphen"/>mate:
The entrance into the false bray from the curtaine ought to be made at w,
from one &amp; the other part. The letters q, r, s, t, v, represents the place where I would
maks Catts, if one resolues to make them: but seing I am not resolved about this
point, I will rather speake nothing thereof at this present.</p>
               </div>
               <div type="subsection">
                  <head>Figure 2. 160. &amp; 38. Plate.</head>
                  <p>IF the Bulwarke be not massie, but hollow, ye maye make your entrance into the
Casemate, as here towards o. r. p. l. z. and the entrance into it should be at the
point, l. all the space l. z. p. r. o. being open.</p>
               </div>
            </div>
            <div type="section">
               <head>Of Brasse ordinance.</head>
               <div type="subsection">
                  <head>The 39. &amp; 40. Plates and 161. 162. 163. 164. Figures.</head>
                  <p>WE were minded to haue treated of diverse other dependances belonging to
fortificatio<g ref="char:cmbAbbrStroke">̄</g>, as of bridges, gates, ports, foundations &amp;c. how townes &amp; publick
places ought to be fortified; but the Printer not willing to stay any longer for the
finishing of this booke, it is not possible for me to effect my intention, so that my
project also touching the casting of brasse ordina<g ref="char:cmbAbbrStroke">̄</g>ce is for this reaso<g ref="char:cmbAbbrStroke">̄</g> also frustrated,
having bene minded to haue described the proportion, aswell of their carriages as
of their charges, and other dependances about them. To which end I had orday<g ref="char:EOLhyphen"/>ned
these 4 brasse peeces which are vsually cast in the vnited provinces, according
to the scale herevnto annexed: whereof the least carries a bullett of 6 pound weight
with the Figure noted 161: the second is the Figure 162 &amp; carries a bullet of 12 pound
<pb n="47" facs="tcp:1568:51"/>
weight, the third 163 carries a bullett of 24 pound, and the fourth marked with the
Figure 164. carries a bullet of 48 pound, of the two last, the first is a halfe Canon,
and the last a vvhole canon, or peeces for batterie: the two others are field-peeces,
bearing a bullet of 6, and 12 pound. In the meane while, he that desires to know
the proportions of them maye make vse of this scale, till we vvrite more at large
thereof.</p>
               </div>
            </div>
            <div type="translators_note">
               <head>ALBERT GIRARD.</head>
               <p>BEfore vve come to describe the tvvo tables, vvhereof vve haue made mention before,
supputed of a nevv: vvee vvil explaine some termes, vvhich vve haue introduced, be<g ref="char:EOLhyphen"/>cause
they vvere namelesse before. To that end vve vvil take one of the Figures of the
eleventh Plate excepting the last vvhich is the 68, and the line N C being dravvne, vvhich
vve vvill terme the gullet (to distinguish it from N A, or A C, the gorges) vvhich comes to
cutt through the <hi>Capitall,</hi> being dravvne further vvithin the Figure, in a point, vvhere
the letter Z, is made, then E, Z shalbe called <hi>(the extention)</hi> that is the lengthned capitall,
for the Bulvvarks extends so farre outvvard. Then the angle G, A, C, <hi>(the forme-flanck).</hi>
Also in the 60, or 61, Figure E L, shalbe called <hi>the Raid majour,</hi> and L A, <hi>the Raid minour,</hi>
finally, in the sixth Plate, the line D, F, or K, L, is called <hi>the surface</hi> as being placed before the
face (for <hi>surface</hi> is a vvord not much vsed, and as <hi>superficies</hi> signifies all one thing: ye
must not thinke that the second table is calculated amisse; because the progression of the
second flanks doe encrease, euen to that of the <hi>Heptagone,</hi> and then diminisheth: for if one
should continevv the table from the one end to the other, it vvould follovv, that the angles
of a <hi>Polygone,</hi> should be <hi>equidistant</hi> 130, degrees (vvhich vvell nigh containes <hi>the second flanke majour</hi> 8. 412) &amp; so haue the second flanks equal. vve vnderstand <hi>equi<g ref="char:EOLhyphen"/>distants</hi>
the one so much more then 130, as the oth<gap reason="illegible" resp="#TECH" extent="2 letters">
                     <desc>••</desc>
                  </gap> lesse. Likevvise <hi>the defense flanc<g ref="char:EOLhyphen"/>king,</hi>
diminisheth even to a <hi>Pentagone</hi> &amp; then augmenteth. The least that vve can ob<g ref="char:EOLhyphen"/>serue
is, vvhere the angle of the <hi>Polygone</hi> is 113, degrees, to vvit, of 53, 366, &amp; the <hi>Equi<g ref="char:EOLhyphen"/>distant</hi>
are equal. One maye say the like of the first table, vvhich decreaseth to 48 rod, and
aftervvard encreaseth. The fortification of a right line holding not vvith the one or the
other table, is placed betvveene them both. Those that vvill make vse of them proportio<g ref="char:EOLhyphen"/>nally,
for the building of <hi>irregular</hi> Figures commits noe small errours, though <hi>Marolois</hi>
vvas of this opinion, and so much the more, because the angles of the <hi>Polygone</hi> are about the
right angles, for the other <hi>Polygones</hi> differ alvvaies lesse one fro<g ref="char:cmbAbbrStroke">̄</g> an other, the further they
fall from the <hi>quadrate:</hi> so that vve to this end, if vve vvere vvilling to make vse of them,
the tables vvhereof the angles of the Polygones are progressiue of 3, or 4, degrees of space,
vvould be of a better choise, &amp; should here take place if time vvould permit vs. Let there
be here some small exemple thereof, and suppose, that one vvould fortifie an angle of 99,
degrees, vvhereof the tvvo sides are each of them 36 rod, and 3 primes, &amp; take a <hi>Pentagone,</hi>
or <hi>a quadrate</hi> to imitate, and let vs take <hi>a quadrate</hi> by vvhich meanes, he shall finde the
lines as they are herevnto annexed: vvhich done, let vs take the 7, Figure of the second Plate:
to speake more intelligibly thereof let vs demaund of him, hovv much the angle C B Evvilbe.
<list>
                     <item>BF Capitall 13, 15</item>
                     <item>BE The face 16, 00</item>
                     <item>ED The flank 5, 16</item>
                     <item>DF The gorge 6, 15</item>
                     <item>BA Defen. Flanc. 33. 94</item>
                     <item>Angles required</item>
                     <item>FBE 32 deg. 15. min.</item>
                     <item>BFD 130. 30</item>
                     <item>EDF 90.</item>
                     <item>Angles of a quadrate</item>
                     <item>30 degrees</item>
                     <item>135.</item>
                     <item>90.</item>
                  </list>
He vvill say, that to the halfe of 99 he hath added 15, and the summe is for the said angle C, B, E, and that the angle B, F, D, is adjunct of the halfe of 99, to vvit, 130, 30, aftervvard he can<g ref="char:EOLhyphen"/>not
<pb n="48" facs="tcp:1568:52"/>
denie, but the number of lines, vvhich he hath found maye receiue the angles of the
square-Bulvvarks halued as there annexed: for the lines are dravvne proportionally from
thence: as then the consequence vvilbe absurd, seing that the <hi>quadrangle,</hi> having the foure
lines knovvn &amp; D the right, vvhich are 5 common termes of both sorts of a <hi>quadrangle</hi>
abouesaid: The vnknovvne angles shall receiue each of them a certaine number of degrees,
as appeareth by our <hi>Trigonometrie,</hi> and not tvvo sorts of numbers for each angle, so that
if F, comes to be 135 degrees as it is, it can neuer make 130, and 30, and so of the rest. Novv
of one should take the angles as he requireth it, and the tvvo sides F D, D E, the other lines
vvilbe othervvise, then he hath calculated them, for in stead of 16, 00, the face, one shall
haue 51, 04; and in stead of its flanking 35, 94, ye shall finde onely 32, 44, and so of the rest,
vvhich is an errour of 3<gap reason="illegible" resp="#TECH" extent="1 letter">
                     <desc>•</desc>
                  </gap> rod, vpon 32, here then are small lines &amp; great faults, vvhat would
those be then in great and solid fortifications. To conclude, vve vvill propound one question
asvvell to exercise those vvhich are addicted therevnto, as for to end this discourse: A square
fortresse regular hath the face 24 rod, &amp; the curtaine 36, vvith an angle forming the flancke
of 40 degrees: vvithout a second flanck: hovv many then vvill the other angles and lines
be? The manner to resolue this, and the solution ye shall see hereafter, vvhen vvee haue made
some treatie vpon that subject, vvith hope shortly to bring to light, the restauration of
<hi>Geometrie,</hi> touching the parts thereof, vvhich haue bene lost hitherto, vvhereof the Au<g ref="char:EOLhyphen"/>thours
are <hi>Euclid, Aristeus</hi> the elder, <hi>Eratosthenes,</hi> and <hi>Apolonius Pergeus,</hi> vvith some
other parts of the mathematiques all according to our vveake povver, by the helpe and grace
of God.</p>
               <trailer>FINIS.</trailer>
               <pb facs="tcp:1568:52"/>
            </div>
         </div>
         <div type="illustrations">
            <p>
               <pb facs="tcp:1568:53"/>
               <pb facs="tcp:1568:54"/>
               <figure/>
            </p>
            <p>
               <pb facs="tcp:1568:55"/>
               <figure/>
            </p>
            <p>
               <pb facs="tcp:1568:56"/>
               <figure/>
            </p>
            <p>
               <pb facs="tcp:1568:57"/>
               <figure/>
            </p>
            <p>
               <pb facs="tcp:1568:58"/>
               <figure/>
            </p>
            <p>
               <pb facs="tcp:1568:59"/>
               <figure/>
            </p>
            <p>
               <pb facs="tcp:1568:60"/>
               <figure/>
            </p>
            <p>
               <pb facs="tcp:1568:61"/>
               <figure/>
            </p>
            <p>
               <pb facs="tcp:1568:62"/>
               <figure/>
            </p>
            <p>
               <pb facs="tcp:1568:63"/>
               <figure/>
            </p>
            <p>
               <pb facs="tcp:1568:64"/>
               <figure/>
            </p>
            <p>
               <pb facs="tcp:1568:65"/>
               <figure/>
            </p>
            <p>
               <pb facs="tcp:1568:66"/>
               <figure/>
            </p>
            <p>
               <pb facs="tcp:1568:67"/>
               <figure/>
            </p>
            <p>
               <pb facs="tcp:1568:68"/>
               <figure/>
            </p>
            <p>
               <pb facs="tcp:1568:69"/>
               <figure/>
            </p>
            <p>
               <pb facs="tcp:1568:70"/>
               <figure/>
            </p>
            <p>
               <pb facs="tcp:1568:71"/>
               <figure/>
            </p>
            <p>
               <pb facs="tcp:1568:72"/>
               <figure/>
            </p>
            <p>
               <pb facs="tcp:1568:73"/>
               <figure/>
            </p>
            <p>
               <pb facs="tcp:1568:74"/>
               <figure/>
            </p>
            <p>
               <pb facs="tcp:1568:75"/>
               <figure/>
            </p>
            <p>
               <pb facs="tcp:1568:76"/>
               <figure/>
            </p>
            <p>
               <pb facs="tcp:1568:77"/>
               <figure/>
            </p>
            <p>
               <pb facs="tcp:1568:78"/>
               <figure/>
            </p>
            <p>
               <pb facs="tcp:1568:79"/>
               <list>
                  <item>1. De oude polder.</item>
                  <item>2. Cassemat.</item>
                  <item>3. Het nieuwe west ravelyn.</item>
                  <item>4. De west poort.</item>
                  <item>5. Nieu porcespic.</item>
                  <item>6. Helmont.</item>
                  <item>7. De oude Sluis.</item>
                  <item>8. Santhil.</item>
                  <item>9. Halve maen so hooch als de wal.</item>
                  <item>10. Sluyseerst gemaeckt omt'water inde graft te setten.</item>
                  <item>11. Trencement.</item>
                  <item>12. Bolwerck.</item>
                  <item>13. Contrescherp.</item>
                  <item>14. Halve maen.</item>
                  <item>15. Een sluyseerst gemaeckt.</item>
                  <item>16. Sorte nae de polder halve maen.</item>
                  <item>17. Eee sorte.</item>
                  <item>18. Nieu polder.</item>
                  <item>19. Sorte.</item>
                  <item>20. Nieu helmont.</item>
                  <item>21. Sorte.</item>
                  <item>22. Nieu west poort.</item>
                  <item>23. Vlammenburch.</item>
                  <item>24. Peeckels bolwerck.</item>
                  <item>25. Nieu Polder.</item>
                  <item>26. Spaens bolwerck.</item>
                  <item>27. Koestal. oft Suyt oost bolwerck.</item>
                  <item>28. Suyt bolwerck oft Treurenburch.</item>
                  <item>29. De vrygaerden.</item>
                  <item>30. Polder halve maen.</item>
                  <item>31. Baterie.</item>
                  <item>32. Catte.</item>
                  <item>33. Hier leggen de schepen.</item>
                  <item>34. Nieu Santhil daer de oude kerck plachte sta<gap reason="illegible" resp="#TECH" extent="3 letters">
                        <desc>•••</desc>
                     </gap>
                  </item>
                  <item>35. Nieurve haven.</item>
                  <item>36. Noortwest bolwerck.</item>
                  <item>37. De oost poort en het ravelyn.</item>
                  <item>38. Oost ravelyn.</item>
                  <item>39. Spaens halve maen.</item>
                  <item>40. Slimmers halve maen.</item>
                  <item>41. Elcks verdriet.</item>
                  <item>42. Suyt oost ravelyn.</item>
                  <item>43. Suyt ravelyn.</item>
               </list>
            </p>
            <p>
               <pb facs="tcp:1568:80"/>
               <figure/>
            </p>
            <p>
               <pb facs="tcp:1568:81"/>
               <figure/>
            </p>
            <p>
               <pb facs="tcp:1568:82"/>
               <figure/>
            </p>
            <p>
               <pb facs="tcp:1568:83"/>
               <figure/>
            </p>
            <p>
               <pb facs="tcp:1568:84"/>
               <figure/>
            </p>
            <p>
               <pb facs="tcp:1568:85"/>
               <figure/>
            </p>
            <p>
               <pb facs="tcp:1568:86"/>
               <figure/>
            </p>
            <p>
               <pb facs="tcp:1568:87"/>
               <figure/>
            </p>
            <p>
               <pb facs="tcp:1568:88"/>
               <figure/>
            </p>
            <p>
               <pb facs="tcp:1568:89"/>
               <figure/>
            </p>
            <p>
               <pb facs="tcp:1568:90"/>
               <figure/>
            </p>
            <p>
               <pb facs="tcp:1568:91"/>
               <figure/>
            </p>
            <p>
               <pb facs="tcp:1568:92"/>
               <figure/>
            </p>
            <pb facs="tcp:1568:93"/>
            <pb facs="tcp:1568:93"/>
         </div>
      </body>
   </text>
</TEI>
