The art of fortification, or architecture militaire as vvell offensiue as defensiue, compiled & set forth, by Samuell Marolois revievved, augmented and corrected by Albert Girard mathematician: & translated out of French into English by Henry Hexam

THE SECOND PART, TREATING OF THE FORTIFICATION OF PLACES IRREGVLAR. BY SAMVELL MAROLOIS, Revewed, Corrected, & Augmented BY ALBERT GIRARD SAMIELOIS. (Book 2)

THe Fortification irregular being more variable by an infinite deale then the regular, 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 equilaterall, that is, of equal sides; which is well cōtained amonge the regular Polygones. 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∣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∣fies such a place out of the enclossure, then otherwise, as I hope I shall demonstrate vnto you hereafter.

The 18 Plate & 84. Figure.

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∣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 Hexangular, built as a tenaille, 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 presēt figure. But if thē afterward, ye finde that the matter requires, that the angles exteriour maye be made, and reduced into Bul∣warks, as then ye must follow our generall rule, giuen for our regular fortification, noted before in the 10, & 11 Plates, and shall draw the vtmost angles, to wit privie lines, as from G to A, then having resolued to laye out the proportiō 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 frō H an other arch of 4 parts towards the same point I. cutting the first at the point I▪ 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 diagonall that is, vvhich extends it selfe from one corner to the other) at S. and so AS wilbe the Ca∣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, & the angle being made 40 degrees, you shall haue the capitall line Q, S, and R, T the flanke S, T the Gorge, & 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∣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∣cation; but also of all others, as wee hope shall appeare by the rest.

How to fortifie a square fortresse with a Tenaille.

Figure 85.

FIrst ye must consider, whither it were more fitting, to fortifie the angles of a quadrate, thē to fortifie it with a tenaille, 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, & OPQ, in the midst of the sides of the squares, so that the lines, which forme the tenailles be all alike among themselues; as A B C D E F G H &c, and the angles also equall one to another, which is done by drawing the two diagonal lines frō 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 Isoceles &c, from the distance D E, ye shall haue the figure Octoan∣gular formed into a tenaille, whereof all the angles wilbe right, which afterwards may be made angles of the Bulwarks, when there is accommodation to make a fort royall thereof, & that the distance frō 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∣ction, and such a fortificatiō 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 & expēce, 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 thē 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. & 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, & 5, and cutting the Diagonall G, R, in the point X, vvhich shalbe the center of the Bulwarke through vvhich point X a para∣lell line, being drawne to the line I Gas X X, and from the point 2, drawing a per∣pendicular line vpon it, as Y 2, ye shall haue all the essentiall parts of this fortifica∣tion, namely, the line I 2. shalbe the face, 2 Y the flanke: Y X the line of the gorge: YT the curtaine; & ZI the line of defēse flanking. According to vvhich the angles G, E, C, A, &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 & G, & nothing altered in all this fortification; but the lines of the tenailles 2, H. 5 placed vpon ST, TY, & 2 Y, vvhich in all are but a litle longer then the abouesaid 2, H, & 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∣out makeing any alteration in it. And because that in such places, noe false∣brayes cann be made, but with great expence; in regard they are made on the out∣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∣ter

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 & 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∣ces: but also by the continuall shooting of the muskettiers lodged in the said tra∣verses, which would doe great spoile & 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.

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 tenaille will be changed but a very litle, by the addition of Bul∣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, & 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∣couver the superficies of the water (if there bea••••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∣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∣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∣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.

To fortifie a Quadrilatera irregular in the forme of a trapeze.

Figure. 86.

LEt the Trapezoide (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.

To doe this, let there be described two Bulwarks vpon the angles B, C, the one being the angle of the Pentagone, and the other C approching, all in proportio∣ning the gorges, flanks, and faces according to the distance BC, saying by rule of three, if 56, 88 the Polygone interiour in the tables, giues the face 24, what will 40 rod giue, the side of the Polygone given B, C? the like doe with the flanke, gorge and

second flanke, according to which Dimensions afterward the said bulwarkes FGHIK, & LMNHE. are described.

And as the distance AD is two great, to describe two Bulwarkes vpon the an∣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∣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 Pentagone is defended, and from the other sides, are the flanks of the said Curtaines 2. A & 4. D defended: so that the flanks 1. 2. & 3. 4. are also sufficient to defend the two lengths A. 2. & 4. D. & forasmuch as it is to be doubted, that the neerer one approches to the abouesaid flanks of the said angles A & 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. & 3. 4. be not made too great, nor too farre assunder from the said angles A. & D. that the lines of defence coming out of the curtaine be made in the same sort, as the defenses of the Pentagone are, as is seene vpon the cur∣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∣formes, will beare: in such sort, that the parts A 2 & 4. D. are but 15 rod, & the flanks 2. 1. & 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, & 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 demy Bulvvarke P. Q. M. N, having the flanke N M. 10 rod, which is more capa∣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.

An other way.

The 19. Plate, and 88. Figure.

NOw in such a fortification, which hath but one simple defense, the angles of the tenaille maye lightly be taken in, because that in the figure 86 N M. & N.

D. are so short: It were better in my opinion, to fortifie the said figure in this forme following.

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 Dodecagone, whereof the gullet (which is the distance from the one flanke to the other) ma∣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 Dode∣cagone hath the angle in the circumference of 150 degrees, the flanks will fall per∣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 Dodecagone, which is 150 degrees, makeing for euery angle of the flanke 75 degrees, and as much will the angles A 12, & 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∣portion: If the curtaine interiour and exteriour, vvhich are here alike contay∣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 Polygone interiour or exteriour in a right curtaine (which are equall) giueth for the face 24, what vvil the side of the Polygone A. 6. 34 1/2 rod, giue? ye shall haue for the face 11, 83 rod, which being placed from 3 to 4, & from 3 to 2 (first the angles 6. 3. 4. & 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 vpō 15 degrees, and shall make the lines 1. 2 & 4. 5 of such an inclinatiō, 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, & S, T, V, W, X. dessigned in the midst of the sides A, K, & R, P, according to their length. But be∣fore they are layd out, the tvvo sides A B, & C, D, ought to be lengthened so farre, that one maye make the angles B, K, L & 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∣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 Quadrilatere 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 obliquely, 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.

An other way to make the fortification of such a place regular.

The 19. Plate and 89. Figure.

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. & of the greatnesse of the poligone 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 Polygons, asvvel interiour as exteriour, to the intent, that the side of the Quadrilatere A, D, may serue for the curtaine. Then the angles I, F, E, & 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 & 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 sesquilatera, 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 regular, and royall, which will not cost much more, then the former irregular fortification abouesaid, the benefit whereof sur∣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∣mit it: As for the moates, ramparts, and parapets, they must be made as wee haue taught in the places of regular fortifications.

The fortification of a Pentagone irregular.

The 19. Plate and 90. 91 Figures.

LEt the Pentagone 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∣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.

rod

• A B 57.
• B C 50.
• C D 46.
• D E 56:

degrees

• A 72.
• B 135.
• C 111.
• D 97.
• E 125.
• 540.

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∣grees, and flanking greater then 150 degrees, against our former maximes, accor∣ding

to which ye shall make of the same angle A. an angle of the bulwarke, ma∣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∣warks, takeing heede, that the angle of the Polygone show what forme of a Bul∣warke one must built vpon, to wit, a Quadrate, a Pentagonall or an exagonall, pro∣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∣tion can beare of our regular figurs precedent: It wilbe necessary, that betweene the two Bulwarks D & 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∣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 Quadrate, 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 Pentagone, according to vvhich I take the shortest line of the tvvo BC; & 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 Pentagone, and will say by the rule of proportion, if a Polygone 56, 88 giu•••• 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 Pentagonall: holding this for an infallible rule, that the angles of the Poly∣gone, 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 competēt to builde a Bulwarke vpon, as appeareth by the 90 figure in the an∣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 Polygones interiour, then ye shall take them for sides of the Polygones exteriour, in tracing out the said fortresses vvithin them, & that according to the kinde of euery angle F, G, C, D, I, and in so doing your Pentagone vvilbe fortified.

An other way.

The 19 Plate & 91 Figure.

LEt the Pentagone 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

vpon the angles ofte figure to be fortified, observing wel by what meanes the said place maye be best made vp & with the least expenses, according to our former Maximes, 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 Pentagone 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 Pentagone, or else the Bulwarke of a Pentagone, 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, & F, I, serving for curtaines, and meeting with the other two sides of the Pentagone lengthned in the points G, & 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 & 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 fichant, 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∣said, to supply thereby the defect of the said line, & the better to blinde the flanks which by that great distance would lye very open.

An other way.

The 20. Plate & 92. Figure.

IF the place permits to alter the angles a litle, then the fortification wilbe the better, as is seene in the Pentagone A, B, C, D, E, which is the same with the for∣mer, where the angles of the Bulwarks are changed, and some faces of them vne∣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∣ned that the curtaines comes or runns a litle out of the sides of the Pentagone, 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 Exagone; I take the Bulvvarke of the Exagone, and place it at B, turning and removing it so long, till the line of the tenaille 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∣ritie, that the one receiue noe preiudice by the other, and so the faces F, H, and

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AL. wilbe equall, but FH, wilbe vnequall with FG. the second face of the bul∣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, & I. wilbe of a greater distance then the Bulwarks F, & 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. & K, I, according to the distance F, I, remayning notwithstanding within the bounds of regular fortification; and within the compasse of the maximes groun∣ded therevpon, vvritten before. And ye must note besides, that the interiour an∣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 tenaille 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∣quisite in such a case, and so accommodate the said bulvvarks cutt out in past∣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 Polygone as B. C. & C. D, and as this figure represents it to your eye.

Yet an other way.

The 20. Plate & 93. Figure.

IF you are desirous that the flanks of the Bulvvarks B, & C, fall vpon the side of the Polygone 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: thē ye shall make the line paralell, F, G, distant from the line B, C, as farre as the Polygone exteri∣our is distant from the Polygone interiour, in the Pentagone; because that the an∣gle G, ought to be Pentagonall, and if the line F, G, is shorter, then the Polygone exte∣riour in our table of lengths; ye shall sinde out a proportionable distance, in say∣ing: If the side of the Polygone exteriour 8125. giueth distance to the Polygones 1677 vvhat distance vvill FG, giue, that vvhich this rule wil produce shalbe the distance of the paralells B, C, & 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, & 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 Polygone irregu∣lar,

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. & 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 & 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∣taine must fall vvithin the inside of the figure Pentagonall 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 & flanks of the Bul∣warks, vvhich are vpon the one side of the Polygone, be alike amonge themselues, as those vvhich are noted in the 92. Figure, & according to our former rules giuen in our regular fortifications.

A way how to fortifie a right Curtaine.

The 20. Plate & 94. Figure.

IF it be needefull to fortifie a right Curtaine, vvhereof the angles of the Bul∣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∣culars A F, B G, C H, D I, & 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∣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∣gle of the Tenaille 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 Polygone 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 face being 24, the curtaine 36, the flank 12, rod, and the angle flanked right, that then the Capitall wilbe wel nigh 29, the gorge 17, the defense flanking 41. the line of the Poligone interiour, or exteriour 70. rod, the formed-flanked is 35 degrees, and 16 minutes.

How to fortifie a Hexagone irregular.

The 21. Plate, & 95, 96. Figure.

LEt the figure Hexagonall 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: & 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 & F, are but 108, & 110½ degrees, vvhich are the angles of a Pentagone, 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 & H, of a competent greatnesse to the cur∣taines, proportioning out the Capitall lines, the gorge, flanks and faces, according to the greatnesse of thē, & as we haue said before in saying: If 70, (which is the distāce 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 Capitall line, and in the like manner shall ye finde the line of the gorge, the flank, and the face of the Bulvvarks H, &, 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 Pentagone ye shalbe vpon the foresaid angle E describe the angle of a Pentagone, and seing that the line E, D makes 80 rod, vve vvill make the angles flanking interiour of the forme of a Pentagone, 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 & D is equall, reason requi∣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, & 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 & the faces, flanks and Cur∣taines in that forme, as vvee haue said aboue, euen as this figure Hexagonall 95. de∣monstrateth.

The 96. Figure.

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∣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 Pentagone, 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, vpō 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

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, & so made that O, W, and O, V, and ES, are of an equall greatnes, & 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 Exagone, 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 & 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.

Note.

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∣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; & the more spacious and larger the flanks and gorg•••• 〈◊〉〈◊〉, the Bulwarks are the better for them, according to our former Maxims 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 & drawne out vpon the same mea∣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∣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 & fasten them together with a litle waxe, that after∣wards he maye overcast the advantages, and disadvantages, which he is to expect.

How to fortifie an Irregular place lying vpon the side of a river.

The 22. Plate & 102. Figure.

LEt the forme irregular, which ye would haue▪ be the plate of Hardervvijck, noted by the numbers 1, 2, 3, 4, 5, 6, 7, 8, whereof the extremities (or vtmost ends) are 1 & 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∣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∣fend the other: for this reason we haue made the line of defense about 60. rod,

which is a longer distance then is giuen when one is to defend them with the Mus∣kett, or caliver. The others that must be defended with the Canō, maye be 1000 foot distant one from an other, or there abouts: because at the least, it will carry so farr over, that of••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∣ders much more Besiegers dessignes then that which is made by Canon shott, be∣cause that in the interim, while they are a chargeing and makeing readie, the Besie∣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 &, to blow it vp: but if the Besieged haue good store of ordinance so that they may play conti∣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 & 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 Sultan, 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∣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 Casemates 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.

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∣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

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. & 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, & 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, & 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∣selfe noe disadvantage, for an Ennemy vvho vvill employ all his knowledge & 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∣cient number of Muskettiers, to defend the space, betvveene the tvvo Bul∣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∣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 cuttingh off: 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 Polygone were drawne towards the point C. for the preventing of the smalnesse of the angle, 5. which causeth the smallnesse of the angles P & R. for with∣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∣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,

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∣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∣ses, villages, together vvith the ruine of man and beast. Which an Ingenier of a sound judgment ought wel to consider & 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.

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. & 10. 11. A, and the Demy V, X, ••, 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∣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, & Z doe, and yet is neere enough to defend well the face X, ••, as also the moate: euen as this forme demonstrateth, marked vvith the double blinde lines, 12, 9, 10, 11, A.

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∣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 & accō∣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∣soeuer they bee, either regular, or irregular.

Note.

THat in maritimate places, such as are situated by a riuer side, where the banks, or d••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.

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.

The 23. Plate, & 103. Figure.

LEt the tovvne irregular be A, B, C, D, E, F, G, & 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 & 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∣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 tenailles, 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 tenaille 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 Polygone begetteth the smallnesse of the angle flanking, & 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 avenues 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 avenue stronger, by dimi∣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•• other, without hurting, and weakning of an other, which one ought maturely to

consider, and not yeeld easely therevnto vvithout good and pregnant reasons. And seing these Countries, which lye lowe, and are subject to invndations & over∣flowings, the rivers are commonly bounded in vvith Banks and Dikes, for the pre∣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, & A.) vvhich sometimes are separa∣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 Doudan made in the forme of an Asses back, nar∣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 Beer that is, a Beare; in regard of the strength, vvhich makes it almost inviolable. Therefore the Basis, 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 Beares 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∣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∣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 vpō 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. & 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∣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 circular forme (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 Octogone, or thereabouts, that the Bulwarks, O & 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, & E. ye must make the two Bulwarks S, T. whereof the faces are 16 rod, the flanks 8 rod, & 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

also therein some speciall cuttings off, as wee shall declare vnto you hereafter.

Note that if the lines D, B, F, & E, be too short to make the Bulwarks vpon them, marked S, & 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 & 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 & 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∣fications, termed Royall, 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 Polygones, 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 Hexagone, because the angels X, and Z, make each of them 120 degrees, which are (indeed) the angles of an Hexagone as appeareth by the said table, in which are taken all the demensions belonging to an Hexagone, aswell the gorges, flanks, as the faces: and from them, ye maye drawe out your Bulwarkes X and Z, abouesaid, which wilbe more royall, 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∣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, & 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.

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∣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∣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.

How to fortifie a place situated by the sea-side, and to make therevnto a commodious Haven.

The 23 & 24. Plates, and the 103. & 104. Figures.

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∣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

ought to be made with free-stone, 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:

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 diameter, and some 8. or 10. foote longe, as the 24, Plate, and the 104, & 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 Hye, 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 Hye, 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.

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, cubicall 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, & 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 quadrangular chambers, 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. & 107. Figures.

This being done, then ye shall laye the Basis 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 Gridiron 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 t••lude, 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 Masonrie teacheth) and some sixe foote distant one from an other: then by this meanes, ye

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 paralellogramma) 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 Ostend 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∣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∣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∣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 & the Figure 112, in vvhich towne hath bin practized & 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∣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∣bions, or great Bassketts filled with Earth & 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 & sapps (whereof we in∣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 & B.

Of some loose Peeces in regular fortresses.

The 23. Plate & 111. Figure.

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 Decagone, 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, & NO, equall to the flanks TY, or SZ, and finally the lines IK, & OP, ansvvering to the points Q, and R. & 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, & V 6, but then the defenses of the Bulvvarks vvilbe of noe vse, because they blinde the faces LM, & 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.

How to make a fortresse, where two great riuers are not aboue 15, or 18, rod assunder one from an other, or thereabouts.

The 26. Plate & 113. Figure.

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 Admi∣rant of Arragon, that yeare as he withdrew his army from the siege of Bommel, which is a Fort situated in Bommelsvvard, betweene these two great rivers called the Mase, and the VVhale, haueing noe great distance betweene A & C, then some 80, rod, being the narrovvst place of the whole Iland, and consequently stronge by nature and situation, having but two avenues, or passages to come to it, to wit, one vpon the left side from Rossems field, and the other on the right side from Hervverden situated at the vtmost end of Bommelsvvard, opposite against the Vorne, or Nassaus Fort, 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

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 Tenailles 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, & C, R, D, and finally the other two D, E, F, & F, G, H, &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 Pentagonall: 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∣cation and especially the angles D, & 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.

Note.

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.

How a Generall shall come to besiege a Towne.

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.

The 27, 28, Plates, and 114, & 115. Figures.

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 & 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 & wood for hutting and makeing of paillasses. The said Quartermaster Generall then having viewed all the grounds & chosen the best, shall drawe a draught of it, and show it to the Generall of the Army, which

being done and resolued, he shall then goe in all diligence with all the other parti∣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∣termasters shall line & 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, & 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▪ 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, & other quarters: and the rowes betweene them, which make the streets & back streets, shall be likewise & must be 8 foote: which rowes in their depth shalbe divided into 25 parts▪ 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∣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, ••, 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••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∣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∣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.

The Colonell is lodged in the midst of his regiment leaving a streete of 80 foote, as the Figures 114 & 115 demonstrate, to lodge therein his traine and the officers of his Regiment, as the Quartermaster, the Marshall, Chirurgian, & 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∣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∣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∣nie directly before his Captaines lodging & their to draw vp in parado & 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 & Gentlemen of the armes in the reere next the 〈◊〉〈◊〉, 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, & 114 Figure, wee haue here represented the quarter of an English Regiment consisting of 20 Companies, as they were quartered (as I remember) be∣fore Gulick whereof the Plate K, L, M, N, O, P, is the Colonels lodging, Q, R, S, T, his Kitchin & 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, & 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.

The 28, Plate, and 115. Figure.

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, & 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 & 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,

are lodged in this streete, behinde the Colonell. 2, & 3, are the Captaines tents, 16, & 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 & 3, and M, & N, maye be in a right line, whereby the alarme place should be of an equall bredth.

The 29. Plate & 121. Figure.

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∣ding as the place will afford it, having their front towards the place of armes, & euery regiment quartred together, being commonly 8 troupes in a regiment allo∣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, & 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∣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∣ging of the Horsmen 110 foote & 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∣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∣cause he commandeth for that time: but the army being in garnison, hath noe com∣maund ouer them.

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

part; to the end that those which haue neede of any thing, maye goe presently thi∣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 thē all manner of victuals and com∣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.

In the quarter of the Master of the ordinance is 〈◊〉〈◊〉 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▪ 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∣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∣penters which attends vpon the ordinance: E, the quarter of the saylours follo∣wing the traine of the ordinance. F, G. the Pioniers quarter. I, is the master Gun∣ners haueing 100, or 150. Canoniers vnder him, and the Provost marshall of ordi∣nance. H, The Miners quarter. L, the Magazine for the amunition, and his Com∣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 entrenchmēt. 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

things in good order, and that they maye presently be employed vpon any occa∣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.

Figure 123.

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▪ 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 & H are the French Regiments, namely F, Monsieur Chastillon his Regi∣ment, H, Monsieur Bethunes. A, the Regiment of Count Ernest of Nassou: B English companies commaunded by Monsieur Medkercke Lieut. Colonell to Ge∣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, & the greatnesse of the whole quarter in Generall.

Figure 124. & 125.

ANd because commonly the Captaines, after their souldiers are hutted, build Hutts in the place, where their tents stood, being warmer, & 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.

Figure 126.

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∣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. & 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, & 4) to the intent that one maye lodge more men in them to defend the skirt AB, the Overtures 13, 14, 15, & 16, are the avenues, passages and entrances into the generall quarter: whence it is necessa∣rie, that a Quartermaster Generall ought to haue true notice of the number and qualitie of the Regiments & companies, that he maye dispose of them according as the place and the nature of the ground will afford, and for the better effectua∣ting of what is said before, it would be good, to draw out a draught of the great∣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 & 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,

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∣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.

The 29 Plate, Figures 116, 117, 118, 119, & 120.

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, & 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 thē, and not to entrench the inside (to wit in the entrenchments of the campe) as appeareth by the en∣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∣ment, that the space A & C, being open, would be sooner taken in then the square: but I leaue this to your consideratiō, 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∣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∣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∣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∣nemie, to hinder their Victuals & 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

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∣ding good in such entrenchments, which are made without the circuit of the quar∣ter, especially, vpon the Avenues that they maye lodge in them some 25, or 30 men to gard them, & 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, & 117, demonstrate, because they are wholly enclossed, having but one entrance as narrovv as possibly maye be, being advanta∣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∣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∣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∣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•• 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 Advenues and passa∣ges, to hinder thereby the attempts of an Ennemie, vvhich secks as much as possi∣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 & perfe∣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, & 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, & 5, or 6, foote high, with a footebanke some 3 foote with the taluds, accor∣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∣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

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∣banke, a foote and a halfe high, that ye maye the better descend from the other to charge & 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.

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, & an O omitted at the interfection of F, H, and of a paralell through E, to B, C.

A B C D.

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.

B E F I.

F, H, 5, being multiplyed by I, H, 1/•• the halfe of the product vvilbe 1 1/4 for the triangle F, H, ••, 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. & 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.

L M K, and all the rasing.

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 & 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, & O P Q, 1 1/••, vvhich make 5 1/••, and vvill remayne 62 7/•• for the trapeze M, T, S, R, which diuided by the depth which is 6, it will giue 10 23/4•• 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.

The 33 Plate, and 140. Figure.

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,

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^r. Francis Vere did in Ostend) 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 frize Ruyter, and by vs a turnepike (as also your quadrangular tanternailes cast dovvne vpon a breach) are of singular vse, to barrocadoe, and stopp vp places▪ A Turne-pike is made in this manner follovving:

The 33 Plate & 141 Figure.

TO make a turne-pike, ye must take a round sparre some 12 or 15 foote longe, and about 5, or 6, ynches in diameter, 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 sexangular forme, that the circuit maye be divi∣ded into three equall parts, and in euery part, ye must boore a hole as is said one vn∣der an other, that the demypikes 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.

These turne-pikes 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 axeltrees 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∣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.

OF APPROCHES.

The 31, & 32 Plates, and 127. 128. 129. 130. 131. 132. 133. 134. Figures.

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 Monsieur Doncker in his life time Controuler of the fortifi∣cations in the vnited provinces, and besides at the siege of Gulick Controuler of the princes of Brandenburgh and of Nieuburgh 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.

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.

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.

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.

The Figure 130 is a pickaxe, well knowne to workemen, vvherewith ye digg vp a stonie & hard ground, into which a spade or a showell will not enter.

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.

The 132 Figure is a hatchet, to be vsed with one hand.

The 133 Figure is an Axe, to be vsed with both hand:

The 134 is a lesse kinde of axe, vsed with both hands not vsuall in these parts.

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 i••nographick 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.

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∣sions, aswell in hutting, as to be vsed in trenches & works.

The 138 Figure is a kind of a crooked bill, serving for the same vse.

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.

The 33 Plate & 144. 145. Figures.

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 thē 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∣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••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∣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

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∣ment ought to be maturely considered, that your dessigne maye not be hindred or fore-slowed.

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 tenaille, 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∣drance there vnto.

The place thē being resolued on, a certaine nūber 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∣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 Sentinell perdues, 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 Corps de garde made pur∣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∣selues to their armes, and cast away their materials, retyring softly (with the gards abouesaid) if they cannot make the place good, to the Corps de garde 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∣ten back, the commaunded men maye fall instantly to their vvorke againe, and

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∣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 thē 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 Corps de garde 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 & encourage his men, that the said Corps de garde maye be in defense before daye, to the end, that if the Ennemie should sallie out vpō the trenches, that from the same Corps de garde 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 & deepe as necessitie shall require. They ought to be made in my opinion in such a manner, that the two opposite an∣gles doe enfile the said thrench as appeareth by the Figure 117, Plate 29, and by the Corps de garde 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 Corps de garde: 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 Corps de garde, and the Trench, and so the said Corps de garde will flanke the said trenches on that side where they lie most open as ye maye note by the Corps de garde in the 4, Figure, 145 & 33 Plate.

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••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 & the Sergants to the souldiers of every company.

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∣tious, as some times 6, 8, foote, or more, as necessity requires. For oftentimes they

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 vpō 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∣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∣dition in such cases hath wrought many great effects.

When you are approched so neere your Ennemie, that by reason of their con∣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 vpō the point or side of the Bulwarke, which ye intend to take in, as the point, I, & 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.

According to which we haue made the Figure 144, whereof P, Q, are two Bul∣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 Corps of the Fortresse) in the angle B is made a Corps de garde 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, & I, E (before ye come to peerce through with your sapp) ye ought to make the lines L, O, & 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, & V, S, as the said Figures 144, & 145. shewes. If the Corps de garde 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∣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.

Figure 142. 143.

WHen ye beginn your trenches of Approche, ye commonly make some batterie, that vnder the favour thereof your men maye worke forward with

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 & 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 Demy-Canon, 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 & 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•••• 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∣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, & the 34, Plate, There are vsually made three sorts of Gabions, to wit, the ordinary of 6 foote high & 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. & 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∣tweene the Axeltrees of each peece one both sides & 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.

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 & 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

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.

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 & 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∣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∣dingly; The said plancks must be layd both at length and sidelings, and the hur∣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∣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∣beares not to offend, yee aswell by hand granadoes as otherwise.

How to pierce through a Counterscharfe, and to make a Gallerie over a moate.

The 34 Plate, and 150. 151. 152. & 153, Figures.

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, & 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∣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

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, & 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∣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.

Being gotten through the Counterscharfe and come to the edge of the moate: ye presently cast abundance of fagots, brush & 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 oakē 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∣lence of canon, and aboue the gall••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∣ring, which fire-rake is described in the 31 Plate, by the Figure A.

The 151 Figure.

WHen you haue putt over your gallerie (as we haue said) then you must be∣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 & wor∣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 & to abandon it, and so beginn an∣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.

These mines are commonly made in the forme of a paralellograme or a long square, to wit, the chamber in which the pouder is layd, must be 4 or 5 foote high,

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∣rour, and hurt of the besieged: when ye would blow vp the vpper part of the ram∣part, thē 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∣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 exhalatiō from breaking out backward, towards the gallerie, which one ought deligently to prevent, in shunning those inconveniences and mischiefs, which of∣tentimes by such casualities haue hapned heretofore.

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, & 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∣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∣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 & more spatious. But seing this is yet vnresolved, I will leaue the judgment thereof to those which haue more experience therein then my selfe.

How one must be prepared against a Siege.

The 35 Plate and 154 & 155. Figures.

HAving succinctly spoken of Approches, Sapps, the descent into a moate, gal∣leries and mines: me thinks it will not be amisse now to treate of the prepara∣tions which must be made against a seige.

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 takē for materials, amunition, and victualls (whereof I doe not in∣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 & 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 defēse, which we intēd to speake of here∣after (according as ye shall finde the weaknesse of the place to require, & as time will permit you to doe it before ye be besieged) as well without the towne as within, to make good entrenchments & 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∣siegers from getting into your moate, and to prolonge the siege with hopes of re∣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•• 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∣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 Gulich 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, & 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∣taine ••, 8, and so might haue saved the Raveline a. And betweene the two Bulwarks of the towne 4, & 5, the Raveline r, & o, betweene 3, & 4, and so haue saved the en∣trenchment n, which runs out farre frō the angle 3, and is of noe great defense. The Raveline k, is made betweene the Bulwarks 2, & 3, to take away the entrenchment m, made in a Tenaille, but the sides being of a very small distance, & for this consi∣deratiō 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

Horneworks, is, that the Horneworkes d, & 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∣tend acknowledging that experience strikes a great stroake in all occurrence, saving that I am onely permitted to giue advise therevpon.

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∣nesse of the Rampart, and as wee haue taught in the Plates of our regular fortifi∣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••ow and hinder an Ennemy from advancing his approches.

The 38 Plate & 159 Figure.

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∣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∣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 Corps de garde, that if the enne∣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, & being so puzled they wilbe constrayned euery time to alter thier des∣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.

Of Cuttings off, aswell generall, as particular.

The 36 Plate & 156 Figure.

IF an Ennemie be gott into the skirt of the Bulwarke g, h, and that one hath not time to cutt it off royally, & yet you are resolued to make him gayne the place

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, & 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 & 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.

The 38 Plate & 159 Figure.

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 tenaille 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, & e.

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, & the ditch p. q. r. s▪ 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.

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∣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, & 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∣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∣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.

How one ought to carrie him selfe vpon an Assault.

The 36, & 38 Plates, & 156, & 159, Figures.

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 & to defend

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 pali∣sadoes, 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∣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 tenaille of the angles t. l. Figure 156, & b, 159) of an easie accesse, being raised as litle as possibly may be, whereof the one maye serue for an entrance, & the other for a comming out, choo∣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.

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∣ventions that are in vse, maye be done by the meanes of the cuttings off, at the lines a, b, & c, d, Figure 159, which are made here right opposite to the angles of the Bul∣warkes from one part to an other, besett with small muskett baskets & filled with Earth as we haue said before.

Of Casemates.

The 37 Plate & 157, & 158, Figures.

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∣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

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••f••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∣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 Hexagone, 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∣proue of them: But seing I cannot resolue of a thing, which I dare not wholly ap∣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, & 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∣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 a ye shall draw a line to u, 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∣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∣forme of the Casemate, some 3 foote, or thereabouts, and seing that t, e, & 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 & 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, & 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∣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, & 5, be not easely stopt, the place l, k, f, g, is about 20 foote vnco∣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∣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.

The entrance into the Casemate must be in that place, where m, n, is, vnder the rampart, and must be vaulted from m, to i, & from n, to o, being some 10 or 12 foote broad, or thereabouts, that ye maye the better draw in your ordinance & all what

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.

The 38, Plate & 160, Figure.

A Fortresse being thus provided with good false-brayes, aswell vnder the Bul∣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: & 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.

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∣mate: The entrance into the false bray from the curtaine ought to be made at w, from one & 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.

Figure 2. 160. & 38. Plate.

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.

Of Brasse ordinance.

The 39. & 40. Plates and 161. 162. 163. 164. Figures.

WE were minded to haue treated of diverse other dependances belonging to fortificatiō, as of bridges, gates, ports, foundations &c. how townes & 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 ordināce is for this reasō 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∣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 & carries a bullet of 12 pound

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.

ALBERT GIRARD.

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∣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 Capitall, being dravvne further vvithin the Figure, in a point, vvhere the letter Z, is made, then E, Z shalbe called (the extention) that is the lengthned capitall, for the Bulvvarks extends so farre outvvard. Then the angle G, A, C, (the forme-flanck). Also in the 60, or 61, Figure E L, shalbe called the Raid majour, and L A, the Raid minour, finally, in the sixth Plate, the line D, F, or K, L, is called the surface as being placed before the face (for surface is a vvord not much vsed, and as superficies 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 Heptagone, 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 Polygone, should be equidistant 130, degrees (vvhich vvell nigh containes the second flanke majour 8. 412) & so haue the second flanks equal. vve vnderstand equi∣distants the one so much more then 130, as the oth•••• lesse. Likevvise the defense flanc∣king, diminisheth even to a Pentagone & then augmenteth. The least that vve can ob∣serue is, vvhere the angle of the Polygone is 113, degrees, to vvit, of 53, 366, & the Equi∣distant 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∣nally, for the building of irregular Figures commits noe small errours, though Marolois vvas of this opinion, and so much the more, because the angles of the Polygone are about the right angles, for the other Polygones differ alvvaies lesse one frō an other, the further they fall from the quadrate: 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, & 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, & take a Pentagone, or a quadrate to imitate, and let vs take a quadrate 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.

• BF Capitall 13, 15
• BE The face 16, 00
• ED The flank 5, 16
• DF The gorge 6, 15
• BA Defen. Flanc. 33. 94
• Angles required
• FBE 32 deg. 15. min.
• BFD 130. 30
• EDF 90.
• Angles of a quadrate
• 30 degrees
• 135.
• 90.

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∣not

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 quadrangle, having the foure lines knovvn & D the right, vvhich are 5 common termes of both sorts of a quadrangle abouesaid: The vnknovvne angles shall receiue each of them a certaine number of degrees, as appeareth by our Trigonometrie, 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•• rod, vpon 32, here then are small lines & 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, & 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 Geometrie, touching the parts thereof, vvhich haue bene lost hitherto, vvhereof the Au∣thours are Euclid, Aristeus the elder, Eratosthenes, and Apolonius Pergeus, vvith some other parts of the mathematiques all according to our vveake povver, by the helpe and grace of God.

FINIS.