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.