To Describe a Fort of Five Bulwarks, or any other; so that the Bastion, or Flanked Angle of 8 Bastions or Bulwarks exceed not 90 Degrees by the Line of Chords.
FIrst, Draw an Obscure Line, as AB; and upon A, as a Center, with the Chord of 60 deg. describe an Arch, as CDE; and from C lay down half the Polygon Angle (which in the Table following the Figure you shall find to be) 54 deg. as CD; also the same again from D to E, and draw the Line AE. Now divide the half Polygon Arches CD and DE each into three equal parts, as in FHIG, and from two of those parts from D, as F and G, draw Lines unto the Bastion Point at A. Then take any convenient Distance, and lay the same on those Lines from A unto K and L, which shall make the Front or Face of the Bulwark. Next, from the shoulder at K let fall a Perpendicular to AB, as KM; and on the Center at K describe an Arch of 60 deg. from M towards N, and from M lay down on the same Arch 50 deg. or more exact 49 deg. 24 min. and so draw KN, which will cut the Se∣midiameter of the Polygon in the Point O; so shall AO be the Capital Line of the Bastion. Then from O draw a Line parallel to AB, as OP; so shall you have OR for the Gorge Line, and RK the Flank. Now for the Curtain, take half the Front AK, as AT, and lay it down three times from R towards P, which will fall in S; so is RS the Curtain. Then on the Point at S erect a Perpendicular, as SV, equal to RK, which shall be the Flank of another Bastion; and so the Front KA being laid from V, shall cut the first Line AB in B; so drawing VB, you have the Front of the same Bastion.
Lastly, Divide AB in the middle, as in W, and from W let fall a Perpendicular to AB, which will cut the Semidiameter of the Polygon in the Point D; so is D the Center of the Polygon. And with the same Semidiameter DA you must describe a whole Circle, of the which AB is the ⅕ part thereof, which Distance will reach from B unto X, and from X unto Y, and so to Z, and your first Point at A, where you begun your Work.
For the other Bastions, they may be easily transported from the first Bastion. And note, That if your Fort exceed 8 Bulwarks, you must add 15 deg. to half the Poly∣gon Angle, so have you the Bastion Angle; and then work as before. But in the Forts that exceed not 8 Bulwarks, where the Bastion Angle will not be above 90 deg. you must take the 2/3 part of the Angle of the Polygon.
The longest Line of Defence is from A unto Q, and should not exceed 720 Foot (because of being within Musket-shot) the Curtain RS about 420 Foot, and the Front AK 280 Foot: And for the Flank RK, and Gorge RO, their proportion commonly is as 6 to 7: but the Angle KOR forming the Flank is about 40 gr. by which the Proportion is neer as 5 to 6.