600 FORTIFICATION. 
tke following Table flews the Meaflrts of the principal Lines and Angles in all regular Fortrefs , from Four to Twelve Sides 
incluftve } calculated, from the exterior Side , Normal and Face being taken as known Quantities in Yards* 
' Dodeca- 
■ gon. 
Undeca- 
gon. 
Deca¬ 
gon. 
Nona- 
gon. 
06 !agon. 
Hepta¬ 
gon. 
Hexa¬ 
gon. 
Penta¬ 
gon. 
Square. 
Names of the polygons. 
360 
360 
360 
360 
360 
360 
360 
360 
360 
The exterior fide in yards. 
695-46 
638-73 
582-50 
526-28 
470-36 
414-82 
360-00 
306-24 
254-56 
Radius of exterior fide in yards. 
296-20 
292-60 
2S8 -52 
285-86 
280-06 
272*44 
261•26 
247*90 
231*00 
Interior fide in yards. 
57 2 '14 
5 1 9 - 36 
466-90 
417-86 
3 6 5'96 
3 i 3'96 
261-26 
2T090 
163-34 
Radiusof interiorfide in yards. 
123-32 
I19*42 
115-60 
108-42 
104-40 
100-96 
98-68 
95-34 
91*22 
Capital in yards. 
86 
82 
78 
72 
68 
64 
60 
54 
+5 
Normal in yards. 
138-68 
142*90 
I 47‘34 
I 49 " 4 ° 
i 5 o '54 
151-80 
152-80 
154-22 
156-06 
Curtain in yards. 
76*18 
73 '96 
71-66 
6592 
62-12 
58-32 
54’54 
48-92 
4 o -54 
Flank in yards. 
104 
102 
100 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
Face inyards. 
2 76'34 
276-30 
2 75'46 
274-32 
272-86 
271-62 
270-28 
268-42 
265-96 
Line of defence in yards 
78-76 
74-84 
7 °' 5 S 
68 24 
64-76 
60-32 
54-26 
46-84 
37'48 
Demigorge in yards. 
3°° 00' 
3 2 ° 44 ' 
36° 00' 
40° 00' 
0 
0 
0 
5>° 26' 
6o°oo l 
7 2° 00' 
90° 00' 
Angle of the center. 
150 OO 
147 16 
144 OO 
140 OO 
135 0° 
123 34 
I 20 OO 
10S 00 
90 OO 
Angle of the polygon. 
102 46 
102 15 
101 43 
100 54 
IOO 21 
99 47 
99 13 
98 21 
97 01 
Angle of the curtain. 
128 18 
126 45 
125 09 
I 22 42 
121 03 
l 19 21 
*»7 39 
115 03 
hi 03 
Angle of the fhoulder. 
98 56 
98 16 
97 °8 
96 24 
93 36 
89 26 
83 08 
74 36 
61 56 
Angle of baflion,or flanked angle. 
25 32 
24 30 
23 26 
21 48 
20 42 
19 34 
18 26 
16 42 
14 02 
Diminifhed angle. 
I2 8 56 
13 I OO 
133 °S 
136 24 
138 36 
140 52 
143 08 
146 36 
i 5 ' 56 
Exterior flanking angle. 
46 yards. 
44 yards. 
42 yards. 
40 yards. 
40 yards. 
40 yards. 
36 yards. 
30 yards. 
30 yards. 
Breadth of the fofs, in yards. 
__;- , 
By the help of the preceding table, every thing rela¬ 
tive to the mafter-line of any fortrefs may readily be con- 
ftrudted. 
Prob. I.— To defcribc any of the polygons in the table.— 
Required to confirm?! a polygon in a circle : With the 
exterior radius of the given polygon, firftdefcribea circle, 
as fliewn in Plate II. fig. i. Apply the exterior fide 
equal to 360 yards within the circumference of that 
circle, from A to B, B to C, C to D, &c. as many times 
as the propofed polygon has fides. Then draw the lines 
AB, BC, CD, &c. and the polygon will be completed. 
To conftruEl a polygon on the exterior fide ; as fhewn at 
fig. 2.—Draw the exterior tide AB equal to 360 yards. 
At the ends A, B, make angles equal to the angle of the 
polygon, and in that pofition draw the lines AE, BC, 
each of -the length of AB. At the points E, C, make 
angles as before, and in thofe polltions draw the lines ED, 
CD, each of the fame length as AB; and thus proceed 
until the polygon is regularly formed. 
Prob. II.— To fortify any regular polygon in the table ; 
tr, to draw the mafler-hne of a regular fortrefs. —Firft.— 
From the exterior fide, fig. 3.—Make the exterior fide AB 
equal to* 360 yards, and find its middle C. Draw CD at 
right angles to AB, and make CD equal to the normal. 
Through D draw the lines of defence ADH, BDG. 
Make the faces AE, BF, each of their proper lengths. 
Transfer the diftance FE from F to G, and from E to H. 
Draw the curtain GH, and the flanks EG, FI-I. This 
being projected for every front or fide, the marter-line of 
the whole fortrefs will be defcribed. 
Secondly.— From the curtain, fig. 3.—Make the curtain 
GH of its proper length, for the given polygon. Make 
the angles of the curtain HGE, GHF, as in the table. 
In the lines GE, HF, take the flanks GE, HF, of their 
proper length. Make the angles of the fhoulders GEA, 
HFB, as in the table. Make the faces FB, EA, of their 
proper lengths. This method is adopted when the re¬ 
mains of an old fortification is to ferve for a curtain to 
fave time and expence. 
Thirdly.— From the interior fide , fig. 3.—Make the inte¬ 
rior fide IK of the length giveni a she table for the pro¬ 
pofed polygon. From each end fet off its proper demi- 
gorge KH and GI. On K and I as centers, with the ex¬ 
tent of the capital, as in the table, defcribe arcs at B and 
A. On H and G as centres, with the length of the 
line of defence, as in the table, cut the former arcs in A. 
and B. Draw the lines AH, BG ; in which take the 
faces AE, BF, and draw the flanks EG, FH.—This me¬ 
thod is convenient when modern ramparts and baftionS 
are to be annexed to any old walls furrounding a garrifon. 
Prob. III.— To corflruSl the plan of a baflion. —Draw* 
the line BK, fig. 4, and make the angles MBK, FBL* 
each equal to half the flanked angle. Take the lineal 
BF, BM, each of the length of the face. At the points 
F, M, make the angles of the fhoulder BFH, BMN, 
Make the lines FH, MN, each of the length of the flank. 
At the points H, N, make the angles FHG, MNa, equal 
to the angle of the curtain, and draw the pieces of the 
curtain HG, Na. 
Prob. IV.— The maflcr-line of a fortrefs being given; tt 
draw the plan of the rampart. —Draw the lines a, g, fig. 5, 
perpendicular to each face, flank, and curtain. In each 
of the lines a, g, take ag—z\ yards, abz= 20 yards, ac =8 
yards, ad ~6 yards. Through the points d, c, b, g, draw 
lines parallel to the mafter-line ; that is, to each face, 
flank, and curtain, interfering one another. Then the 
breadth of the rampart is reprefented by ^=24 yards ; 
of the parapet, by a</=6 yards; of the foot-bank, by 
dc—z, yards; of the walk of the rampart, by cb—\i yards j 
of the Hope of the rampart, by bg— 4 yards. 
When the baftions are made folid, the rampart fills up 
the whole fpace contained within the faces, flanks, and 
neck. The plans of fuch are reprefented by continuing 
the pair of lines b, g, forming the inner Hope of the ram¬ 
part, again!! the adjacent curtains, till they meet the ca¬ 
pital in the bread of the baflion, as at R ; but then this 
pair of lines is to be omitted again!! the flanks and faces 
of fuch baftions. 
In the center of baftions, as at fig. 8, it is ufual to 
erec! magazines for the ftores of powder, bombs, and 
other military engines; and alfo for provifions for the 
troops, and lodging. In tliefe pofitions, they are not only 
more 
