CONSTRUCTION, 
oe or at oie very nearly fo to the lines of defence. 
en an enemy once makes a lodgment on the counter- 
frp, fe Mer a ee them whether they be fo placed or 
if flanks be difcovered, they alfo difcover, and 
bei Sher reveted or demi-reveted and formed of earth that 
is ay fettled, they are by no-means fo eafily ruined as the 
Datteries of the befiegers, which are formed of gabions and 
newly raifed earth. 
Count Pagan’s method of conftrudtion on a polygon, (fg: 
2.) is widely different from that of Errard, and alfo much pre- 
ferable. For inftead of making the angle of the flank acute in 
s being commonly made in them. 
thor makes his ace of defence Tike Errard’s, always rafant, 
but doeg not like him make'go degrees the maximum of his 
flanked angle, or angle of his baftion. 
- He delivers conftruGtions for three forts oe fortifications, 
namely, the great, the mean, andthe little. He fortifies or 
confiru&ts inwards, and in the great fortification makes the 
exterior fide equal to 200 toifes, in the mean' equal to 180 
toiies, and in-the little equal to 160 toifes. He allows 66 
“toifes to each face of a baftion in the great, 55 in the mean, 
and 50 in the little, in all figures above a fquare. 
the perpendicular to the exterior fide in the great fortification. 
in all figures, except the fquare-where it is 27 toifes, equal to 
30 toifes 
nearly, 
a in the mean equal to 24 toifes; and in the-little "’*Y 
equal to 
e dimenfions of thefe principal lines in thefe three kinds. 
of Faiasdiian, are contained in the news Table 
‘| Great Fortifi-\  ntean. Little. 
L4110N. 
| in all |. ‘In all In all 
Square. jother Po-| $quare. eve Po-| Square. luther Po 
; lygons. |. lygons. lygons, 
Extericr Sides.] 200} 200.] 180 | 180 | 160] 160 
}Perpendiculars.| 27 30 24 | 30 at 30 
[Facesofbaftions| 60 | 60 | s5 | 5 | 45 | so 
Suppofing then the exterior fide’ AB, (fee the figure} 
equal to 200 toifes in the in the mean 
aad 
° 
“of 
xe) 
5 
ctr 
= 
o 
oa 
jaa 
oO 
w 
oS 
we 
o 
So 
i 
load 
5 
eo 
= 
a’) 
ae) 
2 
t=} 
ct 
‘Bis 
~~ 
which is perpendicular to A B, take C D equal to 30 toifes, 
in. all regular figures of a greater number of fides than four. 
s EG, F H, ‘perpendicularly to 
the rafant Hines 0 or lines of eure ero 1 Fi, and form the 
his is — Pa- 
e figure i fl ar eae fappofed to have each: 
an a: to a toifes, as in mean fortifica- 
e A, the centre is therefore equal to 
éo degrees, and the angle “of the polygon to 0 120. C,.0 
C, is equal sa go Lipa the a ae aca CD is equal.to 
30, and the fac to 55 by conftruéction. 
: Now by meus of thefe lines and angles, the others are: eas 
fily found. And ia the firtt place, the wre diminué CAD, 
or the angle formed by the exterior fide A‘B, and the line of 
saa ee AA, is formed by ie following analogy, 
As AC, equal to go toifes, 
Is to CD, a to 30 toifes, 
' So is radius a 
To the tangent of the angle CA D=18° 26° ry very 
If this angle be taken from 60 degrees, half the an- 
gle of the poly ygon, we get the angle » or MAE, 
equal to 41° 33’ 54”. But this is, equal to half the faliant 
angle of the baftion, wherefore the whole flanked angle or 
8". nd the flank- 
excefs ef 180 de- 
143° 
The ‘eauille AD, being equal to VAC+E] Dy, is = 
/GO00= 10 ./90= 943868329895 nearly. Or it is found. 
by this analog By: 
As radiu 
Is to the fon of the angle det Cc: = D; : 
So is A C, half the exterior fide A B 
To the tenaille A D. 
Tf from this there be taken the face A E, which is eat 
‘by conftru@tion to 55 toifes, we get the right line b E, an 
the following analogy for the flank E G. 
As radius 
Is to the fine of double the angle diminué CAD; 
So is the right line D1 
te the flank EG. 
nee equal to twice 
a a B formed by the Hank. 
and line of defence, the G is known, and D-G. i 
acersined by the the anal teed 
cm _ ihe fine of the angle DE G, 
So is the right line D E 
To the right line 
> angle "E GH of the flank, is in this conftruction 
equal to go degrees, together with the angle diminué, or the 
sng ° ormed by the exterior fide, and one of the lines of 
defen 
“The. complement, DG, or D-H, being thus found,. the: 
curtain G Hi is afcertained — the following analogy. 
ie 
As the fine of the angle diminué D 
Is to the fine of double the faid angle, - - 
So is the oe D G 
To the curtain G H. 
The aera curtain M H, or GN, is dl by: 
ogy: 
Oy ’ the eee lee 
e fine of half the angle of the polygon. 
Ts to the fine of half the flanked angle, 
So is the rafant line, or on of AH, 
To the lengthened curtai m which, 
eurtain i H, the inward or: eis fide MNi is immediately 
obtaine 
And “The capital A Mi is afcertained. by this analogy.. 
s the fine of half the angle of the polygon 
Is to the fine of the angle diminué, 
So is the rafant line, or - of defence A H,. 
To the capital A.M of th e baftion 
fubtends in the fquare an male of about 15° 6! 34” sac and: 
in-all other regular figures of about 16° 41’ 57” nearly ; that 
in. his mean fortification. it fabtends i in. the {quare an angle of: 
abo 
