Chap. XXV.
ON STONE BRIDGES.
1491
48 Feet Opening .
AF = 41 feet 7 inches 11 lines 6| points.
ft.
in.
P*
ft.
in.
1.
P-
ft.
in.
1.
P-
ft.
in.
1.
AB =
16
9
9
2
EC = 14
4
9
7
A F =
25
2
7
9
E C =21
7
2
4f
BG =
8
0
7
2§
EL= 2
2
1
n
B G =
12
0
10
9
E L = 3
3
2
2
GO =
2
9
7
2
LK= 1
7
2
9
GO =
4
2
4
9
LK = 2
4
10
2
ON =
S
8
9
8
K I = 4
7
5
7
ON =
5
7
2
4 i
KI = 6
11
2
2
NM =
4
11
10
0
I H = 7
10
0
0
NM =
7
0
0
0
X H =11
9
0
0
MF =
5
3
4
4
H F=ll
0
4
0
MF =
8
4
9
7
IX F = 16
6
6
4
AF =
41
7
11
6?
Idem. 41
7
n
«|vj 1
to
AF =
62
5
11
2|
Idem. 62
5
11
n
54 Feet Opening.
A F=46 feet 10 inches 5 lines 5§ points.
ft.
in.
1.
P-
ft.
in.
1.
P-
ft.
in.
1.
p.
ft.
in.
I.
p.
A B =
18
10
11
10
EC =
16
2
4
9|
AB =
31
6
3
9
E C =
27
0
0
0
BG =
9
0
7
E I, =
2
5
4
9'i
BG =
15
6
EL =
4
0
0
GO =
3
1
8
°j
LK =
1
9
7
7
GO =
5
3
0
0
LK =
3
0
0
7
ON =
4
2
8
4 i
K I =
5
o
4
9
ON =
7
0
0
0
K I =
8
8
0
0
SM=
5
3
0
0
III =
8
9
9
0
NM =
8
9
0
0
III =
14
8
3
0
MF =
6
3
6
2$
HF =
12
4
10
6
M F =
10
6
0
0
HF =
20
8
1
8
A F =
46
10
5
5§
Idem.
46
10
5
1 i
b
A F =
78
5
3
Idem.
78
5
3
60 Feet Opening.
AF = 52 feet 0 inches 11 lines 6 points.
66 Feet Opening.
AF = 57 feet 3 inches 5 lines 2§ points.
AB =
ft.
in.
1.
P*
ft.
in.
t.
P-
ft.
in.
1.
P-
ft.
in.
1.
P-
23
1
5
ij
EC =
19
9
7
n
A B =
35
0
4
2
EC =
30
0
0
0
B G =
11
0
9
10
EL =
2
11
11
n
BG =
16
9
3
0
EL =
4
6
5
4
GO =
3
10
2
4f
LK =
2
2
5
4
GO =
5
10
0
0
LK =
3
4
0
10
ON=
5
1
7
2
K I =
6
4
3
2
ON=
7
9
4
0
K I =
9
7
6
8
NM =
6
5
0
0
III =
10
9
3
0
NM=
9
8
8
0
I H =
16
3
10
0
MF =
7
8
4
9
II F =
15
1
11
5
MF =
11
8
0
0
HF =
22
11
8
4
A F =
57
3
5
2%
Idem.
57
3'
5
2?
AF =
86
9
n
2
Idem.
86
9
7
2
72 Feet Opening.
A F = 62 feet 5 inches 11 lines 2| points.
90 Feet Opening .
AF = 78 feet 1 inch 5 lines 3 points.
95 Feet Opening.
A F = 82 feet 5 inches 6 lines 2| points.
ft.
in.
p-
ft.
in.
I.
P-
ft.
in.
1.
P-
ft.
in.
1.
AB =
21
0
2
6
E C =18
0
0
0
AB =33
3
3
Hi
EC =28
6
0
0
BG =
10
0
9
0
EL= 2
8
8
0
B G = 15
11
2
3
EL= 4
3
.8
8
G 0 =
3
6
0
0
LK = 2
0
0
6
GO ='5
6
6
0
I.K= 3
2
0
9 i
ON =
4
8
0
0
K I = 5
9
4
0
0 N= 7
4
8
0
K I = 9
1
9
4
NM =
5
10
0
0
IIX = 9
9
6
0
NM= 9
2
10
0
I H =15
6
0
6
111 =
7
0
0
0
H F = 13
9
5
0
M F = 11
1
0
0
IIF=21
9
10
11
A F =
52
0
11
6
Idem. 52
0
11
6
A F =82
5
6
23
Idem. 82
5
6
2i
100 Feet Opening.
AF = 86 feet 9 inches 7 lines 2 points.
Rondelet gives in his “ L’Art de Batir,” the following methods for drawing archesformed of several circular arcs. For that represented in fig. 2709.. after having deter-mined the semi-diameter. AC at 60 feet, and the length of the radius Ad of the arcsat the springing at one-third of AC, divide d C into fifteen equal parts; give one to di,two to ik , three to hi, four to Im , and five to mC : having then fixed CH at twice AC,divide it into five equal parts, and from the points of division D, E, F, G, II, drawlines through the divisions on the horizontal line d C, and prolong them sufficiently to de-termine the form of the arc which results from their intersection, as Ddl, EiK, FAL,GZM, and HmN, whose points of intersection, e,fg,h, give the centres of the intermediatearcs; thus d is the centre of the arc A I, e that of the arc IK, / that of the arc KL,g that of the arc EM, h that of MN, and II that of N B. The intersections markedx,x,v, indicate the curvature of a regular ellipsis, and is here introduced in order to showthe difference of the two curves.
Fig. 2710. is an arch composed of six arcs of a circle, which increase in arithmeticalprogression from the centre of the key to the springing. After having drawn the diagonalPC, and described the quarter circle AQ, the angle APw is made equal to the angle oPQ,and the prolongation of the line Vn gives the point d on the semi-diameter AC, and the
5 c 2