Gravesande, Willem Jacob 's - An essay on perspective

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8739on PERSPECTIVE. the Station Point, and A the Point wherein the
Perpendicular meets the Geometrical Plane.

Operation,
Without Compaſſes.

Having firſt found the Perſpective a of 1131. Point A, draw the Line A S cutting the Baſe
Line in E, through which Point E draw the
Line Ea; then from the Point B draw a Line
B a to the Point a, cutting the Horizontal Line
in F. Again through F draw a Line to the
Point L, cutting E a in I; and a I is the Repre-
ſentation ſought.

Demonstration.

To prove this, let G N be a Perpendicular to
the Baſe Line drawn from the Point G, wherein
the ſaid Baſe Line is cut by the Line B F; alſo
let G D be equal to the Perpendicular whoſe Ap-
pearance is ſought, and a H parallel to the Baſe
Line.

It is plain that the Perſpective of E A is
E a: But E A paſſes through the Station Point;
and conſequently its Repreſentation is 2241. dicular to the Baſe Line; therefore we are 3356. to prove, that a I is equal to a H.

Now the Triangles B G C and B F M are ſimi-
lar; and ſo

B C : B M : : B G: B F.

But B M by Conſtruction is the double of B C;
whence B F is alſo the double of B G, which,
conſequently, is equal to G F.

Becauſe the Triangles F G N and F B L are
ſimilar, therefore

F G : F B : : G N : B L.

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Scan	Original
61	28
62	29
63	30
64
65
66
67
68
69
70	31
71	32
72	33
73	34
74	35
75	36
76
77
78
79
80
81
82
83
84
85	37
86	38
87	39
88	40
89	41
90	42

Scan	Original
61	28
62	29
63	30
64
65
66
67
68
69
70	31
71	32
72	33
73	34
74	35
75	36
76
77
78
79
80
81
82
83
84
85	37
86	38
87	39
88	40
89	41
90	42

Scan	Original
61	28
62	29
63	30
64
65
66
67
68
69
70	31
71	32
72	33
73	34
74	35
75	36
76
77
78
79
80
81
82
83
84
85	37
86	38
87	39
88	40
89	41
90	42