Gravesande, Willem Jacob 's - An essay on perspective

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257on PERSPECTIVE. the Geometrical Plane, make Angles with the baſe
Line, equal to thoſe Angles that the Lines whereof
they are the Appearances, make with the Parallels
to the baſe Line, which cut them; and conſequently
the ſaid Appearances are parallel between them-
ſelves.

This is evident, becauſe the Appearances of
Lines parallel to the baſe Line, are parallel to
the ſaid Line; and the Appearances of the in-
clined Lines are parallel to theſe Lines.

Theorem II.

8, 9. The Repreſentation of a Figure, parallel to
the perſpective Plane, is ſimilar to the ſaid Figure; and
the Sides of the ſaid Figure are to their Repreſen-
tations, as the Diſtance of the Eye from the Plane
of the Figure, to the Diſtance of the Eye from the
perſpective Plane.

The given Figure is A B C D. We are firſt to
11Fig. 4. prove, that its Repreſentation a b c d, is ſimilar
thereto; that is, that the correſponding Angles
of theſe two Figures A B C D, a b c d, are equal,
and their Sides proportional.

I. The Angles are equal, becauſe the 224. of which the two Figures conſiſt, are parallel be-
tween themſelves.

II. In the ſimilar Triangles A D O, and a d o,
we have
A D: a d : : O D : O d.

And in the ſimilar Triangles O D C, and O d c,
we have
D C : d c : : O D : O d.
then
A D: a d : : D c : d c.
altern.
A D : D C : : a d : d c.

And conſequently the Sides A D, and D C of
the Figure A B C D, are Proportional to

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Scan	Original
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54
55	25
56	26
57
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60	27
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63	30
64
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68
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70	31
71	32
72	33
73	34
74	35
75	36
76
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79
80

Scan	Original
51	24
52
53
54
55	25
56	26
57
58
59
60	27
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

Scan	Original
51	24
52
53
54
55	25
56	26
57
58
59
60	27
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