Gravesande, Willem Jacob 's - An essay on perspective

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7132An ESSAY

To demonſtrate which, draw the Line D L M
thro’ the Point D, parallel to a b s. Then, be-
cauſe the Triangles D M O and D L i are ſimi-
lar, we have,

D M = as: D L = ab: : M O: L i. Again,
in the precedent Figure, the Triangles A S C and
A B E are ſimilar: Whence,
A S: A B: : C S: E B.

The three firſt Terms of theſe two Progreſſions
are the ſame: For CS is equal to M O, ſince
they are each the Difference of the Height of the
Eye, and that of the given Point; and conſe-
quently, E B is equal to L i: But B I was made
equal to B E, pl{us} FC the Height of the given
Point above the Geometrical Plane; and b i is
equal to Li, pl{us} b L; which being equal to aD,
is likewiſe the Height of the given Point above
the Geometrical Plane; whence the Lines B I
and b i are equal. Which was to be demon-
ſtrated.

Note, When the Height of the given Point is
greater than the Height of the Eye, E B muſt
be taken from that firſt Height, to have the
Magnitude of B I.

Prob. VI.

52. To throm a Pyramid, or Cone, into Perſpective.

Now, to throw a Pyramid into perſpective,
11Fig. 20. the Appearance of its Baſe and Center muſt 2246. found : After which, Lines muſt be drawn 3350. the Repreſentation of the Vertex, to the Ap-
pearance of thoſe Angles of the Baſe that are
viſible; and then the Perſpective ſought will be
had.

And to throw a Cone into perſpective, the
44Fig. 21. Repreſentation of its Baſe and Vertex muſt 5546.

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97	46
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Scan	Original
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
91
92
93
94	43
95	44
96	45
97	46
98
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100

Scan	Original
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
91
92
93
94	43
95	44
96	45
97	46
98
99
100