Gravesande, Willem Jacob 's - An essay on perspective

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4420An ESSAY

Now, it is evident, that to prove the 1127. pearance of A is in the Line C H, we need but
demonſtrate that O D is parallel to A E; which
may be done thus:

Becauſe the Triangles O G V, and A B F, are
ſimilar.
A F: A B: : O G: O V:
altern.
A F: O G: : A B: O V:
Divid. and altern. the firſt
Proportion.
AF—AB (=CF): O G—O V=HG: :AB: OV.

But becauſe the Triangles E C F, H G D are
ſimilar.
C F: H G : : E F : G D.

Now, by obſerving the two laſt Proportions of
the other two Triangles,
E F: G D: : A F: O G,
And the Angle A F E, being equal to the Angle
O G D, the Triangles A E F and O D G are
ſimilar; and therefore A E is parallel to O D:
Which was to be demonſtrated.

After the ſame manner we prove, that the
Appearance of the Point A is in the Line L I,
and conſequently is in the Interſection of this
Line and HC.

Remark.

Altho’ this Method appears more difficult than
the precedent one, as to the Geometrical Conſi-
deration thereof, yet the Operation is eaſier, if
the Points are not too far diſtant from the Baſe
Line: For Lines may well enough be drawn by
Gueſs, or Sight only, to touch Circles, and Cir-
cles to touch Lines.

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Scan	Original
41	17
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50	23
51	24
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55	25
56	26
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63	30
64
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70	31

Scan	Original
41	17
42	18
43	19
44	20
45
46
47
48	21
49	22
50	23
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