Gravesande, Willem Jacob 's - An essay on perspective

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10248An ESSAY might be done) the Point on the Semicircle
h z m, as far as the Parallels (as 9 m) are uſeful:
For when theſe Parallels are uſeleſs, the Point
q will fall beyond the Point m: But then the
Perſpective of the Torus is entirely drawn alrea-
dy, if thoſe Parallels were firſt begun to be drawn
near to 6 3 z, and the others continually going
from it.

In order to demonſtrate this Problem, the fol-
lowing Lemma is neceſſary.

Lemma.

65. If two Circles C D H E and D E F L cut
11Fig. 34. each other, thro’ whoſe Centers C and B the Line
C L paſſes, and D E joyns their Interſections;
then, if the Radius A C or A H be called a, and
B F or BL, b, and the Diſtance A B between the
two Centers c, I ſay A G is equal to {bb—aa/ec}—{1/2}C.

Demonstration.

Let us call A G, x, and G D or G E, y.
Then by the Property of the Circle, if y be conceiv’d
as an Ordinate of the Circle, C D H; yy=aa—xx.
And if it be likewiſe conſider’d as an Ordinate of
the Circle F D L, yy=bb—cc—2cx—xx: Whence
aa—xx=bb—cc—2cx—xx, and ſo 2cx=bb
—aa—cc; and dividing each Side of this laſt Equa-
tion by 2c, we have a x={bb—aa/2c}{1/2} c. Which was
to be Demonſtrated.

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56	26
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Scan	Original
51	24
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55	25
56	26
57
58
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60	27
61	28
62	29
63	30
64
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66
67
68
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70	31
71	32
72	33
73	34
74	35
75	36
76
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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