Gravesande, Willem Jacob 's - An essay on perspective

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7031on PERSPECTIVE.

Prob. V.

50. To find the Repreſentation of a Point, elevated
above the Geometrical Planc.

Let G S be the Geometrical Line, and S the
11Fig. 18. Station Point: Make S F, in the Geometrical
Line, equal to the Height of the Eye; and let
A be the Seat of the given Line.

Operation.

Aſſume F C in the Geometrical Line, equal to
the Height of the Eye, above the Geometrical
Plane: Then draw Lines from the Point A to
the Points S and C, and on the Point B, the In-
terſection of the Line AS and the Baſe Line,
raiſe the Perpendicular BI to the Baſe Line,
equal to E B, plus FC; and the Point I will be
the Perſpective ſought.

Demonstration.

51. Let us ſuppoſe a Plane to paſs thro’ the
given Point, and the Eye perpendicular to the
Geometrical Plane; then it is manifeſt, that the
Interſection of theſe two Planes is the Line
A B S, and the Interſection of the ſaid ſuppos’d
Plane and the perſpective Plane, is B I. Now,
let X be this ſuppos’d Plane; a, b, s, the Point
22Fig. 19. mark’d with the ſame Letters in the precedent
Figure, bi the Interſection of this Plane and
the perſpective Plane; O the Eye, and D the
propos’d Point: We are to prove, that if O D
be drawn, the Line B I of the precedent Figure
will be equal to b i in this Figure.

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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

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