Gravesande, Willem Jacob 's - An essay on perspective

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10952An ESSAY viſible Portions of the ſaid Baſes. Note, This
Method may be demonſtrated without Algebra,
but it would be very long.

Problem IX.

68. To find the Accidental Point of ſeveral pa-
rallel Lines, which are inclin’d to the Geome-
trical Plane.

Let A B be the Direction of one of the Lines,
11Fig. 36. whoſe accidental Point is ſought; and ECP, the
Angle that the ſaid Lines make with the Geo-
metrical Plane.

Operation.

Draw a Line, O D, thro’ the Eye O, parallel
to A B, and thro’ the Point D, wherein it cuts
the Horizontal Line, and which is the acciden-
tal Point of the Directions of the given Lines,
draw D F perpendicular to the ſaid Horizontal
Line; in which aſſume D G, equal to DO. Fi-
nally, thro’ the Point G, draw the Line G F,
making an Angle with the Horizontal Line, equal
to E C P; and then the Point F, (the Interſection
of this Line) and the Perpendicular D F, is the
accidental Point ſought.

Note, When the Lines are inclin’d towards
the perſpective Plane, D F and G F muſt be
drawn below the Horizontal Line: And, contra-
riwiſe, when the ſaid Lines are inclin’d towards
the oppoſite Part of the perſpective Plane, the
aforeſaid Lines muſt be drawn above the ſaid
Horizontal Line, as is done here.

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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
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

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