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
101	47
102	48
103
104
105
106	49
107	50
108	51
109	52
110
111
112
113	53
114	54
115	55
116	56
117
118
119
120	57
121	58
122
123
124
125	59
126	60
127
128
129
130	61

Scan	Original
101	47
102	48
103
104
105
106	49
107	50
108	51
109	52
110
111
112
113	53
114	54
115	55
116	56
117
118
119
120	57
121	58
122
123
124
125	59
126	60
127
128
129
130	61

Scan	Original
101	47
102	48
103
104
105
106	49
107	50
108	51
109	52
110
111
112
113	53
114	54
115	55
116	56
117
118
119
120	57
121	58
122
123
124
125	59
126	60
127
128
129
130	61