Gravesande, Willem Jacob 's - An essay on perspective

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15776An ESSAY Plane; and at the Points R and S, raiſe the in-
definite perpendiculars R G and S M; and aſſume
the Point M at Pleaſure on S M; from which
raiſe the Perpendicular M N, equal to the given
Line, and draw the Lines M O and N O, cutting
11Fig. 41. the Line R G in the Points E and G. Then
having drawn a Line at Pleaſure in the per-
ſpective Plane through the Point T, which is
that wherein a Perpendicular falling from the
Eye on the perſpective Plane meets it, aſſume
T H in the ſaid Line, equal to R E, and T I e-
qual to R G; draw the Lines Ta, Ha, through
the Point a, the Perſpective of the Foot of the
given Perpendicular, and through the Point I,
the Line I X, parallel to Ha, and cutting Ta
in X, then a X will be the Appearance ſought.

Demonstration.

It is manifeſt , that the Point T, is the 2213, 14. dental Point of Lines perpendicular to the Geo-
metrical Plane; and conſequently the Per-
ſpective ſought is a Part of T a. Moreover, it
is manifeſt , that if the Feet and 334. of two equal right Lines, perpendicular to the
Geometrical Plane be joyn’d by Lines, theſe
Lines of Junction will have parallel Repreſen-
tations; becauſe they are parallel to each other,
as likewiſe to the perſpective Plane. And con-
ſequently, ſince H I, by Conſtruction, is the
Perſpective of a Line perpendicular to the
Geometrical Plane, and equal to the given Line,
and H a paſſes through the Appearances of the
Foot of the ſaid Perpendicular, and the given
Perpendicular; I ſay, that X I, which is paral-
lel to Ha, and paſſes through the Extremity of
the Appeaarance H I, likewiſe paſſes through
the Extremity of the given Line; and

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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