3110An ESSAY
a right Line drawn from the Eye parallel to the pro-
poſed Line, terminates.
poſed Line, terminates.
The Line C D being continued, will meet
11Fig. 5. the perſpective Plane in the Point E. We are
to prove, that its Appearance is a Part of the
Line E H, drawn from the Point E, to the
Point H, whereat the Line O H proceeding
from the Eye parallel to the given Line C D,
terminates.
11Fig. 5. the perſpective Plane in the Point E. We are
to prove, that its Appearance is a Part of the
Line E H, drawn from the Point E, to the
Point H, whereat the Line O H proceeding
from the Eye parallel to the given Line C D,
terminates.
The Interſection of the perſpective Plane,
and the Plane O D C, is the Repreſentation of the
given Line. Now the Plane O D C, is a Part of the
Plane paſſing through the parallels O H and EC.
and the Plane O D C, is the Repreſentation of the
given Line. Now the Plane O D C, is a Part of the
Plane paſſing through the parallels O H and EC.
Therefore, this Repreſentation is a Part of the
Interſection of the laſt mentioned Plane, and
perſpective Plane; which Interſection is E H.
Interſection of the laſt mentioned Plane, and
perſpective Plane; which Interſection is E H.
Corollary I.
14.
All Lines parallel between themſelves, and be-
ing produced, do fall upon the perſpective Plane, have
Repreſentations, which being produced, will all con-
cur in one Point.
ing produced, do fall upon the perſpective Plane, have
Repreſentations, which being produced, will all con-
cur in one Point.
This is evident, becauſe but only one Line
O H can be drawn from the Eye O, to the per-
ſpective Plane, parallel to the ſaid Parallels, and
becauſe all their Repreſentations are Parts of
Lines concurring in the Point H.
O H can be drawn from the Eye O, to the per-
ſpective Plane, parallel to the ſaid Parallels, and
becauſe all their Repreſentations are Parts of
Lines concurring in the Point H.
And this Point is called the accidental Point of the
22Def. 17. ſaid Parallels.
22Def. 17. ſaid Parallels.
Corollary II.
15.
Two or more parallel Lines, which being produ-
ced, do fall on the perſpective Plane, parallel to the Geo-
metrical Plane, have their accidental Point in the
Horizontal Line.
ced, do fall on the perſpective Plane, parallel to the Geo-
metrical Plane, have their accidental Point in the
Horizontal Line.
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