309on PERSPECTIVE.
right, is alſo perpendicular to the Geometrical
Plane, and the third is then in the Direction of the
firſt.
Plane, and the third is then in the Direction of the
firſt.
Corollary II.
11.
If tworight Lines, equal between themſelves, and
parallel to the perſpective Planes, be equally diſtant
from the perſpective Plane, their Appearances will be
equal.
parallel to the perſpective Planes, be equally diſtant
from the perſpective Plane, their Appearances will be
equal.
For, becauſe they are in a Plane, parallel to
the perſpective Plane, they will have the ſame
Proportion to each other, as their Repreſentations.
the perſpective Plane, they will have the ſame
Proportion to each other, as their Repreſentations.
Theorem III.
12.
If a Line parallel to the Perſpective Plane, be
view’d by two Eyes, both being in a Plane, parallel
to the perſpective Plane, the Repreſentations of the
ſaid Line will be equal.
view’d by two Eyes, both being in a Plane, parallel
to the perſpective Plane, the Repreſentations of the
ſaid Line will be equal.
If we ſuppoſe a Plane, parallel to the Per-
ſpective Plane, to paſs through the propoſed
Line, this Proportion will be had; viz. As 119. Diſtance of the Eyes from this Plane, is to their
Diſtance from the Perſpective Plane, ſo is the
given Line to the Repreſentation thereof. But
the three firſt Terms of this Proportion are
the ſame for each of the Eyes, which are
in one and the ſame Plane parallel to the Per-
ſpective Plane: Therefore, the fourth Term of
the Proportion will likewiſe be the ſame in both
Caſes: Which was to be demonſtrated.
ſpective Plane, to paſs through the propoſed
Line, this Proportion will be had; viz. As 119. Diſtance of the Eyes from this Plane, is to their
Diſtance from the Perſpective Plane, ſo is the
given Line to the Repreſentation thereof. But
the three firſt Terms of this Proportion are
the ſame for each of the Eyes, which are
in one and the ſame Plane parallel to the Per-
ſpective Plane: Therefore, the fourth Term of
the Proportion will likewiſe be the ſame in both
Caſes: Which was to be demonſtrated.
Theorem IV.
13.
If a right Line, being continued, meets the per-
ſpective Piane in one Point, the Appearance thereof
will be a Part of the Line drawn from the ſaid Point
in the perſpective Plane, to another Point,
ſpective Piane in one Point, the Appearance thereof
will be a Part of the Line drawn from the ſaid Point
in the perſpective Plane, to another Point,
zoom in
zoom out
zoom area
full page
page width
set mark
remove mark
get reference
digilib