14772An ESSAY
draw S N perpendicular to the ſaid Line A B,
cutting the Baſe Line in N, and draw the Line
N D. Then about the Point D, as a Center, and
with the Radius D O, deſcribe the Circular Arc
O o: And about N, as a Center, with the Radius
N S, draw the Circular Arc S s. This being done,
draw the Line s o touching the ſaid two Arcs,
and the Line D o perpendicular to s o. Then
draw o F, making an Angle with o D, equal to
the Angle of the Inclination of the Lines given,
and cutting N D continued in F: Now I ſay F
is the Accidental Point ſought when the Lines
do not incline towards the Perſpective Plane:
But if they do, o F muſt be drawn below o D.
cutting the Baſe Line in N, and draw the Line
N D. Then about the Point D, as a Center, and
with the Radius D O, deſcribe the Circular Arc
O o: And about N, as a Center, with the Radius
N S, draw the Circular Arc S s. This being done,
draw the Line s o touching the ſaid two Arcs,
and the Line D o perpendicular to s o. Then
draw o F, making an Angle with o D, equal to
the Angle of the Inclination of the Lines given,
and cutting N D continued in F: Now I ſay F
is the Accidental Point ſought when the Lines
do not incline towards the Perſpective Plane:
But if they do, o F muſt be drawn below o D.
Demonstration.
If a Plane be ſuppoſed to paſs thro’ the Eye
parallel to theinclin’d Lines; the common Secti-
ons of this Plane, and the Horizontal and Geo-
metrical Planes, will be O D and S N. It is
now manifeſt, that if a Line be drawn in the
ſaid Plane, below the Horizontal Plane, when
the Lines incline towards the perſpective Plane,
and above it when they incline the other way,
making an Angle with O D equal to the Angle
of Inclination of the propoſed Lines; I ſay it is
manifeſt, that the ſaid Line will be parallel to
the propoſed Lines, and will meet the 1113, 14. ctive Plane in the Accidental Point ſought. If
now the before ſuppoſed Plane be conceiv’d to
turn about the Line N D, the Eye, and the
Station Point in the ſaid Plain, will then meet
the perſpective Plane in the Points o and s; for
the Lines D o and N s are equal to D O and N S,
and form right Angles with the Line s o joyning
their Extremities. Now the two Points s and o
anſwer to the Situation of the Eye and
parallel to theinclin’d Lines; the common Secti-
ons of this Plane, and the Horizontal and Geo-
metrical Planes, will be O D and S N. It is
now manifeſt, that if a Line be drawn in the
ſaid Plane, below the Horizontal Plane, when
the Lines incline towards the perſpective Plane,
and above it when they incline the other way,
making an Angle with O D equal to the Angle
of Inclination of the propoſed Lines; I ſay it is
manifeſt, that the ſaid Line will be parallel to
the propoſed Lines, and will meet the 1113, 14. ctive Plane in the Accidental Point ſought. If
now the before ſuppoſed Plane be conceiv’d to
turn about the Line N D, the Eye, and the
Station Point in the ſaid Plain, will then meet
the perſpective Plane in the Points o and s; for
the Lines D o and N s are equal to D O and N S,
and form right Angles with the Line s o joyning
their Extremities. Now the two Points s and o
anſwer to the Situation of the Eye and