6330An ESSAY
preſentations being join’d, will give the Perſpe-
ctive ſought. The ſame may be done, in draw-
ing the Chords thro’a Point, whoſe Repreſenta-
tion is known.
ctive ſought. The ſame may be done, in draw-
ing the Chords thro’a Point, whoſe Repreſenta-
tion is known.
Remarks.
49.
Let G I be the Geometrical Line;
and thro’
11Fig. 16. the Center P of the Circle, whoſe Perſpective is
ſought, let fall the Perpendicular P F upon the ſaid
Line G I, which biſect in the Point R. About R,
as a Center, and with the Radius R P, deſcribe an
Arc of a Circle M P N, cutting the given Circle in
the Points M and N. Now, if the Perſpective of
L H and N M be found, the two Conjugate Dia-
meters of an Ellipſis, which is the Repreſentation of
the given Circle, will be bad. And, an Ellipſis may
be drawn by ſome one of the Methods laid down by
thoſe who have treated of Conick Sections.
11Fig. 16. the Center P of the Circle, whoſe Perſpective is
ſought, let fall the Perpendicular P F upon the ſaid
Line G I, which biſect in the Point R. About R,
as a Center, and with the Radius R P, deſcribe an
Arc of a Circle M P N, cutting the given Circle in
the Points M and N. Now, if the Perſpective of
L H and N M be found, the two Conjugate Dia-
meters of an Ellipſis, which is the Repreſentation of
the given Circle, will be bad. And, an Ellipſis may
be drawn by ſome one of the Methods laid down by
thoſe who have treated of Conick Sections.
I ſhall not ſpend time here in demonſtrating the
Truth of this. See Prop. 10. lib. 2. of the great
Latin Treatiſe of Conic Sections, written by M. de
la Hire; the Demonſtration of which may be here
apply’d. If we conſider, 1. That Lines drawn from
the Points M and N to the Point F, will touch the
Circle in the ſaid Points M and N. 2. That the
viſual Rays, going from the Eye towards all the Parts
of the Circumference of the Circle, form a Cone,
3. That the Appearance of the Circle, is the Section
of a Cone, made by the perſpective Plane. Finally,
That the Line G I ought to be conceiv’d, as being
the Interſection of the Geometrical Plane, and a
Plane paſſing thro’ the Eye parallel to the perſpective
Plane.
Truth of this. See Prop. 10. lib. 2. of the great
Latin Treatiſe of Conic Sections, written by M. de
la Hire; the Demonſtration of which may be here
apply’d. If we conſider, 1. That Lines drawn from
the Points M and N to the Point F, will touch the
Circle in the ſaid Points M and N. 2. That the
viſual Rays, going from the Eye towards all the Parts
of the Circumference of the Circle, form a Cone,
3. That the Appearance of the Circle, is the Section
of a Cone, made by the perſpective Plane. Finally,
That the Line G I ought to be conceiv’d, as being
the Interſection of the Geometrical Plane, and a
Plane paſſing thro’ the Eye parallel to the perſpective
Plane.
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