An ESSAY Line G E, in the Points p, from every of which
raiſe Perpendiculars p q, each of which muſt
be continued on each Side the Line G E, equal
to m n the Part of the correſpondent Line p m. Now if a great Number of the Points q be thus
found, and they are joyn’d by an even Hand,
you will have a Curve Line which will be the
Repreſentation ſought.

86. Demonstration .

The Rays by which we perceive a Sphere, do form
an upright Cone, whoſe Axis paſſes through the Cen-
ter of the Sphere, and whoſe Section made by the
Perſpective Plane, is the Repreſentation ſought: from
whence it follows, that I is the Point in the Perſpe-
ctive Plane, through which the Cone’s Axis paſſes. But when an upright Cone is ſo cut by a Plane, that
the Section is an Ellipſis, as in this Caſe, the tranſ-
verſe Diameter of this Ellipſis, will paſs through
the Point of Concurrence of the ſaid Plane, and
Axis of the Cone, and that Point wherein a Per-
pendicular drawn from the Vertex of the Cone, cuts
the ſaid Plane. This will appear evident enough
to any one of but mean Knowledge in Conick Secti-
ons. Therefore the tranſverſe Axis of the Ellipſis,
which is the Repreſentation of the Sphere, is ſome
Part of V I; for the Eye is the Vertex of the Cone
formed by the viſual Rays of the Spbere.

Now let us conceive a Plane to paſs through the
Eye, and the Line I V; this will paſs through the
Center of the Sphere: And if a Perpendicular be
let fall from the Center upon the principal Ray con-
tinued, that Part of the ſaid Ray included between
the Point of Sight, and the Point wherein this Per-
pendicular falls, which is always parallel to the Per-
ſpective Plane, will be equal to the Diſtance from
the Center of the Sphere to the Perſpective Plane,