9544An 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.
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.
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.
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
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
zoom in
zoom out
zoom area
full page
page width
set mark
remove mark
get reference
digilib