9746An ESSAY
G m T, biſects the Axis G E:
For if a Line be
drawn from T to E, it will be perpendicular to G T,
and conſequently parallel to m n: Whence the con-
jugate Axis of the Curve G q E, is equal to the
conjugate Axis of the Ellipſis to be drawn: And
therefore we are only to prove, that the Curve paſ-
ſing through the Points q, is an Ellipſis. Which may
be ſbewnthus.
drawn from T to E, it will be perpendicular to G T,
and conſequently parallel to m n: Whence the con-
jugate Axis of the Curve G q E, is equal to the
conjugate Axis of the Ellipſis to be drawn: And
therefore we are only to prove, that the Curve paſ-
ſing through the Points q, is an Ellipſis. Which may
be ſbewnthus.
The Parts G n of the Line G T, are Propor-
tional to the Parts G p of the Line G E: Whence
the Rectangles under G p and p E, are Proportional
to the Rectangles under G n and n T; but theſe laſt
Rectangles are equal to the Squares of the Ordinates
n m, which Squares are equal to the Squares of the
Ordinates p q; therefore theſe laſt Squares are Pro-
portional to the Rectangles under G p and p E, which
is a Property of the Ellipſis.
tional to the Parts G p of the Line G E: Whence
the Rectangles under G p and p E, are Proportional
to the Rectangles under G n and n T; but theſe laſt
Rectangles are equal to the Squares of the Ordinates
n m, which Squares are equal to the Squares of the
Ordinates p q; therefore theſe laſt Squares are Pro-
portional to the Rectangles under G p and p E, which
is a Property of the Ellipſis.