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.
Definition.
The ſemicircular Part h m of a Column, en-
11Fig. 33. compaſſing the ſame like a Ring, is called the
Torus.
11Fig. 33. compaſſing the ſame like a Ring, is called the
Torus.
Problem XI.
64.
To throw the Torus of a Column into Per-
ſpective.
ſpective.
Let B N C be the Baſe of the Column in the
22Fig. 32. Geometrical Plane; draw a Line from the Cen-
ter A to the Station Point S, which biſect in the
Point R, and deſcribe the Arc of a Circle B A C
about the Point R, as a Center with the Radius R A.
22Fig. 32. Geometrical Plane; draw a Line from the Cen-
ter A to the Station Point S, which biſect in the
Point R, and deſcribe the Arc of a Circle B A C
about the Point R, as a Center with the Radius R A.
Let X be the Profile of the Column, in which
33Fig. 33. draw the Line z 36, through the Center of the
ſemicircle h m, parallel to the Baſe of the Co-
lumn; and in the Line s a, which goes through
the Center of the Column, parallel to its
33Fig. 33. draw the Line z 36, through the Center of the
ſemicircle h m, parallel to the Baſe of the Co-
lumn; and in the Line s a, which goes through
the Center of the Column, parallel to its