An 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.

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.

##
88.
Definition
.

The ſemicircular Part h m of a Column, en-

compaſſing the ſame like a Ring, is called the

Torus.

##
89.
Problem
XI.

64. To throw the Torus of a Column into Per-

ſpective.

Let B N C be the Baſe of the Column in the

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

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 Sides,