377 ' 
the Elliptic Representation of a Circle. 
Cor. 2. The centroid remains fixed, if the circle and direct- 
ing line remain : although the eye move, in the same directing 
plane; or the picture move parallel to itself; or vary its 
angle with the circle, the eye so moving as to preserve the 
same directing line. ' • 
Prop. III. Fig. 2. In conjugate chords, each is the tangent- 
chord of the directing point of the other. 
'Dem. Let GH and ST be conjugate chords. Produce them 
to their directing points R and L. Then, because st * and gh 
are conjugate diameters, st is parallel to the tangents to the 
ellipse at g and h : whence the tangents to the circle at G and 
H have J the same director, and the same directing point L, 
with ST ; or GH is the tangent-chord of L the directing point 
of ST. In like manner ST is the tangent-chord of R the 
directing point of GH. Q. E. D. 
Cor. 1. If GH, the tangent-chord of any point L in the 
directing line, will cut that line in any point R; L and R will 
be the directing points of conjugate chords. For ST the 
tangent-chord of R will§ pass through L; whence the 
tangents to the ellipse at^ and h arc parallel to st. And those 
at s and t are parallel io gh. Therefore st and gh are conjugate 
diameters. 
Cor. 2 . If M be the || mean point, and L and R the directing 
'points of conjugate chords, LMR is ^ a rig^it angle. And, if 
LR be the directing line and LMR a rig'it angle, L and R will 
be the directing points ot conjugate cho 'ds. F./r the tangent-^ 
chord of each point will p iss through th^j oh 'v. 
• See what is subjoined to the .iefi:u;iofis. f B; c - ons. 
J A necessary converse of Cor, i. to ThCo. V of Brook Ta • ■ 
^ Jntrod. prop. Ill, i| In trod. prop', def, 3. > . ' Ih. 
lb, prop. IV^. 
