The Conics of Apollonius

L K : A K.k Therefore B L = A K. Andl consequently C L = C K;m this is X H = X G.n Therefore C D is a diameter, specifically because it bisects the line G H itself, and similarly all lines parallel to A B.
> Corollary 1. If G K = H L, then A K = B L; and B K = A L. And from this, B K A K = A L B L.
> 2. Conversely, if A K = B L, or B K = A L, then G K = H L, and B K A K = A L B L.
### SECOND DEFINITIONS.

Fig. 24. 25.

1. The point (C), which divides the diameter (A B) of a hyperbola and ellipse into two equal parts, is called the Center of the section.
2. And the line (C B) which is led from the center (C) to the section is called the radius of the section.
3. Similarly, the point (C) which divides the transverse side (A B) of opposite sections into two equal parts is also called the Center.
4. That line (D E) which is led from the center, equidistant to that (G K) which is applied as an ordinate, and which has a mean proportion between the sides of the figure (A B, B F) and is bisected by the center (C), is called the second diameter.
For the sake of brevity, we shall designate the Transverse side, the Rectum side, and the second diameter with the elements T, R, M: whence

Cor. 20. 6.

> Corollary T sq. : M sq.