The Conics of Apollonius

3
APOLLONIUS'S Conics BOOK I.

XVI.

Each of the equidistant lines (C D or E F to A B; and C E or D F to Z Y) is said to be applied orderly to the diameter.

XVII.

Figure 4.

I call the conjugate diameters of a curved line (A Z B Y), and of two curves (C A D, E B F), the straight lines (A B, Z Y), of which each is a diameter and bisects the straight lines (C D, C E).

XVIII.

The axis of a curved line and of two curves is a straight line which, while being a diameter of the curved line or of the two curves, cuts the equidistant lines at right angles.

XIX.

The conjugate axes of a curved line and of two curves are the straight lines which, while being conjugate diameters, cut the lines equidistant to them at right angles.

Axes do not differ from diameters, except that the latter cut indiscriminately, while the former cut only at right angles.

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