APOLLONIUS

CONICS

BOOK I.

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DEFINITIONS.

I.

Figure 1.

If a straight line (A B) is joined from any point (A) to the circumference of a Circle (B H C), which is not in the same plane in which the point lies, and if this line is produced in both directions, and while the point (A) remains fixed, it is rotated around the circumference of the circle until it returns to the place from which it began to move; I call the surface (D A E F G) described by the straight line, and consisting of two surfaces (D A G, E A F) joined together at the vertex (A), each of which extends infinitely—indeed, the straight line (E A B D) that describes it, being extended infinitely—a Conic surface.

II.

Its vertex is the remaining point (A).

III & VI.

The axis is the straight line (A G), which is drawn through the point (A) and the center of the circle (G).

IV.

I call the cone the figure (A B C) contained by the circle (B H C) and the conic surface (B A C), which is situated between the vertex and the circumference of the circle.