The Conics of Apollonius

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APOLLONIUS'S Conics BOOK I.

The base is the circle itself (B H C).

I call those right cones which have axes at right angles to their bases.

I call those scalene cones which do not have axes at right angles to their bases.

Figure 2.

I call the diameter of any curved line (A B C) existing in one plane the straight line (B D), which, being drawn from the curved line, divides all lines (A C) that are drawn within it equidistant to a certain line (A C) into two equal parts.

The vertex is the limit of the straight line (A) which is on the line itself (A B C).

Each of the equidistant lines (A C) is said to be applied orderly to the diameter original: "ordinatim applicari".

Figure 3.

Similarly, for two curved lines (C A D, E B F) existing in one plane, I call the transverse diameter the straight line (A B), which divides all lines (C D, E F) drawn in each of them, equidistant to a certain straight line (C D or E F), into two equal parts (at X).

The vertices are the limits of the diameter (A, B) which are on the lines themselves (C A D, E B F).

I call the rect diameter (Z Y) that which is placed between the two lines (C A D, E B F), and which bisects all lines (C E, D F) drawn equidistant to a certain straight line (A B) and situated between them (at Z or Y).