The Conics of Apollonius

4
APOLLONIUS'S Conics BOOK I.

Apollonius to Eudemus.

If you are in good health of body, and your other affairs are according to your own mind, it is well; we are doing quite passably. At the time I was with you in Pergamum, I noticed you were eager to understand the Conics which have been written by us. Therefore, I have sent you the first book, corrected, intending to send the rest in succession when I am in a more tranquil state of mind; for I do not think you have forgotten what you received from me, namely, what the reason was for my having undertaken to write these things; I was requested by the geometer Naucrates, at the time he came to us in Alexandria; and why we, once we had dealt with those eight books, immediately applied greater diligence to them. For since Naucrates himself was about to sail as soon as possible, we did not correct them, but wrote down whatever offered itself to us, as one who was to go through them last. Therefore, having now obtained the time, we are publishing them as we correct each part. And since it happened that some others of those who were with us had the first and second book before they were corrected, do not be surprised if you come upon certain things that are otherwise. Of the eight books, the first four contain the Elements of this discipline: the first of which encompasses the generations of the three conic sections, and those which are called opposite, and also their principal accidents, elaborated by us more richly and more universally than by those who have written on that subject. The second Book treats those things which pertain *asymptotically original: "ἀσυμπτώτως". to the diameters and to the axes of the sections, and to those lines which do not meet with the section; then it discusses other things, which provide both a general and necessary utility for determinations. The third book contains many and admirable [things]...