APOLLONIUS OF PERGA

BOOK I OF THE CONICS.

WITH THE COMMENTARIES OF EUTOCIUS OF ASCALON AND FEDERICO COMMANDINO.

An ornamental woodcut initial 'S' features floral and scrollwork patterns.

IF you are in good health, and your other affairs are proceeding according to your wishes, that is well; we are also faring quite well. During the time I was with you in Pergamum an ancient Greek city in Anatolia, I noticed you were eager to understand the conics which have been written by us. Therefore, I have sent you the first book, corrected; I will send the rest in turn when I am in a more tranquil state of mind. For I do not think you have forgotten what you heard from me, namely, the reason why I undertook to write these, having been requested by Naucrates a geometrician the geometer when he came to us while traveling to Alexandria the capital of Ptolemaic Egypt. And why, when we had dealt with those eight books, we immediately applied greater diligence to them. For since Naucrates was to set sail as soon as possible, we did not correct them, but wrote down whatever came to our minds, being those who would look over them last. Therefore, having now found the time, as we correct each part, so we publish it. And since it happens that some others of those who had been with us had the first and second books before they were corrected, do not be surprised if you encounter some things that are otherwise. Of the eight books, the first four contain the elements of this discipline: of which the first indeed comprises the generations of the three conic sections and those which are called opposite; likewise, their principal properties, elaborated by us both more fully and more universally than by others who have written on this subject. The second book treats matters pertaining to the diameters and the axes of the sections, and those lines which do not meet the section, which are called asymptoti asymptotes by the Greeks; then it discusses others which bring both general and necessary utility to determinations. You will learn from this book which ones I call diameters and which axes. The third book contains many admirable theorems that will be useful both for the compositions of solid loci and for determinations, many of which are both very beautiful and new. Considering these things, we noticed that the method of composing the locus to three and four lines had not been set down by Euclid the Greek mathematician...