The Conics of Apollonius

On Apollonius of Perga, from Vossius on Mathematical Writers:

Of those who remain from the antiquity immediately following Euclid, the most prominent is Apollonius of Perga, for he flourished under Ptolemy Euergetes.

Page 54.

He was born in Perga, a city of Pamphylia. Regarding his age, the authority for what I have said is Heraclius in the life of Archimedes, and from there Eutocius of Ascalon at the beginning of the commentaries on the Conics of Apollonius. There, from the sixth book of Geminus’s Mathematical Doctrines, he reports that on account of this science of conics, he was named the "Great Geometer" by the men of his own age. He heard Euclid’s disciples in Alexandria, which also indicates his age. Having received many things from them, it was not difficult to illustrate the four books of Euclid’s Conics with a commentary and to add as many others, so that in total there were eight books of conics, just as Pappus of Alexandria is the authority in the seventh book of the Mathematical Collection.

Page 55.

And in the same book, he also mentions other works of the same Apollonius: namely, two books περὶ λόγου ἀποτομῆς On the Cutting-off of a Ratio; as many περὶ χωρίου ἀποτομῆς On the Cutting-off of a Space; also two διωρισμένης τομῆς On Determinate Section; and as many ἐπαφῶν On Tangencies; also two νεύσεων On Inclinations; and similarly two τόπων ἐπιπέδων On Plane Loci. Of these, Pappus calls some ἐφεκτικοὺς self-contained and others διεξοδικοὺς outward-reaching.

Page 434.

Furthermore, there were some in the past who thought that the Conics were not by Apollonius of Perga, but by Archimedes. That Heraclius, who reported the life of Archimedes, held this view. Eutocius brings forward his words, in which he says that Archimedes was the first of all to commit the Elements of Conics to writing, but that Apollonius, knowing they had not yet been published by the author, stole them and published them as his own. And it seems this can be confirmed by the words of Archimedes himself. For he himself mentions the work on Conic Elements, partly in the book περὶ κωνοειδέων, καὶ σφαιροειδέων On Conoids and Spheroids, before the fourth proposition. For in both places, he says that the thing about which he speaks was demonstrated in the books on Conics. Unless one thinks that he is referring to the four books of Euclid’s Conics, which Pappus mentions in the seventh book of the Mathematical Collections. Truly, if Archimedes were marking another man's work, he would not speak in this way. For he is accustomed to say that "those before us demonstrated this." And indeed, that it was not unknown to Archimedes that cones could be cut by planes having an inclination different from the side of the cone is sufficiently proven against Eutocius and others by Guido Ubaldus at the beginning of his Commentary on the second book of Archimedes's ἰσοῤῥοπικῶν On Equilibrium. When I consider these things, I would not wish to contend much over the author. And perhaps Apollonius obtained Archimedes's rougher notes and perfected them. Be that as it may, before these works on Conics were published by Apollonius, knowledge of them was imperfect, as Eutocius of Ascalon reports at the beginning.