Euclid, Elements
Thomas L. Heath, Sir Thomas Little Heath, Ed.

concluded that, since it appears as Γεμῖνος in all Greek MSS. and as Γεμεῖνος in some inscriptions, it is Greek and possibly formed from γεμ as Ἐργῖνος is from ἐργ and Ἀλεξῖνος from ἀλεξ (cf. also Ἰκτῖνος, Κρατῖνος). Tittel is equally positive that it is Gem[icaron]nus and suggests that Γεμῖνος is due to a false analogy with Ἀλεξῖνος etc. and Γεμεῖνος wrongly formed on the model of Ἀντωνεῖνος, Ἀγριππεῖνα. Geminus, a Stoic philosopher, born probably in the island of Rhodes, was the author of a comprehensive work on the classification of mathematics, and also wrote, about 73-67 B.C., a not less comprehensive commentary on the meteorological textbook of his teacher Posidonius of Rhodes.

It is the former work in which we are specially interested here. Though Proclus made great use of it, he does not mention its title, unless we may suppose that, in the passage (p. 177, 24) where, after quoting from Geminus a classification of lines which never meet, he says, “these remarks I have selected from the φιλοκαλία of Geminus,” φιλοκαλία is a title or an alternative title. Pappus however quotes a work of Geminus “on the classification of the mathematics” (ἐν τῷ περὶ τῆς τῶν μαθημάτων τάξεως）¹, while Eutocius quotes from “the sixth book of the doctrine of the mathematics” (ἐν τῷ ἕκτῳ τῆς τῶν μαθημάτων θεωρίας）². Tannery³ pointed out that the former title corresponds well enough to the long extract⁴ which Proclus gives in his first prologue, and also to the fragments contained in the Anonymi variae collectiones published by Hultsch at the end of his edition of Heron⁵; but it does not suit most of the óther passages borrowed by Proclus. The correct title was therefore probably that given by Eutocius, The Doctrine, or Theory, of the Mathematics; and Pappus probably refers to one particular portion of the work, say the first Book. If the sixth Book treated of conics, as we may conclude from Eutocius, there must have been more Books to follow, because Proclus has preserved us details about higher curves, which must have come later. If again Geminus finished his work and wrote with the same fulness about the other branches of mathematics as he did about geometry, there must have been a considerable number of Books altogether. At all events it seems to have been designed to give a complete view of the whole science of mathematics, and in fact to be a sort of encyclopaedia of the subject.

I shall now indicate first the certain, and secondly the probable, obligations of Proclus to Geminus, in which task I have only to follow van Pesch, who has embodied the results of Tittel's similar inquiry also⁶. I shall only omit the passages as regards which a case for attributing them to Geminus does not seem to me to have been made out.

First come the following passages which must be attributed to Geminus, because Proclus mentions his name:

(1) (In the first prologue of Proclus⁷) on the division of mathematical