# Greek Mathematics

# XIX. Apollonius of Perga

## (a) The Conic Sections

### (i.) Relation to Previous Works

### Eutoc. Comm. in Con., Apoll. Perg. ed Heiberg ii. 168. 5–170. 26

Ἀπολλώνιος ὁ γεωμέτρης, ὦ φίλε ἑταῖρε Ἀνθέμιε, γέγονε μὲν ἐκ Πέργης τῆς ἐν Παμφυλίᾳ ἐν χρόνοις τοῦ Εὐεργέτου Πτολεμαίου, ὡς ἱστορεῖ Ἡράκλειος ὁ τὸν βίον Ἀρχιμήδους γράφων, ὃς καί φησι τὰ κωνικὰ θεωρήματα ἐπινοῆσαι μὲν πρῶτον τὸν Ἀρχιμήδη, τὸν δὲ Ἀπολλώνιον αὐτὰ εὑρόντα ὑπὸ Ἀρχιμήδους μὴ ἐκδοθέντα ἰδιοποιήσασθαι, οὐκ ἀληθεύων κατά γε τὴν ἐμήν. ὅ τε γὰρ Ἀρχιμήδης ἐν πολλοῖς φαίνεται ὡς παλαιοτέρας τῆς στοιχειώσεως τῶν κωνικῶν μεμνημένος, καὶ ὁ Ἀπολλώνιος οὐχ ὡς ἰδίας ἐπινοίας γράφει· οὐ γὰρ ἂν ἔφη “ἐπὶ πλέον καὶ καθόλου μᾶλλον

# Apollonius Of Perga

## XIX. Apollonius of Perga

## (a) The Conic Sections

### (i.) Relation to Previous Works

### Eutocius, Commentary on Apollonius’s Conic. Apoll. Perg. ed. Heiberg ii. 168. 5–170. 26

Apollonius the geometer, my dear Anthemius, flourished at Perga in Pamphylia during the time of Ptolemy Euergetes,^{a} as is related in the life of Archimedes written by Heraclius,^{b} who also says that Archimedes first conceived the theorems in conics and that Apollonius, finding they had been discovered by Archimedes but not published, appropriated them for himself, but in my opinion he errs. For in many places Archimedes appears to refer to the elements of conics as an older work, and moreover Apollonius does not claim to be giving his own discoveries; otherwise he would not have described his purpose as “to investigate these properties more fully and more

^{a}Scarcely anything more is known of the life of one of the greatest geometers of all time than is stated in this brief reference. From Pappus, Coll. vii., ed. Hultsch 67 (quoted in vol. i. p. 488), it is known that he spent much time at Alexandria with Euclid’s successors. Ptolemy Euergetes reigned 246–221 b.c., and as Ptolemaeus Chennus (apud Photii Bibl., cod. cxc., ed. Bekker 151 b 18) mentions an astro- norner named Apollonius who flourished in the time of Ptolemy Philopator (221–204 b.c.), the great geometer is probably meant. This fits in with Apollonius’s dedication of Books iv.–viii. of his Conics to King Attalus I (247–197 b.c.). From the preface to Book i., quoted infra (p. 281), we gather that Apollonius visited Eudemus at Pergamum, and to Eudemus he dedicated the first two books of the second edition of his work.^{b}More probably Heraclides, v. supra, p. 18 n. a.