(Ὑψικλῆς), was of Alexandria, or, as the Arabic writers say, of Ascalon. Both may be right, for to say that a Greek mathematician or astronomer was of Alexandria, fixes his place of birth or general residence about as much as we do when we name an Englishman of the same stamp as of Oxford or Cambridge. The time at which he lived will require some discussion, inasmuch as we intend to differ from the account generally received, and our theory on the matter involves the period at which Diophantus wrote, which is of somewhat more importance.

It is generally stated that Hypsicles lived A. D. 160, on the authority of Suidas, who states that his teacher, Isidore the philosopher, ἐφιλοσόφησε ὑπο τοῖς ἀδελφοῖς; hence, says Fabricius, he lived sub Divis Fratribus, and the Divi Fratres are Antoninus and Verus. [ANTONINUS PIUS.] But Fabricius (or Harless) adds a note to the effect that it is possible this Isidore may be stated to have studied under his own brothers, and that he may be the Isidore whose life was written by DAMASCIUS. August, the editor of Euclid, assumes, without an allusion to any other opinion, that Isidore was Isidore of Miletus, Justiniasn's architect, and the preceptor of EUTOCIUS. Whether this last supposition be true or not, it is certain that the former one must be correct, for Suidas, at the word Syrianus, mentions Isidore "the philosopher" again, and cites Damascius by name for his information. Now Photius, who has given a long commentary on the life of Isidore by Damascius, repeats again and again that Isidore was the successor of Marinus, the successor of Proclus, and that Damascius was his fellow pupil. This brings Isidore fairly into the reign of Justinian; and if we look at the strong feeling of admiration which Eutocius and Hypsicles both express for their teachers (Hypsicles calls his the great), we cannot suppose that these two Isidores were two different persons. Again, the Isidore of Damascius was a Christian, and Suidas calls him ἐπιμελὴς ἐν ἱεροῖς. If an editor of Archimedes in the second century had been a Christian, the fact must have been noted in many forms, and probably he would have been one of the saint Isidores from whom Suidas always distinguishes him by the title of the philosopher.

There are other strong presumptions against Hypsicles having lived in the second century. Neither Pappus, Proclus, nor Eutocius, mentions his name. Now Proclus names the commentators on Euclid: it is unlikely he would have forgotten the editor who added two whole books to the Elements. Moreover, he specifies it as the ultimate object of the Elements to investigate the properties of regular solids: it is very unlikely that he should have suppressed the fact of two books on those very solids having been written as an appendix to Euclid. Again, Marinus, in his preface to the states the Elements to consist of thirteen books, which is a presumption against the additional books of Hypsicles having been added before his time. Putting all these things together, we feel that we may confidently assert Hypsicles to have written not earlier than A. D. 550.

Diophantus mentions Hypsicles in the work on polygonal numbers (prop. viii.), and seems to attribute to him the notion and definition of polygonal numbers. We must accordingly place Diophantus at least something later than Hypsicles, perhaps at the beginning of the seventh century. Achilles Tatius also mentions Hypsicles (Isag. in Phaenom. Arati) as one of those who wrote on the harmony of the planetary motions, περὶ τῆς ἐναρμυνίου κινήσεως: and thus the date of Achilles Tatius is considerably altered. * The date of Achilles Tatius is supposed to be settled by a passage of Julius Firmicus (4.10), in which he announces his intention to defer certain astrological topics till he treats of the barbarian sphere, quae dixinus ille Abranm et prudlentissimus Achilles xerissimis conati sunt rationibus invenire et otis tradere. But Achilles Tatiuss does not show the least symptom of astrology; and we are inclined to suppose, with Fabricius, Wiedler, &c., that the Achilles mentioned by Firmicus is another person. And moreover, in looking at the above quotation, it seems as likely as not that Firmicus only means to say that his two friends, Abraam and Achilles, had endeavoured to supply him, and not the public, with some information.