Polyaenus of Lampsacus

Polyaenus of Lampsacus (Πoλύαινoς Λαμψακηνός, Polyainos Lampsakēnos; c. 340 – c. 285 BCE), also spelled Polyenus, was an ancient Greek mathematician and a friend of Epicurus.

Life
He was the son of Athenodorus. His friendship with Epicurus started after the latter's escape from Mytilene in 307 or 306 BC when he opened a philosophical school at Lampsacus associating himself with other citizens of the town, like Pythocles, Colotes, and Idomeneus. With these fellow citizens he moved to Athens, where they founded a school of philosophy with Epicurus as head, or hegemon, while Polyaenus, Hermarchus and Metrodorus were kathegemones.

A man of mild and friendly manners, as Philodemus refers, he adopted fully the philosophical system of his friend, and, although he had previously acquired great reputation as a mathematician, he now maintained with Epicurus the worthlessness of geometry. But the statement may be at least doubted, since it is certain Polyaenus wrote a mathematical work called Puzzles (Aπoριαι) in which the validity of geometry is maintained. It was against this treatise that another Epicurean, Demetrius Lacon, wrote Unsolved questions of Polyaenus (Πρὸς τὰς Πoλυαίνoυ ἀπoρίας) in the 2nd century BCE. Like Epicurus, a considerable number of spurious works seem to have been assigned to him; one of these was Against the Orators, whose authenticity was attacked both by Zeno of Sidon and his pupil Philodemus.

Writings
The works attributed to Polyaenus include:
 * On Definitions
 * On Philosophy
 * Against Aristo
 * Puzzles (Aporiai)
 * On the Moon
 * Against the Orators
 * His collected Letters.