References For The Discussion Of Polyaenus

  • [ADMIN EDIT: This is a copy of a post from Don that was placed originally in another thread.]

    Poor Polyaenus! He has such an unfortunate English pronunciation to his name (Yes, evidently I'm 12 years old! "Many an.." you get the idea.) I saw the technical Latin pronunciation is po-lee-EE-nuhs. The Greek is Πολύαινος (Polyainos), something like pol-Ü-eye-nos in Ancient Greek or modern Greek sort of like pol-EE-ehnos (I think).

    He's not mentioned a lot in the ancient texts, but I think the dictionary entry above doesn't include Philodemus. I seem to remember mention of him mentioning Polyainos in his works.

    DL mentions him by name, X.24:


    Next came Polyaenus,37 son of Athenodorus, a citizen of Lampsacus, a just and kindly man, as Philodemus and his pupils affirm.

    and footnote 37 reads


    One of the four pillars of the school : a great geometer until he became an Epicurean (Cic. Ac. Pr. 106 and De fin. i. 20). A letter of Epicurus to him is mentioned by Seneca (Ep. 18. 9).

    Cicero's Academics seems to just mention him by name. De Fin has this:


    It is also unworthy of a natural philosopher to deny the infinite divisibility of matter; an error that assuredly Epicurus would have avoided, if he had been willing to let his friend Polyaenus teach him geometry instead of making Polyaenus himself unlearn it.

    and Seneca mentions this


    (Seneca’s Letters – Book I – Letter XVIII) Even Epicurus, the teacher of pleasure, used to observe stated intervals, during which he satisfied his hunger in a stingy (maligne) fashion; he wished to see whether he thereby fell short of full and complete happiness, and, if so, by what amount be fell short, and whether this amount was worth purchasing at the price of great effort. At any rate, he makes such a statement in the well known letter written to Polyaenus in the archonship of Charinus. Indeed, he boasts that he himself lived on less than a penny, but that Metrodorus, whose progress was not yet so great, needed a whole penny. Do you think that there can be fullness on such fare? Yes, and there is pleasure also, – not that shifty and fleeting Pleasure which needs a fillip now and then, but a pleasure that is steadfast and sure.

    That's not a lot to go on. There's the Wikipedia article that mentions an Italian translation of fragments.

    I think it's also worth noting the "stated intervals" of Epicurus fasting or eating minimally. This implies that he in fact didn't live on bread and water all the time (as some try to say) but it sounds like he did experiment from time to time during "stated intervals" to ascertain his limits as to what would satisfy him and provide pleasure/absence of pain of hunger. (Side note: it appears the actual coin mentioned by Seneca is the Roman as: Epicurus didn't require a whole "as" but Metrodorus did: Et quidem gloriatur non toto asse se pasci, Metrodorum, qui nondum tantum profecerit, toto.Here is a site talking about the purchasing power of Roman coins.)

  • Don has summarized much of the reliable information about Polyaenus above. The following does not rise to the same level of authority, but Frances Wright devoted a section of "A Few Days In Athens" to this topic, and gave her opinion on how the story of Polyaenus's focus on mathematics after he became an Epicurean should likely be interpreted.

    Most of Chapter 9 of A Few Days In Athens is relevant, but here is the central part as it relates to Polyaenus:

    “But,” said Leontium, “the young Corinthian may be curious to know the sentiments of our master, and his advice regarding the pursuit of the sciences and the liberal arts. I can readily perceive,” addressing herself to Theon, “the origin of the two contradictory reports you have just mentioned. The first you would hear from the followers of Aristippus, who, though not acknowledging the name, follow the tenets of his philosophy, and have long been very numerous in our degenerate city. These, because Epicurus recommends but a moderate culture of those arts, which by them are too often made the elegant incentives to licentious pleasure, accuse him of neglecting them altogether. The cynics, and other austere sects, who condemn all that ministers to the luxury, ease, or recreation of man, exaggerate his moderate use of these arts into a vicious encouragement of voluptuousness and effeminacy. You will perceive, therefore, that between the two reports lies the truth. Every innocent recreation is permitted in the garden. It is not poetry, but licentious poetry, that Epicurus condemns; not music, but voluptuous music; not painting, but licentious pictures; not dancing, but loose gestures. Yet thus he displeases alike the profligate and the austere; for these he is too moderate, and for those too severe. “With regard to the sciences, if it be said, that they are neglected among us, I do not say that our master, though himself versed in them, as in all other branches of knowledge, greatly recommends them to our study but that they are not unknown, let Polyoenus be evidence.

    “He, one of the most amiable men of our school, and one most highly favored by our master, you must have heard mentioned throughout Greece as a profound geometrician.”

    “Yes,” replied Theon, “but I have also heard, that since entering the garden, he has ceased to respect his science.”

    “I am not aware of that,” said Leontium, “though I believe he no longer devotes to it all his time, and all his faculties. Epicurus called him from his diagrams, to open to him the secrets of physics, and the beauties of ethics; to show him the springs of human action, and lead him to the study of the human mind. He taught him, that any single study, however useful and noble in itself, was yet unworthy the entire employ of a curious and powerful intellect; that the man who pursued one line of knowledge, to the exclusion of others, though he should follow it up to its very head, would never be either learned or wise; that he who pursues knowledge, should think no branch of it unworthy attention; least of all, should he confine it to those which are unconnected with the business, and add nothing to the pleasures of life; that further not our acquaintance with ourselves, nor our fellows; that tend not to enlarge the sphere of our affections, to multiply our ideas and sensations, nor extend the scope of our inquiries. On this ground, he blamed the devotion of Polyoenus to a science that leads to other truths than those of virtue, to other study than that of man.”

    “I am obliged to you for the explanation,” said Theon; “not because I could any longer have given credit to the absurd reports of your master’s enemies; but because, whatever opens to me the character and opinions of such a man, interests and improves me.”

    “You will find this,” said Metrodorus, ” the more you consider them. The life of Epicurus is a lesson of wisdom. It is by example, even more than precept, that he guides his disciples. Without issuing commands, he rules despotically. His wishes are divined, and obeyed as laws; his opinions are repeated as oracles; his doctrines adopted as demonstrated truths. All is unanimity in the garden. We are a family of brothers, of which Epicurus is the father. And I say not this in praise of the scholars, but the master. Many of us have had bad habits, many of us evil propensities, many of us violent passions. That our habits are corrected, our propensities changed, our passions restrained, lies all with Epicurus. What I myself owe him, none but myself know. The giddy follower of licentious pleasure, the headstrong victim of my passions, he has made me taste of the sweets of innocence, and brought me into the calm of philosophy. It is thus — thus, by rendering us happy, that he lays us at his feet — thus that he gains, and holds the empire of our minds — thus that by proving himself our friend, he secures our respect, our submission, and our love. He cannot but know his power, yet he exerts it in no other way, than to mend our lives, or to keep them innocent. In argument, as you may have observed, he always seeks to convince rather than sway. He is as free from arrogance as from duplicity; he would neither force an opinion on the mind, nor conceal from it a truth. Ask his advice, and it is ever ready — his opinion, and he gives it clearly. Free from prejudice himself, he is tender to that of others; yet no fear of censure, or desire of popularity, ever leads him to humor it, either in his lessons or his writings. Candor, as you have already remarked, is the prominent feature of his mind; it is the crown of his perfect character. I say this, my young Corinthian, who know him. His soul, indeed, is open to all; but I have approached very near it, and considered its innermost recesses. Yes, I am proud to say it — I am one of those he has drawn most closely into his intimacy. With all my imperfections and errors, he has adopted me as a son; and, inferior as I am in years, wisdom and virtue, he deigns to call me his friend.”

  • Wikipedia's Entry as of 08/09/20:

    Polyaenus of Lampsacus (/ˌpɒliːˈiːnəs/ POL-ee-EE-nəs; Greek: Πoλύαινoς Λαμψακηνός, Polyainos Lampsakēnos; c. 340 – c. 285 BCE), also spelled Polyenus, was an ancient Greek mathematician and a friend of Epicurus.


    1 Life 2 Writings 3 Notes 4 References


    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.[1][2] But the statement may be at least doubted, since it is certain Polyaenus wrote a mathematical work called Puzzles (Greek: Aπoριαι) in which the validity of geometry is maintained. It was against this treatise that another Epicurean, Demetrius Lacon, wrote Unsolved questions of Polyaenus (Greek: 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.


    The works attributed to Polyaenus include:[3]

    • On Definitions
    • On Philosophy
    • Against Aristo
    • Puzzles (Aporiai)
    • On the Moon
    • Against the Orators
    • His collected Letters.

  • Cassius

    Changed the title of the thread from “Information in the Texts About Polyaenus” to “References For The Discussion Of Polyaenus”.