ὑπεπιμόριος: Difference between revisions
αἰτῶ δ' ὑγίειαν πρῶτον, εἶτ' εὐπραξίαν, τρίτον δὲ χαίρειν, εἶτ' ὀφείλειν μηδενί → first health, good fortune next, and third rejoicing; last, to owe nought to any man
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|Definition=ον, an arithmetical term, the reciprocal of <b class="b3">ἐπιμόριος</b>, represented by the fraction 1/(1 + 1/n) or n/(n + 1), <span class="bibl">Arist.<span class="title">Metaph.</span> 1021a2</span>:—so ὑφημιόλιος is the reciprocal of <b class="b3">ἡμιόλιος</b> (<span class="bibl">2</span>/<span class="bibl">3</span> of <span class="bibl">3</span>/<span class="bibl">2</span>), ὑπεπίτριτος of <b class="b3">ἐπίτριτος</b> (<span class="bibl">3</span>/<span class="bibl">4</span> of <span class="bibl">4</span>/<span class="bibl">3</span>), ὑπεπιτέταρτος of <b class="b3">ἐπιτέταρτος</b> (<span class="bibl">4</span>/<span class="bibl">5</span> of <span class="bibl">5</span>/<span class="bibl">4</span>), ὑπεπόγδοος of <b class="b3">ἐπόγδοος</b> (<span class="bibl">8</span>/<span class="bibl">9</span> of <span class="bibl">9</span>/<span class="bibl">8</span>), etc., <span class="bibl">Nicom.<span class="title">Ar.</span>1.19</span>, <span class="bibl"><span class="title">Exc.</span>2</span>, Theo Sm.<span class="bibl">p.75</span> H., etc.; and so ὑπεπιμερής is the reciprocal of <b class="b3">ἐπιμερής</b>, Nicom.<span class="title">Ar.</span>l.c.—These ratios are called <b class="b3">ὑπόλογοι, ἐπιμόριος</b> etc. being <b class="b3">πρόλογοι</b>. | |Definition=ον, an arithmetical term, the reciprocal of <b class="b3">ἐπιμόριος</b>, represented by the fraction 1/(1 + 1/n) or n/(n + 1), <span class="bibl">Arist.<span class="title">Metaph.</span> 1021a2</span>:—so ὑφημιόλιος is the reciprocal of <b class="b3">ἡμιόλιος</b> (<span class="bibl">2</span>/<span class="bibl">3</span> of <span class="bibl">3</span>/<span class="bibl">2</span>), ὑπεπίτριτος of <b class="b3">ἐπίτριτος</b> (<span class="bibl">3</span>/<span class="bibl">4</span> of <span class="bibl">4</span>/<span class="bibl">3</span>), ὑπεπιτέταρτος of <b class="b3">ἐπιτέταρτος</b> (<span class="bibl">4</span>/<span class="bibl">5</span> of <span class="bibl">5</span>/<span class="bibl">4</span>), ὑπεπόγδοος of <b class="b3">ἐπόγδοος</b> (<span class="bibl">8</span>/<span class="bibl">9</span> of <span class="bibl">9</span>/<span class="bibl">8</span>), etc., <span class="bibl">Nicom.<span class="title">Ar.</span>1.19</span>, <span class="bibl"><span class="title">Exc.</span>2</span>, Theo Sm.<span class="bibl">p.75</span> H., etc.; and so ὑπεπιμερής is the reciprocal of <b class="b3">ἐπιμερής</b>, Nicom.<span class="title">Ar.</span>l.c.—These ratios are called <b class="b3">ὑπόλογοι, ἐπιμόριος</b> etc. being <b class="b3">πρόλογοι</b>. | ||
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|lstext='''ὑπεπιμόριος''': -ον, ἀριθμητικὸς ὅρος, [[ἀντίστροφος]] τῷ [[ἐπιμόριος]], παριστανόμενος διὰ τοῦ κλάσματος, x / x-1, ὡς ἀντίστοφον τῷ x-1 / x, Ἀριστ. Μετὰ τὰ Φυσ. 4. 15, 3, [[ἔνθα]] ἴδε Bonitz.· [[οὕτως]] [[ὑφημιόλιος]] [[εἶναι]] τὸ ἀντίστροφον τοῦ [[ἡμιόλιος]] (2/3 καὶ 3/2), ὑπεπίτριτος τοῦ [[ἐπίτριτος]] (2/3 καὶ 3/2), ὑπεπιτέταρτος τοῦ [[ἐπιτέταρτος]] (3/4 καὶ 4/3),κτλ.· οὕτω καὶ ὑπεπιμερὴς [[εἶναι]] ἀντίστροφον τοῦ [[ἐπιμερής]], ἴδε Νικομ. Ἀριθμ. 1. 19. - Οἱ λόγοι οὗτοι καλοῦνται ὑπόλογοι, τὰ δὲ [[ἐπιμόριος]] κτλ. καλοῦνται πρόλογοι. | |||
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Revision as of 11:16, 5 August 2017
English (LSJ)
ον, an arithmetical term, the reciprocal of ἐπιμόριος, represented by the fraction 1/(1 + 1/n) or n/(n + 1), Arist.Metaph. 1021a2:—so ὑφημιόλιος is the reciprocal of ἡμιόλιος (2/3 of 3/2), ὑπεπίτριτος of ἐπίτριτος (3/4 of 4/3), ὑπεπιτέταρτος of ἐπιτέταρτος (4/5 of 5/4), ὑπεπόγδοος of ἐπόγδοος (8/9 of 9/8), etc., Nicom.Ar.1.19, Exc.2, Theo Sm.p.75 H., etc.; and so ὑπεπιμερής is the reciprocal of ἐπιμερής, Nicom.Ar.l.c.—These ratios are called ὑπόλογοι, ἐπιμόριος etc. being πρόλογοι.
Greek (Liddell-Scott)
ὑπεπιμόριος: -ον, ἀριθμητικὸς ὅρος, ἀντίστροφος τῷ ἐπιμόριος, παριστανόμενος διὰ τοῦ κλάσματος, x / x-1, ὡς ἀντίστοφον τῷ x-1 / x, Ἀριστ. Μετὰ τὰ Φυσ. 4. 15, 3, ἔνθα ἴδε Bonitz.· οὕτως ὑφημιόλιος εἶναι τὸ ἀντίστροφον τοῦ ἡμιόλιος (2/3 καὶ 3/2), ὑπεπίτριτος τοῦ ἐπίτριτος (2/3 καὶ 3/2), ὑπεπιτέταρτος τοῦ ἐπιτέταρτος (3/4 καὶ 4/3),κτλ.· οὕτω καὶ ὑπεπιμερὴς εἶναι ἀντίστροφον τοῦ ἐπιμερής, ἴδε Νικομ. Ἀριθμ. 1. 19. - Οἱ λόγοι οὗτοι καλοῦνται ὑπόλογοι, τὰ δὲ ἐπιμόριος κτλ. καλοῦνται πρόλογοι.
