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ὑπεπιμόριος: Difference between revisions
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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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