ὑπεπιμόριος: Difference between revisions
δυοῖν κακοῖν προκειμένοιν τὸ μὴ χεῖρον βέλτιστον → the lesser of two evils, the less bad thing of a pair of bad things, better the devil you know, better the devil you know than the devil you don't, better the devil you know than the devil you don't know, better the devil you know than the one you don't, better the devil you know than the one you don't know, the devil that you know is better than the devil that you don't know, the devil we know is better than the devil we don't, the devil we know is better than the devil we don't know, the devil you know is better than the devil you don't
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|Definition=ον, an arithmetical term, the reciprocal of [[ἐπιμόριος]], 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 [[ἡμιόλιος]] (<span class="bibl">2</span>/<span class="bibl">3</span> of <span class="bibl">3</span>/<span class="bibl">2</span>), ὑπεπίτριτος of [[ἐπίτριτος]] (<span class="bibl">3</span>/<span class="bibl">4</span> of <span class="bibl">4</span>/<span class="bibl">3</span>), ὑπεπιτέταρτος of [[ἐπιτέταρτος]] (<span class="bibl">4</span>/<span class="bibl">5</span> of <span class="bibl">5</span>/<span class="bibl">4</span>), ὑπεπόγδοος of [[ἐπόγδοος]] (<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 [[ἐπιμερής]], Nicom.<span class="title">Ar.</span>l.c.—These ratios are called [[ὑπόλογοι]], [[ἐπιμόριος]] etc. being [[πρόλογοι]]. | |Definition=ον, an arithmetical term, the reciprocal of [[ἐπιμόριος]], 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 [[ἡμιόλιος]] (<span class="bibl">2</span>/<span class="bibl">3</span> of <span class="bibl">3</span>/<span class="bibl">2</span>), ὑπεπίτριτος of [[ἐπίτριτος]] (<span class="bibl">3</span>/<span class="bibl">4</span> of <span class="bibl">4</span>/<span class="bibl">3</span>), ὑπεπιτέταρτος of [[ἐπιτέταρτος]] (<span class="bibl">4</span>/<span class="bibl">5</span> of <span class="bibl">5</span>/<span class="bibl">4</span>), ὑπεπόγδοος of [[ἐπόγδοος]] (<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 [[ἐπιμερής]], Nicom.<span class="title">Ar.</span>l.c.—These ratios are called [[ὑπόλογοι]], [[ἐπιμόριος]] etc. being [[πρόλογοι]]. | ||
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|mltxt=και [[ὑποεπιμόριος]], -ον, Α<br />(για αριθμό) [[αντίστροφος]] του [[ἐπιμόριος]], που παριστάνεται με το [[κλάσμα]] <i>x</i>/<i>x</i>-1 ως αντίστροφο του <i>x</i>-1/<i>x</i>.<br />[<b><span style="color: brown;">ΕΤΥΜΟΛ.</span></b> <span style="color: red;"><</span> <i>ὑπ</i>(<i>ο</i>)- <span style="color: red;">+</span> [[ἐπιμόριος]] «[[αριθμός]] που περιέχει ένα ακέραιο [[κλάσμα]] με αριθμητή τη [[μονάδα]]»]. | |mltxt=και [[ὑποεπιμόριος]], -ον, Α<br />(για αριθμό) [[αντίστροφος]] του [[ἐπιμόριος]], που παριστάνεται με το [[κλάσμα]] <i>x</i>/<i>x</i>-1 ως αντίστροφο του <i>x</i>-1/<i>x</i>.<br />[<b><span style="color: brown;">ΕΤΥΜΟΛ.</span></b> <span style="color: red;"><</span> <i>ὑπ</i>(<i>ο</i>)- <span style="color: red;">+</span> [[ἐπιμόριος]] «[[αριθμός]] που περιέχει ένα ακέραιο [[κλάσμα]] με αριθμητή τη [[μονάδα]]»]. | ||
}} | }} | ||
Revision as of 12:58, 30 November 2022
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.
German (Pape)
s. ὑπεπιμερής.
Russian (Dvoretsky)
ὑπεπιμόριος: мат. находящийся в обратном отношении (sc. ἀριθμός Arst.; так, напр., если 3 есть ἐπιμόριος по отношению к 2, то 2 есть ὑ. по отношению к 3).
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.
Greek Monolingual
και ὑποεπιμόριος, -ον, Α
(για αριθμό) αντίστροφος του ἐπιμόριος, που παριστάνεται με το κλάσμα x/x-1 ως αντίστροφο του x-1/x.
[ΕΤΥΜΟΛ. < ὑπ(ο)- + ἐπιμόριος «αριθμός που περιέχει ένα ακέραιο κλάσμα με αριθμητή τη μονάδα»].
