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ὑπεπιμόριος: Difference between revisions
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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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|elrutext='''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). | |||
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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]]»]. | ||
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