ὑπεπιμόριος: Difference between revisions

|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 <b class="b3">ὑπόλογοι, ἐπιμόριος</b> etc. being [[πρόλογοι]].