ὑπεπιμόριος: Difference between revisions

|Definition=ὑπεπιμόριον, an arithmetical term, the reciprocal of [[ἐπιμόριος]], represented by the fraction 1/(1 + 1/n) or n/(n + 1), [[Aristotle|Arist.]]''[[Metaphysics|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]].