ὑπ·επιμόριος, ος, ον, c. ὑπεπιμερής ARSTT. Metaph. 4, 15, 3 ; NICOM. Arithm. 1, 19.

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 (⅔ of 3/2), ὑπεπίτριτος of ἐπίτριτος (¾ of 4/3), ὑπεπιτέταρτος of ἐπιτέταρτος (⅘ 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.

s. ὑπεπιμερής.