διαίρεσις

εως, ἡ
A. divisibility, Arist. Metaph. 1016b4, al.
2. Medic., dissection, ζῴων Gal. 4.664.
b. venesection, Antyll. ap. Orib. 7.9.2.
c. surgical operation, Phld. Lib. p.56O.
d. pl., wounds, Diod.Rh.p.53H.
II. dividing, distribution, of money, Hdt. 7.144; of spoil, X. Cyr. 4.5.55; ἐν διαιρέσει [ψήφων] in the reckoning of the votes on either side, A. Eu. 749; ἀντίγραφον διαιρέσεως BGU 1013.1 (i A.D.).
III. distinction, ἀγνωσίας τε καὶ γνώσεως Pl. Sph. 267b; [τῆς δημοκρατίας καὶ τῆς ὀλιγαρχίας] Arist. Pol. 1294a34.
IV. in Logic, division of genus into species, τῶν γενῶν κατ’ εἴδη δ. Pl. Sph. 267d; ἡ διὰ τῶν γενῶν δ. Arist. APr. 46a31; opp. συναγωγαί, Pl. Phdr. 266b.
b. separation of subject and predicate, περὶ σύνθεσιν καὶ δ. ἐστι τὸ ψεῦδος καὶ τὸ ἀληθές Arist. Int. 16a12.
2. ὁ παρὰ τὴν δ. [λόγος] the fallacy of division (cf. σύνθεσις), Id. SE 177a33.
V. Rhet., division or distribution into heads, Hermog. Prog. 7, Stat. 1, Onos. 2 tit., etc.
VI. Gramm., resolution of a diphthong into two syllables, A.D. Pron. 87.2, al.; of one word into two, κατὰ διαίρεσιν ἀναγνωστέον Ath. 11.492a, cf. Trypho Trop. 1.8.
VII. in Metric, division of a line at the close of a foot, diaeresis, Aristid.Quint. 1.24.
VIII. Math., δ. λόγου transformation of a ratio dividendo, Euc. 5 Def. 15; κατὰ διαίρεσιν Archim. Sph.Cyl. 2.6.
IX. division of troops, of the Roman cohors, J. AJ 7.14.9.
Liddell, Scott & Jones
A Greek-English Lexicon, 1940
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