ἑξῆς

A. one after another, in order, in a row, ἑξῆς εὐνάζοντο Od. 4.449; ἑξῆς δ’ ἑζόμενοι ib.580 (elsewh. Hom. uses the form ἑξείης, Il. 6.241, Od. 4.408); πάντας ἑ. . . κτείνοντες Th. 7.29, cf. E. Fr. 657.2; τὰ ἑ. v.l. in Arist. Cael. 310b12.

b. Math., ἑ. ἀνάλογον in continued proportion, Euc. 8.1, al.; οἳ ἑ. ἀριθμοί successive numbers, Archim. Spir.Praef.; γραμμαὶ ἑ. κείμεναι placed in order, ib.11; τούτου ἑ. γινομένου if this be done continually, Id. Sph.Cyl. 1.11.

2. ἑ. διεξελθεῖν, λέγειν, in a regular, consequential manner, Pl. Plt. 257b, 286c; τοῦ ἑ. ἕνεκα περαίνεσθαι τὸν λόγον Id. Grg. 454c; ὁ ἑ. λόγος the following argument, Id. Ti. 20b; ἐν ἅπασι τούτοις ἑ. Longin. 9.14, cf. 4.4.

3. Gramm., τὸ ἑ. grammatical sequence, opp. ὑπερβατόν, A.D. Pron. 41.3,al.; καὶ τὰ ἑ., Lat. et cetera, PTeb. 319.34 (iii A. D.), etc.

4. of Time, thereafter, next, A. Fr. 475, Ar. Ec. 638; τὸν ἑ. χρόνον Pl. Plt. 271b; ἡ ἑ. ἡμέρα Ev.Luc. 9.37; ἐν τῷ (v.l. τῇ)ἑ. next day, ib.7.11; εἰς τὸ ἑ. for the future, POxy. 474.28 (ii A.D.), etc.

b. of Place, next, E. IA 249, Arist. Mu. 392a26.

II. c.gen., next to, τινός Ar. Ra. 765; τὰ τούτων ἑ. Pl. R. 390a; τούτων ἑ. next after . ., D. 18.102; of logical connexion, Pl. Phlb. 42c: c. dat., next to, Λάχητι . . τὴν ἑ. θύραν Ephipp. 16; τούτοις ἑ. next in order to, Pl. Cra. 399d, al.; τὸ ἑ. τῇ γεωμετριᾳ what comes next to . ., Id. R. 528a; τὸ ἑ. ἔργον τοῖς Μαραθῶνι next after, Id. Mx. 241a; ἑ. Ἀριστογείτονι beside A., Ar. Lys. 633; παρὰ τὸ ἑ. τῷ νοερῷ ζῴῳ that which befits . ., M.Ant. 4.5; ἐπεχορήγησα αὐτῇ τὰ ἑ. made suitable provision for her, POxy. 282.7 (i A.D.).