ἀνά
ὁ δὲ πείσεται εἰς ἀγαθόν περ → he will obey you to his profit, he will obey you for his own good end
English (LSJ)
[ᾰνᾰ], Aeol., Thess., Arc., Cypr. ὀν, Prep. governing gen., dat., and acc. By apocope ἀνά becomes ἄν before dentals, as ἂν τὸν ὀδελόν; ἄγ before gutturals, as ἂγ γύαλα; ἄμ before labials, as ἂμ βωμοῖσι, ἂμ πέτραις, etc.;
A ἀμπεπλεγμένας IG5(2).514.10 (Arc.). A WITH GEN., three times in Od., in phrase ἀνὰ νηὸς βαίνειν go on board ship, 2.416, 9.177, 15.284; ἂν τοῦ τοίχου, τᾶς ὁδοῦ, τοῦ ῥοειδίου, IG14.352i40, ii 15,83 (Halaesa). B WITH DAT., on, upon, without any notion of motion, Ep., Lyr., and Trag. (only lyr.), ἀνὰ σκήπτρῳ upon the sceptre, Il.1.15, Pi.P. 1.6; ἂμ βωμοῖσι Il.8.441; ἀνὰ σκολόπεσσι 18.177; ἀνὰ Γαργάρῳ ἄκρῳ 15.152; ἀνὰ ὤμῳ upon the shoulder, Od.11.128; ἀν ἵπποις, i. e. in a chariot, Pi.O.1.41; ἂμ πέτραις A.Supp.351 (lyr.); ἀνά τε ναυσὶν καὶ σὺν ὅπλοις E.IA754; ἂγ Κόσσῳ GDI1365 (Epirus). C WITH ACCUS., the comm. usage, implying motion upwards: I of Place, up, from bottom to top, up along, κίον' ἀν' ὑψηλὴν ἐρύσαι Od.22.176; ἀνὰ μέλαθρον up to, ib.239; [φλὲψ] ἀνὰ νῶτα θέουσα διαμπερὲς αὐχέν' ἱκάνει Il.13.547; ἀνὰ τὸν ποταμόν Hdt.2.96; ἂν ῥόον up-stream, GDI5016.11 (Gortyn); κρῆς ἂν τὸν ὀδελὸν ἐμπεπαρμένον Ar.Ach.796 (Megarian); simply, along, ἂν τὼς ὄρως Tab.Heracl.2.32. 2 up and down, throughout, ἀνὰ δῶμα Il.1.570; ἀνὰ στρατόν, ἄστυ, ὅμιλον, ib.384, Od.8.173, etc.; ἂγ γύαλα A.Supp.550 (lyr.); ἀνὰ πᾶσαν τὴν Μηδικήν, ἀνὰ τὴν Ἑλλάδα, Hdt.1.96, 2.135, etc.; ὀν τὸ μέσσον Alc. 18.3; ἀνὰ τὸ σκοτεινόν in the darkness, Th.3.22. 3 metaph., ἀνὰ θυμὸν φρονέειν, ἀνὰ στόμα ἔχειν, to have continually in the mind, in the mouth, Il.2.36,250; ἀν' Αἰγυπτίους ἄνδρας among them, Od.14.286; ἀνὰ πρώτους εἶναι to be among the first, Hdt.9.86. II of Time, throughout, ἀνὰ νύκτα all night through, Il.14.80; ἀνὰ τὰς προτέρας ἡμέρας Hdt.7.223; ἀνὰ τὸν πόλεμον 8.123; ἀνὰ χρόνον in course of time, 1.173, 2.151, 5.27; ἀνὰ μέσσαν ἀκτῖνα (i. e. in the south) S.OC1247. 2 distributively, ἀνὰ πᾶσαν ἡμέραν day by day, Hdt.2.37,130, etc.; ἀνὰ πᾶν ἔτος 1.136, etc.; ἀνὰ πάντα ἔτεα 8.65: also ἀνὰ πρεσβύτᾱτα in order of age, Test.Epict.4.28. III distributively with Numerals, κρέα εἴκοσιν ἀν' ἡμιωβολιαῖα 20 pieces of meat at half an obol each, Ar.Ra.554; τῶν ἀν' ὀκτὼ τὠβολοῦ that sell 8 for the obol, Timocl. 18; ἀνὰ πέντε παρασάγγας τῆς ἡμέρας [they marched] at the rate of 5 parasangs a day, X.An.4.6.4; ἔστησαν ἀνὰ ἑκατόν μάλιστα ὥσπερ χοροί they stood in bodies of about 100 men each. ib.5.4.12; κλισίας ἀνὰ πεντήκοντα companies at the rate of 50 in each, Ev.Luc.9.14; ἔλαβον ἀνὰ δηνάριον a denarius apiece, Ev. Matt.20.10; in doctor's prescriptions, ἀνὰ ὀβολὼ β Sor.1.63, etc.: also ἀνὰ δύο ἥμισυ ζῳδίων amounting to 2 1/2 signs, Autol.1.10; multiplied by, PPetr.3p.198. IV Phrases: ἀνὰ κράτος up to the full strength, i. e. vigorously, ἀνὰ κράτος φεύγειν, ἀπομάχεσθαι, X.Cyr.4.2.30, 5.3.12; ἀνὰ τὸν αὐτὸν λόγον and ἀνὰ λόγον proportionately, Pl.Phd. 110d; esp. in math. sense, Id.Ti.37a, Arist.APo.85a38, etc.; ἀνὰ μέσον in the midst, Antiph.13, Men.531.19; ἀνὰ μέρος by turns, Arist.Pol.1287n17. D WITH NOM. of Numerals, etc., distributively, Apoc.21.21, v. l. in Sor.1.11, 12, cf. Orib.Fr.50,54. E WITHOUT CASE as Adv., thereupon, Hom. and other Poets:— and with the notion of spreading all over a space, throughout, all over, μέλανες δ' ἀνὰ βότρυες ἦσαν all over there were clusters, Il.18.562, cf. Od.24.343:—but ἀνά often looks like an Adv. in Hom., where really it is only parted from its Verb by tmesis, ἀνὰ δ' ἔσχετο; ἀνὰ δ' ὦρτο (for ἀνῶρτο δέ) ; ἀνὰ τεύχε' ἀείρας (for τεύχεα ἀναείρας), etc. F IN COMPOS. 1 as in C. 1, up to, upwards, up, opp. κατά, as ἀνα-βαίνω, -βλέπω, ἀν-αιρέω, -ίστημι: poet. sts. doubled, ἀν' ὀρσοθύρην ἀναβαίνειν Od.22.132. 2 hence flows the sense of increase or strengthening, as in ἀνακρίνω; though it cannot always be translated, as in Homer's ἀνείρομαι:—in this case opp. ὑπό. 3 from the notion throughout (E), comes that of repetition and improvement, as in ἀνα-βλαστάνω, -βιόω, -γεννάω. 4 the notion of back, backwards, in ἀναχωρέω, ἀνανεύω, etc., seems to come from such phrases as ἀνὰ ῥόον up, i. e. against, the stream. G ἄνα, written with anastr. as Adv., up! arise! ἀλλ' ἄνα Il.6.331, Od.18.13:—in this sense the ult. is never elided; cf. ἀλλ' ἄνα, εἰ μέμονάς γε Il.9.247; ἀλλ' ἄνα ἐξ ἑδράνων S.Aj.194. 2 apocop. ἄν after ὤρνυτο, ὦρτο, and up stood . . arose, Il.3.268, 23.837, etc. 3 when used as Prep. ἀνά never suffers anastrophe.