LSJ

ἀρχή , h(, (v. ἄρχω)
A. [select] beginning, origin, “νείκεος ἀ.” Il.22.116; “πήματος” Od.8.81; “φόνου” 21.4, etc.; opp. τέλος, Hdt.7.51, etc.; opp. τελευτή, Thgn.607, cf. Pl.Lg.715e, Hp.Morb.1.1; “ἀ. γενέσθαι κακῶν” Hdt.5.97; “ἀ. ποιήσασθαί τινος” Th.1.128, And.2.37, Isoc.12.120, etc.; “ἀ. λαβεῖν τινός” Aeschin.1.11; “τὰς ἀρχὰς εἰληφέναι” Plb.4.28.3; ἀρχὴν ὑποθέσθαι lay a foundation, D.3.2, etc.; “βαλέσθαι” Pl.Ep.326e (and Pass., “ἀρχαὶ βέβληνται” Pi.N.1.8); “ἀρχὴν ἄρχεσθαί τινος” Pl.Ti.36e; source of action, [“ὁ ἄνθρωπος] ἔχει ἀρχὴν ἐλευθέραν” Plot.3.3.4.
b. [select] with Preps. in adverbial usages, ἐξ ἀρχῆς from the beginning, from the first, from of old, Od.1.188, Xenoph.10, etc.; “οὑξ ἀ. φίλος” S.OT385; “ἡ ἐξ ἀ. ἔχθρα” D.54.3; “τὸ ἐξ ἀ.” X.Cyn.12.6; but “πλουτεῖν ἐξ ἀ. πάλιν” anew, afresh, Ar.Pl.221; “λόγον πάλιν ὥσπερ ἐξ ἀ. κινεῖν” Pl.R.450a; ὁ ἐξ ἀ. λόγος the original argument, Id.Tht.177c, etc.; τὰ ἐξ ἀ. the principal sum, Arist.Pol.1280a30:—also “ἀπ᾽ ἀ.” Hes.Th.425, Hdt.2.104, Pi.P.8.25, A.Supp.344, Pl.Tht.206d; κατ᾽ ἀρχάς in the beginning, at first, Hdt.3.153, 7.5; “αὐτίκα κατ᾽ ἀ.” Id.8.94; “τὸ κατ᾽ ἀ.” Pl. Lg.798a, al.
c. [select] acc. ἀρχήν, abs., to begin with, at first, Hdt. 1.9, 2.28, 8.132; “τὴν ἀρχήν” And.3.20: pl., “τὰς ἀρχάς” Plb.16.22.8: freq. followed by a neg., not at all, “ἀρχὴν μηδὲ λαβών” Hdt.3.39, cf. 1.193, al.; “ἀ. δὲ θηρᾶν οὐ πρέπει τἀμήχανα” S.Ant.92; “ἀ. κλύειν ἂν οὐκ . . ἐβουλόμην” Id.Ph.1239, cf. El.439, Philol.3, Antipho5.73, Pl. Grg.478c; sts. c. Art., “τοῦτο οὐκ ἐνδέκομαι τὴν ἀ.” Hdt.4.25; “τὴν ἀ. γὰρ ἐξῆν αὐτῷ μὴ γράφειν” D.23.93.
2. [select] first principle, element, first so used by Anaximander, acc. to Simp. in Ph.150.23, cf. Arist. Metaph.983b11, etc.; “Ἡράκλειτος τὴν ἀ. εἶναί φησι ψυχήν” Id.de An.405a25; of ὕλη and θεός, opp. στοιχεῖα, Placit.1.3.25; practical principle of conduct, “τῶν πράξεων τὰς ἀρχὰς καὶ τὰς ὑποθέσεις” D. 2.10; principles of knowledge, Arist.Metaph.995b8, al.
3. [select] end, corner, of a bandage, rope, sheet, etc., Hdt.4.60, Hp.Off.9, E.Hipp. 762, Aen.Tact.18.14, Act.Ap.10.11; of a compound pulley, Hero Bel.84.14.
4. [select] Math., origin of a curve, “τῆς ἕλικος” Archim.Spir. 11 Def.2, etc.; “ξυνὸν ἀ. καὶ πέρας ἐπὶ κύκλου περιφερείας” Heraclit. 103.
5. [select] branch of a river, LXX Ge.2.10 (pl.).
6. [select] sum, total, ib.Nu.1.2.
7. [select] vital organs of the body, Gal.1.318, al.
II. [select] first place or power, sovereignty (not in Hom.), “Διὸς ἀρχά” Pi.O.2.64, cf. Hdt.1.6, etc.; “γενέσθαι ἐπ᾽ ἀρχῆς” Arist.Pol.1284b2: metaph., μεγάλην μεντἂν ἀ. εἴης εὑρηκώς, of a stroke of fortune, D.21.196: pl., “ἀρχαὶ πολισσονόμοι” A.Ch.864 (lyr.); “τὰς ἐμὰς ἀρχὰς σέβων” S.Ant.744, etc.: c. gen. rei, “τῆσδ᾽ ἔχων ἀρχὴν χθονός” S.OT737; ἀ. τῶν νεῶν, τῆς θαλάσσης, power over them, Th.3.90, X.Ath.2.7, etc.: prov., ἀ. ἄνδρα δείξει Biasap.Arist.EN1130a1, cf. D.Prooem.48; method of government, “οὐδὲ τὴν ἄλλην ἀ. ἐπαχθής” Th.6.54.
2. [select] empire, realm, Κύρου, Περδίκκου ἀ., Hdt.1.91, Th.4.128, etc.
3. [select] magistracy, office, ἀρχὴν ἄρχειν, παραλαμβάνειν, Hdt.3.80, 4.147; “καταστήσας τὰς ἀ. καὶ ἄρχοντας ἐπιστήσας” Id.3.89; εἰς ἀ. καθ<*>στασθαι Th.8.70; εἰς τὴν α<*>. εἰσιέναι D.59.72, etc.; ἀ. λαχεῖν to obtain an office, Id.57.25; “Ἑλληνοταμίαι τότε πρῶτον κατέστη ἀ.” Th.1.96; “ἐνιαύσιος ἀ.” Id.6.54; ἀ. χειροτονητή, κληρωτή, Lex ap.Aeschin.1.21; withsg. Noun, “Κυθηροδίκης ἀ. ἐκ τῆς Σπάρτης διέβαινεν αὐτόσε” Th.4.53; term of office, “ἀρχῆς λοιποὶ αὐτῷ δύο μῆνες” Antipho6.42; “ἀρχαὶ καὶ λειτουργίαι” POxy.119.16 (iii A.D.).
4. [select] in pl., “αἱ ἀρχαί” the authorities, the magistrates, Th.5.47, cf. Decr. ap. And.1.83; ἐν ταῖς ἀ. ε<*>ναι Th.6.54; ἡ ἀρχή collectively, 'the board', D.47.22, cf. IG1.229, etc.; “παραδιδόναι τινὰ τῇ ἀ.” Antipho5.48; but ἡ ἀ., of a single magistrate, PHal.1.226 (iii B.C.); κατ᾽ ἀρχῆς γὰρ φιλαίτιος λεώς against authority, A.Supp.485; “πομποὺς ἀρχάς” Id.Ag.124 (anap.).
5. [select] command, i.e. body of troops, LXX 1 Ki.13.17, al.
6. [select] pl., heavenly powers, Ep.Rom.8.38, al., cf. Dam. Pr.96; powers of evil, Ep.Eph.6.12, al.
III. [select] = εἶδος μελίσσης ἀκέντρου, Hsch.

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