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ἐπί

Perseus.on, upon with gen., dat., and acc.
prep. with gen., dat., and acc.: Radic. signf. upon.
A.WITH GEN.:
I.of Place,
1.with Verbs of Rest, upon or on, κεῖσθαι ἐπὶ χθονός Il.; ἐφ᾽ ἵππου on horse-back, etc.; ἐπὶ γῆς upon earth, Soph.; ἐπ᾽ ἀγροῦ in the country, Od.; also at or near, ἐπὶ Λήμνου off Lemnos, Hdt., etc.:—with Verbs of motion, the sense is pregnant, ἐπ᾽ ἠπείροιο ἔρυσσαν drew the ship upon the land and left it there, Il., etc.; ἀναβῆναι ἐπὶ τῶν πύργων Xen.
2.not strictly of Place, μένειν ἐπὶ τῆς ἀρχῆς to remain in the command, id=Xen.; ἐπὶ τῶν πραγμάτων engaged in business, Dem.: —of ships, ὁρμεῖν ἐπ᾽ ἀγκύρας to ride at (i. e. in dependence on an) anchor, Hdt.
3.with the person. and reflex. Pron., ἐφ᾽ ὑμείων by yourselves, Il.; ἐφ᾽ αὑτοῦ by himself, Thuc.; αὐτὸς ἐφ᾽ ἑαυτοῦ Xen.
4.with numerals, to denote the depth of a body of soldiers, ἐπὶ τεττάρων four deep, id=Xen.; ἐπ᾽ ὀλίγων i. e. in a long thin file, id=Xen.; ἐφ᾽ ἑνός in single file, id=Xen.
5.c.gen. pers. before, in presence of, Lat. coram, ἐπὶ πάντων Dem.
6.with Verbs of observing, in, ὁρᾶν τι ἐπί τινος Xen.
7.of motion towards, προτρέποντο ἐπὶ νηῶν Il.; πλεῖν ἐπὶ Χίου to sail for Chios, Hdt.; ἐπὶ Βαβυλῶνος ὁδός the road leading to B., Xen.
II.of Time, in the time of, ἐπὶ προτέρων ἀνθρώπων Il.; ἐπὶ Κύρου Hdt.; ἐπ᾽ ἐμοῦ in my time, id=Hdt.
III.in various Causal senses:
1.over, of persons in authority, ἐπὶ τῶν ὁπλιτῶν, ἐπὶ τῶν ἱππέων Dem.; ἐπὶ τῆς διοικήσεως the paymaster, id=Dem.
3.of occasions, and the like, ἐπὶ πάντων on all occasions, Dem.; so in phrases which became adverbial, ἐπ᾽ ἴσης (sc. μοίρας) equally, Soph.
B.WITH DAT.:
I.of Place, upon, ἕξεσθαι ἐπὶ δίφρῳ Il.:—with Verbs of Motion, id=Il.; in pregnant construction, πέτονται ἐπ᾽ ἄνθεσιν fly on to the flowers and settle there, id=Il.:— at or near, ἐπὶ θύρῃσι id=Il.:— on or over, ἐπ᾽ Ἰφιδάμαντι over the body of Iphidamas, id=Il.
2.in hostile sense, against, Hdt.
3.towards, in reference to, ἐπὶ πᾶσι Il.; νόμον τίθεσθαι ἐπί τινι to make a law for his case, whether for or against, Plat.
4.of accumulation, upon, after, ὄγχνη ἐπ᾽ ὄγχνῃ one pear after another, Od.
5.in addition to, ἐπὶ τοῖσι besides, ἐπὶ τούτοις attic
6.of position, after, behind, of soldiers, Xen.
7.in dependence upon, in the power of, Lat. penes, ἐπί τινί ἐστι 'tis in his power to do, c. inf., Hdt.; τὸ ἐπ᾽ ἐμοί as far as is in my power, Xen.
8.of condition or circumstances, Il., etc.; ἐπὶ τῷ παρόντι Thuc.
II.of Time, ἐπὶ νυκτί by night, Il.; αἰεὶ ἐπ᾽ ἤματι every day, Od.
III.in various Causal senses:
1.of the occasion or cause, ἐπὶ σοί for thee, Il.; μέγα φρονεῖν ἐπί τινι to be proud at or of a thing, Plat.; ἀγανακτεῖν ἐπί τινι Xen.
2.of an end or purpose, ἐπὶ δόρπῳ for supper, Od.; ἐπὶ κακῷ for mischief, Hdt.; δῆσαι ἐπὶ θανάτῳ id=Hdt., Xen.; ἐπ᾽ ἐξαγωγῇ for exportation, Hdt.
3.of the condition upon which a thing is done, ἐπὶ τούτοις on these terms, id=Hdt.; ἐφ᾽ or ἐφ᾽ ᾧτε on condition that, id=Hdt.; ἐπὶ οὐδενί on no account, id=Hdt.; ἐπ᾽ ἴσῃ καὶ ὁμοίᾳ on fair and equal terms, Thuc.
5.κεκλῆσθαι ἐπί τινι to be called after, Plat.
6.of persons in authority, ἐπὶ βουσίν over the kine, Od.; ἐπὶ ταῖς ναυσίν Xen.; οἱ ἐπὶ τοῖς πράγμασιν Dem.
C.WITH ACC.:
2.up to, as far as, ἐπὶ θάλασσαν Thuc.:—in measurements, πλέον ἐπὶ δύο στάδια Xen.; with a neut. adj., ὅσον τ᾽ ἔπι as far as, Il.; ἐπὶ πᾶν ἐλθεῖν Xen.; ἐπὶ σμικρόν, a little way, a little, Soph.; ἐπ᾽ ἔλαττον, ἐπ᾽ ἐλάχιστον Plat., etc.
3.ἐπὶ πλέον still more, Hdt.; before, Lat. coram, ἦγον αὐτὸν ἐπὶ τὰ κοινά id=Hdt.
4.in Military phrases, ἐπ᾽ ἀσπίδας πέντε καὶ εἴκοσιν, i. e. 25 in file, Thuc.
5.towards, to, ἐπὶ δεξιά, ἐπ᾽ ἀριστερά Hom., etc.:—also in Military phrases, ἐπὶ δόρυ ἀναστρέψαι, ἐπὶ ἀσπίδα μεταβαλέσθαι, to the spear or shield side, i. e. to right or left, Xen.; ἐπὶ πόδα ἀναχωρεῖν to retire on the foot, i. e. facing the enemy, id=Xen.; ἐπὶ τὸ μεῖζον, with exaggeration, Thuc.; ἐπὶ τὰ γελοιότερα so as to provoke laughter, Plat.
6.in hostile sense, against, Il., etc.
7.of extension over a space, ἐπ᾽ ἐννέα κεῖτο πέλεθρα over nine acres he lay stretched, id=Il.; ἐπὶ πολύ over a large space, Thuc.:—so in many cases, where we say on, rather than over, δράκων ἐπὶ νῶτα δαφοινός Il.; ἵππους ἐπὶ νῶτον ἐΐσας id=Il.
II.of Time, for or during a certain time, πολλὸν ἐπὶ χρόνον id=Il.; ἐπὶ δέκα ἔτη Thuc.
2.up to or till a certain time, ἐπ᾽ ἠῶ καὶ μέσον ἦμαρ Od.
III.in various Causal senses:
1.of the object or purpose for which one goes, ἐπὶ Τυδῆ for (i. e. to bring) tidings of Tydeus, Il.; ἐλθεῖν ἐπ᾽ ἀργύριον Xen.:—with neut. Pron., ἐπὶ τοῦτο ἐλθεῖν for this purpose, id=Xen.; ἐπὶ τί; to what end? Lat. quorsum? Ar.; ἐπὶ τόκον for (i. e. to gain) interest, Dem.
2.as regards, τοὐπ᾽ ἐμέ, τοὐπί σε Eur.
4.according to, by, ἐπὶ στάθμην by the rule, Od.
D.POSITION:— ἐπί may follow its case, when it becomes ἔπι by anastrophe.
E.ABSOL., ἐπί without anastrophe, esp. ἐπὶ δέ, and besides, Hdt.
II.ἔπι, for ἔπεστι, 'tis here, Hom.
F.IN COMPOS.:
I.of Place, denoting Rest upon, as in ἐπίκειμαι, or Motion, upon or over, as in ἐπιβαίνω; to or towards, as in ἐπαρίστερος, ἐπιδέξιος; against, as in ἐπαΐσσω, ἐπιστρατεύω; up to a point, as in ἐπιτελέω; over or beyond boundaries, as in ἐπινέμομαι, ἐπεργασία.
2.Extension over a surface, as in ἐπαλείφω, ἐπάργυρος, ἐπίχρυσος.
3.Accumulation or addition, as in ἐπιβάλλω, ἐπίκτητος.
4.Accompaniment, to, with, as in ἐπᾴδω, ἐπαυλέω.
5.Interest, ἐπίτριτος one and 1/3 more, 1+1/3, Lat. sesquitertius; so ἐπιτέταρτος, etc.
II.of Time and Sequence, after, as in ἐπιγίγνομαι.
III.in Causal senses, of Superiority felt over or at, as in ἐπιχαίρω, ἐπιγελάω; of Authority, over, as in ἐπικρατέω, ἐπιβούκολος; of Motive, for, as in ἐπιθυμέω, ἐπιθάνατος; to give force or intensity to the Verb, as in ἐπαινέω, ἐπιμέμφομαι.

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