ἐπί

197. The preposition ἐπί means over, upοn; sometimes after (as we speak of following upon); with, at (i.e. close upon); in addition, besides, especially οf an addition made to correspοnd with or complete something else; also, attached to, as an inseparable  incident or cοnditiοn of a person or thing; and conversely, οn the cοnditiοn, in the circumstances, etc.

Examples of these meanings in the adverbial use are

Il. 1.462 ἐπὶ δʼ αἴθοπα οἶνον λεῖβε
                poured wine οver (the meat)

Il. 13.799 πρὸ μέν τ ἄλλʼ, αὐτὰρ ἐπʼ ἄλλα
                   in front—behind

Od. 1.273 θεοὶ δʼ ἐπὶ μάρτυροι ἔστων
                   the gods be witnesses there tο

Od. 5.443 ἐπὶ σκέπας ἦν ἀνέμοιο
                   there was thereto (the place was furnished with)
                   a shelter from the wind

Il. 18.529 κτεῖνον δʼ ἐπὶ μηλοβοτῆρας
                   killed the shepherds with the sheep

Il. 1.233 ἐπὶ μέγαν ὅρκον ὀμοῦμαι
                I will swear in confirmation

With a verb understood, ἔπι = is present, is in the case

Od. 2.58 οὐ γὰρ ἔπʼ ἀνήρ
                there is no man (for the purpose)

Il. 1.515 οὔ τοι ἔπι δέος
                there is no fear with or for yοu
                (as part of your circumstances)

Il. 21.110 ἔπι τοι καὶ ἐμοὶ θάνατος
                  death is my lot tοο

Cp. 6.357 οἷσιν ἐπὶ Ζεὺς θῆκε κακὸν μόρον. It is very much used in composition. Note the meaning over in ἐπι-πλέω to sail over, also ἐπ-οίχομαι tο go over, review, ἐπι-πωλέομαι, ἐπ-αλάομαι (Il. 17.650 μάχη δʼ ἐπὶ πᾶσα φαάνθη the fight was lighted up all over); besides, in ἐπι-δίδωμι, etc.; to (of bringing aid, joining, etc.) in ἐπ-αρήγω, ἐπ-αλέξω, ἐπ-αραρίσκω, ἐπ-αλλάσσω, etc.; for, in ἐπι-κλώθω to spin for (so as to attach to); hence of assent, ἐπι-νεύω, ἐπι-τλῆναι, ἐπι-είκω (with a general affirmative meaning, οn as opposed to off, for as opposed to against.

198. With the dative ἐπί has the same group of meanings; note especially

1. ἐπὶ νηυσί
   by the ships

   ἐπʼ ὄεσσι
   with the sheep (of a shepherd)

   ἐπὶ κτεάτεσσι
   with (in charge of) the possessions

   Il. 4.235 ἐπὶ ψεύδεσσιν ἔσσετʼ ἀρωγός
                    will be a helper with (on the side of) falsehood
                    (or false men, reading ψευδέσσι)

2. Il. 4.258 ἀλλοίῳ ἐπὶ ἔργῳ
                   in (engaged upon) other work, so

   ἀτελευτήτῳ ἐπὶ ἔργῳ
   with a work unfinished

   Il. 4.178 ἐπὶ πᾶσι
   in all cases dealt with

3. Od. 17.454 οὐκ ἄρα σοί γʼ ἐπὶ εἴδεϊ καὶ φρένες ἦσαν
                        with form you have not understanding tοο

   Il. 13.485 τῷδʼ ἐπὶ θυμῷ
                     with this spirit (tοο)

   Hes. Theοg. 153 ἰσχὺς . . . μεγάλῳ ἐπὶ εἴδει

4. Od. 11.548 τοιῷδʼ ἐπʼ ἀέθλῳ
                       with such a prize
                      (when such a thing is prize)

   μισθῷ ἔπι ῥητῷ
   for fixed hire (given the hire, hence in view of it).

5. ἐπʼ ἤματι
   for the day
   (i.e. as the day's work, in a single day)

   Note also that ἐπί meaning upon very often takes the dative after verbs of motion, as κατέχευεν ἐπʼ οὔδει poured οn to the ground; hence with the meaning against, as ἐπʼ ἀλλήλοισιν ἰόντες, μάρνασθαι ἐπʼ ἀνδράσι, etc.

Notice under this head the use of ἐπί with a comparative

Od. 7.216 οὐ γάρ τι στυγερῇ ἐπὶ γαστέρι κύντερον ἄλλο
                 nothing else is more shameless with
                 (when you have to do with) a hungry belly

= more shameless than the belly. So Hot. 4.118 οὐδεν ἐπὶ τούτῳ ἔσται ἐλαφρότερον

199. With the accusative ἐπί implies (1) motion directed to a place, seldom (2) to a person; or (3) motion or (4) diffusion, extent, etc., over a space or (5) time.

1. After verbs of motion the accusative does not (like the dative) distinctly express that the motion terminates οn the place : e. g. ἐπὶ χθόνα is merely to or tοwards the ground, but ἐπὶ χθονί implies alighting on it.
   

   Il. 18.565 ἀταρπιτὸς ἦεν ἐπʼ αὐτήν
                     there was a path leading tο it

   Il. 2.218 ἐπὶ στῆθος συνοχωκότε
                   bent in οver the chest

   Hence the phrases expressing attitude, as ἐπὶ στόμα, ἐπὶ γοῦνα, etc. Two forms, ἐπὶ δεξιά and ἐπʼ ἀριστερά, are used even when motion is not expressed.

   Il. 5.355 εὗρεν ἔπειτα μάχης ἐπʼ ἀριστερὰ θοῦρον Ἄρηα
                   ἥμενον

   Note however that ἐπʼ ἀριστεροῖς and ἐπʼ ἀριστερῶν are metrically impossible.

2. The use with persons in the meaning towards, in quest of, is rare, and almost confined to the Iliad.
   

   Il. 2.18 βῆ δʼ ἄρʼ ἐπʼ Ἀτρεΐδην Ἀγαμέμνονα, τὸν δʼ ἐκίχανεν

   Also 5.590; 10.18, 54, 85, 150; 11.343, 805; 12.342; 13.91, 459; 14.24; 16.535; 21.348; Od. 5.149.

3. The meaning over, with verbs of motion, is very common; ἐπὶ πόντον (ἰών, πλέων, φεύγων, etc.), ἐπὶ γαῖαν, ἐπὶ χθόνα, ἐπὶ κύματα, etc. Also with verbs of looking.
   

   Il. 1.350 ὁρόων ἐπʼ ἀπείρονα πόντον.

   Hence such phrases as ἐπὶ στίχας, of troops, etc., moving in ranks, i.e. over or along certain lines.

   Il. 3.113 ἵππους ἔρυξαν ἐπὶ στίχας

   Od. 5.245 ἐπὶ στάθμην ἴθυνε
                     straightened along (hence by) the rule

   Sο with plural nouns

   Il. 14.381 οἰχόμενοι ἐπὶ πάντας
                    going over them all

   Od. 15. 492 πολλὰ βροτῶν ἐπὶ ἅστεʼ ἀλώμενος

   and of a distribution, Od. 16. 385 δασσάμενοι κατὰ μοῖραν ἐφʼ ἡμέας i.e. equally, so as to go round.

4. The instances in which extent (without motion) is implied are chiefly found in the Odyssey (2.370, etc.). Examples from the Iliad are
   

   Il. 9.506 φθάνει δέ τε πᾶσαν ἐπʼ αἶαν
                    she is beforehand all the world over (so 23.742)

   Il. 10.213 κλέος εἴη πάντας ἐπʼ ἀνθρώπους

   Il. 24.202, 535. It will be seen that they are from books 9, 10, 23, 24.

   Notice also the use with neuters expressing quantity.

   Il. 5.772 τόσσον ἔπι θρῴσκουσι
                    to such a distance they bound

   Also ἐπὶ πολλόν a long way, ἐπὶ ἶσα tο an equal extent; and especially the common phrase ὅσον τʼ ἐπί, see Il. 2.616, etc.

5. Of time.
   

   Il. 2.299 μείνατʼ ἐπὶ χρόνον
                   wait for (literally over) a time

   Od. 7.288 εὗδον παννύχιοι καὶ ἐπʼ ἠῶ καὶ μέσον ἦμαρ
                         slept all night aπd on through morning
                         and midday

200. The genitive with ἐπί is used in nearly the same sense as the dative, but usually with less definitely local force; in particular

1. with words expressing the great divisions of space, especially when a contrast is involved (land and sea, etc.); as ἐπὶ χέρσου, ἐπʼ ἠπείρου, ἐπʼ ἀγροῦ
   

   Od. 12. 27 ἢ ἁλὸς ἢ ἐπὶ γῆς ἀλγήσετε (cp. Il. 13.565)

   This is evidently a Genitive of Place, § 149 For the difference of genitive and dative cp. Il. 1.485 ἐπʼ ἠπείροιο ἔρυσσαν ὑψοῦ ἐπὶ ψαμάθοις.

2. where the local relation is a familiar one.
   

   ἐπὶ νηός, ἐπʼ ἀπήνης, ἐφʼ ἵππων, ἐπὶ θρόνου, ἐπʼ οὐδοῦ, ἐπὶ πύργου, ἐπʼ ἀγκῶνος, ἐπὶ μελίης (ἐρεισθείς)

   Thus ἐπὶ νηυσί means on or beside ships, ἐπὶ νηῶν οn board ships.

3. with verbs of motion, upon (of the terminus ad quem).
   

   Il. 3.293 κατέθηκεν ἐπὶ χθονός

   So bearing down on.

   Il. 5.700 προτρέποντο μελαινάων ἐπὶ νηῶν

   Od. 3.17 1 νεοίμεθα νήσου ἔπι Ψυρίης
                       taking the course by the island Psyria

   So perhaps Il. 7.195 (εὔχεσθε) σιγῇ ἐφʼ ὑμείων (keeping the words) to yourselves.

4. of time.
   

   ἐπʼ εἰρήνης (I1. 2.797, etc.)

   ἐπὶ προτέρων ἀνθρώπων (Il. 5.637, etc.)

   Cp. the Genitive of Time, § 150. In later prose the genitive is very common, and the uses become indistinguishable from those of the dative.