ἐξ

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223. 7he Preposition ἐξ (or ἐκ) usually expresses motion out from an object. It is not used purely adverbially, but there are many examples of Tmesis.

ἐξ ἔρον ἕντο, ἐκ δέ οἱ ἡνίοχος πλήγη φρένας his chariοteer lost (lit. was stuck out of) his wits
ἔκ τε καὶ ὀψὲ τελεῖ (Il. 4.161) he brings it to pass (ἐκτελεῖ) late

With a Gen.(ablatival) ἐξ is used of mοtiοn from or out of. Sometimes the idea of motion is implied.

Il. 13.301 ἐκ Θρῄκης Ἐφύρους μέτα θωρήσσεσθον armed themselves to come from Thrace after the Ephyri.
14. 129 ἔνθα δʼ ἔπειτʼ αὐτοὶ μὲν ἐχώμεθα δηίοτῆτος ἐκ βελέων hold back from fighting (goind) out of range: cp. 16.122, 678, 18.152.

So of direction

Il. 14.153 Hρη δʼ εἰσεῖδε . . . στᾶσʼ ἐξ Οὐλύμποιο stοοd and looked from Olympus
Od. 21. 420 (drew the bow) αὐτόθεν ἐκ δίφροιο καθήμενος from the chair as he sat
Il. 19.375 ὅτʼ ἂν ἐκ πόντοιο σέλας ναύτῃσι φανήῃ when a meteor appears to sailors at sea (seeing it from the sea)

of choosing out of

Il. 15.6B0 ἐκ πολέων πίσυρας συναείρεται ἵππους

and similarly

Il. 18.43 ὅσσʼ ἐμοὶ ἐκ πασέων Κρονίδης Σεὺς ἄλγε ἔδωκε to me (taken from, hence) more than all.

ἐξ is also used of an agent as the course of action

ll. 5.384 τλῆμεν . . . ἐξ ἀνδρῶν have endured at the hands of men

cp. Il. 22.280, Od. 7.70, 9.512: also

ll. 24.617 θεῶν ἐκ κήδεα πέσσει endures heaven-sent troubles
Hes. Theog. 94 ἐκ γὰρ ονσάων καὶ ἑκηβόλου Ἀπόλλωνος ἄνδρες ἀοιδοὶ ἔασιν.

The meaning in consequence of (a thing) occurs in ll. 9.566 ἐξ ἀρέων μητρὸς κεχο- λωμένος, and in the Odyssey (3.135, 5.468, etc.).

Of time

ἐκ τοῖο from that time
ἐξ ἀρχῆς from the first (Od. 1.188, etc)
ἐκ νεότητος (l. 14.86).

With an abstract word

Il. 10.107 ἐκ χόλου ἀργαλέοιο μεταστρέψῃ φίλον ἦτορ.

Note also: Il. 10. 68 πατρόθεν ἐκ γενεῆς ὀνομάζων calling them by the father's name according to family; Il. 9.343 (486) ἐκ θυμοῦ from the heart, heartily (but Il. 23.595 ἐκ θυμοῦ πεσέειν to fall away from a person's favor).