223. The 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 genitive (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
Il. 14.129 ἔνθα δʼ ἔπειτʼ αὐτοὶ μὲν ἐχώμεθα δηϊοτῆτος
hold back from fighting (going) out of range
Cp. Il. 16.122, 678, 18.152.
So of direction
Il. 14.153 Ἥρη 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. 15.680 ἐκ πολέων πίσυρας συναείρεται ἵππους
Il. 18.431 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 source of action
Il. 5.384 τλῆμεν . . . ἐξ ἀνδρῶν
have endured at the hands of men
cp. Il. 22.280, Od. 7.70, 9.512: also
Il. 24.617 θεῶν ἐκ κήδεα πέσσει
endures heaven-sent troubles
Hes. Theog. 94 ἐκ γὰρ Μουσάων καὶ ἑκηβόλου Ἀπόλλωνος
ἄνδρες ἀοιδοὶ ἔασιν.
The meaning in consequence of (a thing) occurs in Il. 9.566 ἐξ ἀρέων μητρὸς κεχολωμένος, and in the Odyssey (3.135, 5.468, etc.).
from that time
from the first (Od. 1.188, etc)
ἐκ νεότητος (Il. 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).