246. Genitive Absolute. This is a form of implied predication, in which the noun or pronoun has no regular construction with the governing verb. The participial clause expresses the time or circumstances in which the action of the verb takes place
Il. 1.88 οὔ τις ἐμεῦ ζῶντος κτλ.
no one, while I am living shall, etc.
2. 551 περιτελλομένων ἐνιαυτῶν
as years go round
5. 203 ἀνδρῶν εἰλομένων
where men are crowded
So ἀνδρῶν λικμώντων, ἀνδρῶν τρεσσάντων, πολλῶν ἑλκόντων, etc.
Od. 1.390 καί κεν τοῦτ᾽ ἐθέλοιμι Διός γε διδόντος ἀρέσθαι
that too I would be willing to obtain if Zeus gave it
The subject is understood in Od. 4.19 μολπῆς ἐξάρχοντος when the singer began the music. The aοrist participle is less common in Homer than the present, especially in the Odyssey; the instances are Il. 8.164, 468; 9.426; 10.246, 356; 11.509; 13.409; 14.522; 16.306; 19.62, 75; 21.290, 437; 22.47, 288, 383; Od. 14.475, 24.88, 535 (Classen, Beob. p. 180 ff.)
The Genitive Absolute must have begun as an extension of one of the ordinary uses of the genitive; most probably of the Genitive of Time (§ 150).
ἠελίου ἀνιόντος
within the time of the sun rising
is a genitive like
ἠοῦς
in the morning
νυκτός
by night, etc.
and answers, as a phrase denoting time, to
ἅμʼ ἠελίῳ καταδύντι
at sunset
ἐς ἠέλιον καταδύντα
up to sunset, etc.
So we may compare
τοῦδʼ αὐτοῦ λυκάβαντος ἐλεύσεται
he will come within this year
ἦ σέθεν ἐνθάδʼ ἐόντος ἐλεύσεται
he will come within your being here
and again
περιτελλομένων ἐνιαυτῶν
in the years as they go round
τῶν προτέρων ἐτέων
in the former years.
The transition may be seen in ἔαρος νέον ἱσταμένοιο in the spring when it is beginning. Compare also the phrases ἐπειγομένων ἀνέμων, βορέαο πεσόντος, etc., with νηνεμίης in calm weather, etc.
The circumstance that the ablative is the "absolute" case in Latin is far from proving that the Greek genitive in this use is ablatival. In Sanskrit the case used in this way is the locative, occasionally the genitive; the Latin Ablative Absolute may represent a locative of time at which or an instrumental of circumstance (§ 144). The hypothesis that such participial clauses in Greek expressed space of time within which (rather than point of time, or circumstance) is borne out by the interesting fact, noticed above, that in Homer this construction is chiefly found with the participle which implies continuance (viz. the present) whereas in Latin the Ablative Absolute is commonest with the perfect participle. An approach to a "Dative Absolute" may be seen in such uses as
Il. 8.487 Τρωσὶν μέν ῥ᾽ ἀέκουσιν ἔδυ φάος
Il. 12.374 ἐπειγομένοισι δʼ ἵκοντο
Od. 21.115 οὔ κέ μοι ἀχννμένῳ τάδε δώματα πότνια μήτηρ
λείποι
(= it would be no distress to me if, etc.)
which are extensions or free applications, by the help of the participle, of the true dative (Dativus ethicus).