Herbert Weir Smyth, A Greek Grammar for Colleges

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[*] 2070. Genitive Absolute.—A circumstantial participle agreeing with a genitive noun or pronoun which is not in the main construction of the sentence, stands in the genitive absolute. Like other circumstantial participles, the genitive absolute expresses time, cause, condition, concession, or simply any attendant circumstance.

a. Time: ““ταῦτ᾽ ἐπρά_χθη Κόνωνος στρατηγοῦντος” these things were effected while Conon was in command” I. 9.56, ““τούτων λεχθέντων ἀνέστησαν” this said, they rose” X. A. 3.3.1, ““Ἠϊόνα . . . Μήδων ἐχόντων πολιορκίᾳ εἷλον” they blockaded and captured Eïon which was held by the Medes” T. 1.98.

b. Cause: ““τῶν σωμάτων θηλυ_νομένων καὶ αἱ ψυ_χαὶ ἀρρωστότεραι γίγνονται” by the enfeebling of the body, the spirit too is made weaker” X. O. 4.2.

c. Opposition or Concession: καὶ μεταπεμπομένου αὐτοῦ οὐκ ἐθέλω ἐλθεῖν even though he is sending for me, I am unwilling to go X. A. 1.3.10. καίπερ is usually added (2083).

d. Condition: οἴομαι καὶ νῦν ἔτι ἐπανορθωθῆναι ἂν τὰ πρά_γματα τούτων γιγνομέ- νων if these measures should be taken, I am of the opinion that even now our situation might be rectified D. 9.76.

e. Attendant Circumstance: Κῦρος ἀνέβη ἐπὶ τὰ ὄρη οὐδενὸς κωλύ_οντος Cyrus ascended the mountains without opposition (lit. no one hindering) X. A. 1.2.22 (or since no one opposed him).