Herbert Weir Smyth, A Greek Grammar for Colleges

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[*] 2058. A. Genitive Absolute.—A participle agreeing in the genitive with its own subject, which is not identical with the subject of the leading verb, is said to stand in the genitive absolute. Cp. 2070.

““Κῦρος ἀνέβη ἐπὶ τὰ ὄρη οὐδενὸς κωλύ_οντος” Cyrus ascended the mountains without any one preventing him” X. A. 1.2.22.

N.—The English nominative absolute is represented by the Greek genitive absolute. Cp. Tennyson: “we sitting, as I said, the cock crew loud” = ἡμῶν καθημένων, ὅπερ ἔλεγον, μέγα ᾖσεν ὁ ἀλεκτρυών.