William Watson Goodwin, Syntax of the Moods and Tenses of the Greek Verb

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[*] 851. The participle of an impersonal verb stands in the accusative absolute, in the neuter singular, with or without an infinitive, when other participles with their subjects would stand in the genitive absolute.

Such are ἐξόν, δέον, παρόν, προσῆκον, πρέπον, παρέχον, μέλον, μεταμέλον, δοκοῦν, δόξαν, and the like; also passive participles used impersonally (as προσταχθέν, εἰρημένον, δεδογμένον); and such expressions as ἀδύνατον ὄν, it being impossible, composed of an adjective and ὄν; also τυχόν, perchance. E.g.

Οἱ δ᾽ οὐ βοηθήσαντες δέον ὑγιεῖς ἀπῆλθον; “ and did those who brought no aid when it was necessary escape safe and sound?” PLAT. Alcib. i. 115B. Ἁπλᾶς δὲ λύπας ἐξὸν (sc. φέρειν), οὐκ οἴσω διπλᾶς. I. T. EUR. 688. Παρέχον δὲ τῆς Ἀσίης πάσης ἄρχειν εὐπετέως, ἄλλο τι αἱρήσεσθε; HDT. v. 49. Εὖ δὲ παρασχόν, “and when an opportunity offers.” THUC. i. 120. Οὐ προσῆκον, “improperly.” Id. iv. 95. Συνδόξαν τῷ πατρὶ καὶ τῇ μητρὶ, γαμεῖ τὴν Κυαξάρου θυγατέρα. XEN. Cyr. viii. 5, 28. Εἰρημένον κύριον εἶναι ὅ τι ἂν τὸ πλῆθος τῶν ξυμμάχων ψηφίσηται. THUC. v. 30.So δεδογμένον, id. i. 125; γεγραμμένον, THUC. v. 56; and προστεταγμένον, Leg. 902 D. Καὶ ἐνθένδε πάλιν, προσταχθέν μοι ὑπὸ τοῦ δήμου Μένωνα ἄγειν εἰς Ἑλλήσποντον, ᾠχόμην. L. DEM. 12. Παρεκελεύοντό τε, ἀδύνατον ὂν ἐν νυκτὶ ἄλλῳ τῳ σημῆναι. THUC. vii. 44. Ἔγωγ̓, ἔφη ὁ Κῦρος, οἶμαι, ἅμα μὲν συναγορευόντων ἡμῶν, ἅμα δὲ καὶ αἰσχρὸν ὂν τὸ ἀντιλέγειν, κ.τ.λ. XEN. Cyr. ii. 2, 20. (See 876.) Ἀντιπαρεσκευάζετο ἐρρωμένως, ὡς μάχης ἔτι δεῆσον, “on the ground that there would still be need of a battle.” Ib. vi. 1, Ib. 26. Οἱ δὲ τριάκοντα, ὡς ἐξὸν ἤδη αὐτοῖς τυραννεῖν ἀδεῶς, προεῖπον, κ.τ.λ., i.e. thinking that it was now in their power, etc. Id. Hell. ii. 4, Id. Hell. 1.