When the subject of the infinitive is the same as a genitive or dative depending on the governing verb, it is often omitted.1061
A predicate adjective referring to a genitive regularly stands in the genitive, but a predicate substantive or participle generally stands in the accusative in agreement with the unexpressed subject of the infinitive:
Κύ_ρου ἐδέοντο ώς προθυ_μοτάτου γενέσθαι
ὑπὸ τῶν δεομένων μου προστάτην γενέσθαι
A predicate substantive, adjective, or participle referring to a dative stands in the dative or in the accusative in agreement with the unexpressed subject of the infinitive:
νῦν σοι ἔξεστιν ἀνδρὶ γενέσθαι
Λακεδαιμονίοις ἔξεστιν ὑ_μῖν φίλους γενέσθαι
ἔδοξεν αὐτοῖς . . . ἐξοπλισαμένοις προϊ_έναι
συμφέρει αὐτοῖς φίλους εἶναι μᾶλλον ἢ πολεμίους
For predicate nouns in the nominative or accusative in agreement with omitted subject of the infinitive, see cross1973-1975.
Herbert Weir Smyth [n.d.], A Greek Grammar for Colleges; Machine readable text [info] [word count] [Smyth].