When the subject of the infinitive is the same as that of the governing verb, it is omitted, and a predicate noun stands in the nominative case.
Πέρσης ἔφη εἶναι
ἐγὼ οὐχ ὁμολογήσω ἄκλητος ἥκειν
a. The nominative is used when the infinitive, expressing some action or state of the subject of the main verb, has the article in an oblique case. Thus, τούτων ἀξιωθεὶς διὰ τὸ πατρικὸς αὐτῷ φίλος εναι
τοῦτο δ' ἐποίει ἐκ τοῦ χαλεπὸς εἶναι
b. The nominative stands usually in sentences with δεῖν, χρῆναι etc., dependent on a
ἡγούμην . . . περιεῖναι δεῖν αὐτῶν καὶ μεγαλοψυ_χότερος φαίνεσθαι
c. When the governing verb is a participle in an oblique case, a predicate noun usually agrees with the participle, and rarely stands in the nominative. Thus,
ἀπαλλαγεὶς τούτων τῶν φασκόντων δικαστῶν εἶναι
τὰ_ς ἀρχὰ_ς δίδωσι . . . τοῖς ἀεὶ δόξα_σιν ἀρίστοις εἶναι
Herbert Weir Smyth [n.d.], A Greek Grammar for Colleges; Machine readable text [info] [word count] [Smyth].