Here’s something I just noticed. Perhaps I’ve seen it before and perhaps I’m just sleepy this afternoon (curled up in my chair with the wood stove going–watching three of my grandsons [ages 3, 4, & 5] play on the living room floor; at the moment the legos and trains have been forgotten since the oldest is using his newly developing reading skills to explain a stack of story books to his younger brother and his cousin!). In any event, with linking verbs, infinitives can have either nom or acc subjects and objects.
When a linking verb is used in the infinitive form, e.g. εἶναι, it can have a predicate nominative. This is the only time you’ll see a nominative with an infinitive since the subject of the infinitive (when it is expressed) is normally in the accusative case.
Acts 17:18, ξένων δαιμονίων δοκεῖ καταγγελεὺς εἶναι (He seems to be a preacher of strange gods).
Gal 2:9, Ἰάκωβος καὶ Κηφᾶς καὶ Ἰωάννης, οἱ δοκοῦντες στῦλοι εἶναι (James and Cephas and John, the ones perceived to be pillars).
1 Tim 1:6f, ἐξετράπησαν εἰς ματαιολογίαν 7 θέλοντες εἶναι νομοδιδάσκαλοι (They have wandered into vain talking 7 desiring to be teachers of the Law).
John 9:27, μὴ καὶ ὑμεῖς θέλετε αὐτοῦ μαθηταὶ γενέσθαι; (You don’t wish to be his disciples do you?)
1 Sam 3:21, ἐπιστεύθη Σαμουηλ προφήτης γενέσθαι τῷ κυρίῳ εἰς πάντα Ισραηλ (Samuel was believed to be a prophet of the Lord in all Israel).
It is also possible, however, for linking verbs to follow the usual infinitive pattern and take an accusative subject or a predicate accusative as the following examples show.
Luke 20:41, Εἶπεν πρὸς αὐτούς· πῶς λέγουσιν τὸν χριστὸν εἶναι Δαυὶδ υἱόν; (He said to them, “How do they say that the Messiah is David’s son?”)
1 Tim 6:5, νομιζόντων πορισμὸν εἶναι τὴν εὐσέβειαν (imagining godliness to be gain).
Notice that the “subject” of the infinitive is determined by the same hierarchy of rules as it was with finite forms. In this example, the article indicates that τὴν εὐσέβειαν is the accusative subject of the infinitive εἶναι and πορισμόν is the predicate accusative.
Rom 15:8 λέγω γὰρ Χριστὸν διάκονον γεγενῆσθαι περιτομῆς ὑπὲρ ἀληθείας θεοῦ (For I say Christ became a servant of the circumcision for the truth of God).