As such, it is in the accusative case after the verb believe.
With this accusative infinitive, it agrees, as being part of the same complex idea. And him does the same.
In English we have two methods of expressing one idea; the method in question, and the method by means of the conjunction, that.
1. I believe it to be him.
2. I believe that it is he.
In the first example, it is the object; and it-to-be-him forms one complex term.
In the second, he agrees with it; and it is the subject of a separate, though connected, proposition.
Of these two forms the Latin language adopts but one, viz., the former,—credo eum esse, not credo quod illud est ille.
[§ 565]. The expression ob differentiam.—The classical languages, although having but one of the two previous forms, are enabled to effect a variation in the application of it, which, although perhaps illogical, is convenient. When the speaker means himself, the noun that follows, esse, or εἶναι, is nominative,—φημὶ εἶναι δεσπότης=I say that I am the master: ait fuisse celerrimus=he says that he himself was the swiftest—but, φημὶ εἶναι δεσπότην=I say that he (some one else) is the master; and ait fuisse celerrimum=he says that he (some one else) is the swiftest. This, though not adopted in English, is capable of being adopted,—He believes it to be he (i.e., the speaker) who invented the machine; but, he believes it to be him (that is, another person) who invented it.
[§ 566]. When the substantive infinitive, to be, is preceded by a passive participle, combined with the verb substantive, the construction is nominative,—it is believed to be he who spoke, not it is believed to be him.—Here there are two propositions: