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

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[*] 120. This use of the present infinitive as an imperfect must be carefully distinguished from its ordinary use after past tenses, where we translate it by the imperfect, as in ἔφη τὸ στράτευμα μάχεσθαι, he said that the army was fighting. This has sometimes been called an imperfect infinitive; but here μάχεσθαι refers to time present relatively to ἔφη; whereas, if it had been used as an imperfect, it would have referred to time past relatively to ἔφη, as in ἔφη τὸ στράτευμα τῇ προτεραίᾳ μάχεσθαι, he said that the army had been fighting on the day before. In the former case the direct discourse was μάχεται, in the latter it was ἐμάχετο. Such an imperfect infinitive differs from the aorist in the same construction only by expressing the duration or repetition of an action (as in the indicative); it gives, in fact, the only means of representing in the infinitive what is usually expressed by λέγει ὅτι ἐποίει, he says that he was doing, as opposed to λέγει ὅτι ἐποίησεν, he says that he did. (For the similar use of the present optative to represent the imperfect, see 116, 4.) This construction is never used unless the context makes it certain that the infinitive represents an imperfect and not a present, so that no ambiguity can arise. See the examples.

So sometimes in Latin: “Q. Scaevolam memoria teneo bello Marsico, cum esset summa senectute, cotidie facere omnibus conveniendi potestatem sui.” CIC. Phil. viii. 31. So “Q. Maximum accepimus facile celare, tacere, dissimulare, insidiari, praeripere hostium consilia.” CIC. de Off. i. 108.