Herbert Weir Smyth, A Greek Grammar for Colleges

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[*] 1969. The infinitive was originally a verbal noun in the dative (in part possibly also in the locative) case. The use to express purpose (2008) is a survival of the primitive meaning, from which all the other widely diverging uses were developed in a manner no longer always clear to us. But the to or for meaning seen in μανθάνειν ἥκομεν we have come to learn (for learning) can also be discerned in δύναμαι ἰδεῖν I have power for seeing, then I can see. Cp. 2000, 2006 a. As early as Homer, when the datival meaning had been in part obscured, the infinitive was employed as nominative (as subject) and accusative (as object). After Homer, the infinitive came to be used with the neuter article, the substantive idea thus gaining in definiteness. The article must be used when the infinitive stands as an object in the genitive or dative, and when it depends on prepositions.