Herbert Weir Smyth, A Greek Grammar for Colleges

a. Originally the preposition was a free adverb limiting the meaning of the verb but not directly connected with it: κατ᾽ ἄρ᾽ ἕζετο down he sate him A 101. In this use the preposition may be called a ‘preposition-adverb.’

b. The preposition-adverb was also often used in sentences in which an oblique case depended directly on the verb without regard to the prepositionadverb. Here the case is independent of the preposition-adverb, as in βλεφάρων ἄπο δάκρυα πί_πτει from her eyelids, away, tears fall ξ 129. Here βλεφάρων is ablatival genitive and is not governed by ἀπό, which serves merely to define the relation between verb and noun.

c. Gradually the preposition-adverb was brought into closer connection either (1) with the verb, whence arose compounds such as ἀποπί_πτειν, or (2) with the noun, the preposition-adverb having freed itself from its adverbial relation to the verb. In this stage, which is that of Attic prose, the noun was felt to depend on the preposition. Hence arose many syntactical changes, e.g. the accusative of the limit of motion (1588) was abandoned in prose for the preposition with the accusative.

Prepositions have three uses.