Herbert Weir Smyth, A Greek Grammar for Colleges

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[*] 341. Origin.—Adverbs, like prepositions and conjunctions, were originally case forms, made from the stems of nouns and pronouns. Some of these nominal and pronominal stems have gone out of common use, so that only petrified forms are left in the adverbs. Some of these words were still felt to be live cases; in others no consciousness of their origin survived. Many adverbs show old suffixes joined to the stem or to a case form (342). It is sometimes uncertain whether we should speak of adverbs or of nouns with local endings.

Nominative (rare): πύξ with clenched fist, ἅπαξ once, ἀναμίξ pell-mell.

Genitive: ἕνης day after to-morrow, ἑξῆς next, ποῦ, οὗ where, αὐτοῦ in the very place, ἐκποδών out of the way (ἐκ ¨ ποδῶν); by analogy, ἐμποδών in one's way.

Dative: δημοσίᾳ at public cost, λάθρᾳ in secret, κοινῇ in common, etc. (1527 b), ἄλλῃ otherwise, πῇ how.

Accusative: very common, especially such adverbs as have the form of the accusative of neuter adjectives, as πολύ much, μι_κρόν a little, πρῶτον at first, τήμερον to-day, πολλά often. See 1606-1611.

Locative: οἴκο-ι at home (οἶκο-ς house), Ἰσθμο-ῖ at the Isthmus, ποῖ whither, and all adverbs in -οι. The -ι of the consonantal declension is properly the ending of the locative, as in Μαραθῶν-ι at Marathon; -οισι (234) in O stems, in contrast to -οις; -α_σι (-ησι) in Ā stems (215): θύρα_σι at the doors, Πλαταιᾶσι at Plataea, Ἀθήνησι at Athens; further in πάλαι long ago, ἐκεῖ there, πανδημεί in full force.

Instrumental: ἄνω above, κάτω below, οὔπω not yet, ὧ-δε thus (but the forms in -ω may be ablatives); κρυφῆ and λάθρα_ in secret.

Ablative: all adverbs in -ως, as ὡς as, οὕτως thus, ἑτέρως otherwise. Here, e.g. original ἑτερωδ (cp. Old Lat. altoōd, abl. of altus) became ἑτερω (133), which took on -ς from the analogy of such words as ἀμφίς parallel to ἀμφί.