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From Proto-Hellenic*ə-, from Proto-Indo-European*n̥-. The form ἀν-(an-) appears when followed by a laryngeal and a vowel: that is, in an open syllable of the n̥HV- form. Akin to νη-(nē-), νᾱ-(nā-) and νω-(nō-), which are closed-syllable reflexes of the n̥h₁C-, n̥h₂C-, n̥h₃C- forms, respectively.
The alpha privativum, used to make words that have a sense opposite to the word (or stem) to which the prefix is attached. It is also known as privative a and alpha privative; a-, ab-, an-, anti-, contra-, de-, dis-, ex-, il-, im-, in-, ob-, ne-, non-, not, un-
Usage notes
The alpha is usually short, but long when added to a stem that begins with three short syllables. Thus, words such as ἀ-δάματος(a-dámatos) begin with long alpha in Epic, and frequently also in Lyric, Tragic, or Comic poetry. ἀθάνατος(athánatos) and all its compounds always have long alpha.
Beekes, Robert S. P. (2010) Etymological Dictionary of Greek (Leiden Indo-European Etymological Dictionary Series; 10), volume I, with the assistance of Lucien van Beek, Leiden, Boston: Brill, →ISBN, page 1