mid-15c., "act of making greater," from Old French augmentacion "increase," from Late Latin augmentationem (nominative augmentatio), noun of action from past-participle stem of augmentare "to increase" (see augment). Meaning "amount by which something is increased" is from 1520s. Musical sense is from 1590s, in fugues.
late 14c., "action of adding numbers;" c. 1400, "that which is added," from Old French adition "increase, augmentation" (13c.), from Latin additionem (nominative additio) "an adding to, addition," noun of action from past-participle stem of addere "add to, join, attach" (see add). Phrase in addition to "also" is from 1680s.
"having power or quality of augmenting," c. 1500, from Old French augmentatif (14c.), from Late Latin augmentat-, stem of augmentare "to increase" (see augment). In grammar, "expressing augmentation or increase in the force of the idea conveyed," from 1640s. It is applied both to words and to affixes; also as a noun in grammar, "word formed to express increased intensity of the idea conveyed by it, or an affix which serves this purpose."
a name of God in the Bible, c. 1600, from Hebrew, plural (of majesty?) of Eloh "God" (cognate with Allah), a word of unknown etymology, perhaps an augmentation of El "God," also of unknown origin. Generally taken as singular, the use of this word instead of Yahveh is taken by biblical scholars as an important clue to authorship in the Old Testament, hence Elohist (1830; Elohistic is from 1841), title of the supposed writer of passages of the Pentateuch where the word is used.