1530s, "gather into a heap or mass" (transitive), from Latin cumulatus "heaped, increased, augmented," past participle of cumulare "to heap," from cumulus "mound, heap" (from suffixed form of PIE root *keue- "to swell"). Related: Cumulated; cumulating; cumulant.
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.
"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."