Etymology
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Words related to augment

*aug- (1)

Proto-Indo-European root meaning "to increase." It forms all or part of: auction; augment; augmentative; augur; August; august; Augustus; author; authoritarian; authorize; auxiliary; auxin; eke (v.); inaugurate; nickname; waist; wax (v.1) "grow bigger or greater."

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit ojas- "strength," vaksayati "cause to grow;" Lithuanian augu, augti "to grow," aukštas "high, of superior rank;" Greek auxo "increase," auxein "to increase;" Gothic aukan "to grow, increase;" Latin augmentum "an increase, growth," augere "to increase, make big, enlarge, enrich;" Old English eacien "to increase," German wachsen, Gothic wahsjan "to grow, increase."

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augmented (adj.)
c. 1600, "increased," past-participle adjective from augment. Musical sense of "greater by a semitone than a perfect or major interval" (opposite of diminished) is attested by 1825.
augmentation (n.)

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.

augmentative (adj.)

"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."

august (adj.)
"inspiring reverence and admiration, solemnly grand," 1660s, from Latin augustus "venerable, majestic, magnificent, noble," perhaps originally "consecrated by the augurs, with favorable auguries" (see augur (n.)); or else [de Vaan] "that which is increased" (see augment).