h₂weg-
“to increase, grow”Source of Latin augēre, English augment, auction, author
Root for increasing, producing Latin augēre and English augment, auction, author, authority.
Discussion
The Proto-Indo-European root *h₂weg- meant "to increase, to grow, to become greater" and is one of the most important roots for understanding Latin-derived English vocabulary relating to growth, authority, and enhancement. The initial laryngeal *h₂ coloured the adjacent vowel and was lost in most daughter languages, though its effects persist in vowel quality.
In Germanic, the root produced Old English weaxan "to grow, to increase", the ancestor of modern English wax in the sense of "to grow" (as in "the moon waxes and wanes"). This is unrelated to the noun wax (the substance), which comes from a different root. The verbal wax, once common in everyday speech, now survives mainly in the lunar phrase and in somewhat literary usage ("he waxed eloquent").
Latin augēre "to increase, to make grow" is the dominant reflex for English vocabulary. From it come augment, auction (a sale where the price increases), august (increased in dignity, venerable — also the name of the month, honouring Augustus Caesar, "the augmented one"), author (originally "one who increases or originates"), authority, and authorize. The word auxiliary (helping to increase) also derives from this root. The religious term augur (a Roman diviner who interpreted signs of increase or favour) is related, as is inaugurate (to take auguries before beginning).
Greek auxein "to increase" gave English auxin (a plant growth hormone) and other technical terms. Sanskrit ugra- "mighty, powerful" and ōjas "strength" confirm the Indo-Iranian reflexes.
The semantic development from "to grow" through "to originate" to "author" and "authority" is particularly revealing. In Indo-European thought, the person who causes growth is the originator, the authority, the author. Power was understood not as static domination but as the capacity to generate increase — a deeply agricultural metaphor that shaped political vocabulary for millennia.