Maxim
late Middle English (denoting an axiom): from French maxime, from medieval Latin (propositio) maxima ‘largest or most important (proposition)’.
wiktionary
From Anglo-Norman maxime and Middle French maxime, from Late Latin maxima(“axiom”), noun use of the feminine singular form of Latin maximus (apparently as used in the phrase prōpositiō maxima(“greatest premise”)). Doublet of maxima.
etymonline
maxim (n.)
early 15c., maxime, "an axiom, statement of a self-evident truth," from Old French maxime, from Late Latin maxima, shortened from phrases such as maxima propositio (Boethius), maxima sententarium "axiom," literally "greatest or chief premise, greatest among propositions" (one which is general and absolute), from fem. of maximus "greatest," from PIE *mag-samo-, superlative form of root *meg- "great."
The modern meaning "summary statement of an established or accepted proposition serving as a rule or guide, a proposition ostensibly expressing some general truth" is from 1590s.
Maxim
single-barreled water-cooled machine gun, 1885 (Maxim gun), named for inventor, U.S.-born British engineer Sir Hiram S. Maxim (1840-1916).