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Latin word magis comes from Proto-Indo-European *méǵh₂s (Big, great.), Proto-Indo-European *maḱ-, Proto-Indo-European *méga-, Proto-Indo-European *meg-, English Carolus Magnus, Latin -e (-ly; used to form adverbs from adjectives.)
*méǵh₂s (Proto-Indo-European)
Big, great.
*maḱ- (Proto-Indo-European)
*méga- (Proto-Indo-European)
*meg- (Proto-Indo-European)
great
Carolus Magnus (English)
-e (Latin)
-ly; used to form adverbs from adjectives.
*m̥ǵh₂nós (Proto-Indo-European)
*mag-no- (Proto-Indo-European)
*magnos (Proto-Italic)
Great.
maius (Latin)
magnopere (Latin)
Earnestly, vehemently. Greatly, exceedingly.
magis (Latin)
Better. More. More greatly. Rather.