word-forming element meaning "battle, war, contest, fighting, warfare," from Latinized form of Greek -makhia, from makhē "a battle, fight," related to makhesthai "to fight." Beekes suspects it is from an isolated root, perhaps Pre-Greek: "In the domain of fighting and battle, old inherited expressions can hardly be expected."

word-forming element meaning "great," from Latin magni-, combining form of magnus "great, large, big" (of size), "abundant" (of quantity), "great, considerable" (of value), "strong, powerful" (of force); of persons, "elder, aged," also, figuratively, "great, mighty, grand, important," from PIE *mag-no-, from root *meg- "great."

word-forming element of Greek origin meaning "divination by means of," from Old French -mancie, from Late Latin -mantia, from Greek manteia "oracle, divination," from mantis "one who divines, a seer, prophet; one touched by divine madness," from mainesthai "be inspired," which is related to menos "passion, spirit" (from PIE *mnyo-, suffixed form of root *men- (1) "to think," with derivatives referring to qualities and states of mind or thought). Compare mania.

word-forming element of French origin, "one who has a mania for," ultimately from Greek -manes "ardent admirer," related to mania "madness" (see mania).

word-forming element meaning "of or relating to a mother," also "of or relating to women," from combining form of Latin māter (genitive mātris) "mother" (see mother (n.1)).

word-forming element meaning "maximum, very large or very long for its kind," abstracted from maximum.

before vowels mechan-, word-forming element meaning "pertaining to mechanics or  mechanisms; done by machine," from Latinized form of Greek mekhano-, combining form of mēkhanē "device, tool, machine; contrivance, cunning" (see machine (n.)).

word-forming element meaning "of or pertaining to medical science; from a medical standpoint; pertaining to medicine and," used as a combining form of Latin medicus "physician; healing" (from PIE root *med- "take appropriate measures").

word-forming element meaning "middle," used as a combining form of Latin medius "in the middle, between; from the middle," from PIE root *medhyo- "middle."

word-forming element meaning "large, great, exaggerated," from combining form of Greek megas "large, great" (stem megal-), from PIE root *meg- "great."