1540s, "imaginary motionless straight line around which a body (such as the Earth) rotates," from Latin axis "axle, pivot, axis of the earth or sky," from PIE *aks- "axis" (source also of Old English eax, Old High German ahsa "axle;" Greek axon "axis, axle, wagon;" Sanskrit aksah "an axle, axis, beam of a balance;" Lithuanian ašis "axle").
The general sense of "straight line about which parts are arranged" is from 1660s. The figurative sense in world history of "alliance between Germany and Italy" (later extended unetymologically to include Japan) is from 1936. The original reference was to a "Rome-Berlin axis" in central Europe. The word later was used in reference to a London-Washington axis (World War II) and a Moscow-Peking axis (early Cold War).
1842, "skeletal axis of the vertebrate body," from Greek axon "axis" (see axis). From 1899 as a part of a nerve cell.
"having wings, winged," 1660s, from Latin alatus, from ala "wing, armpit, wing of an army," from *axla, originally "joint of the wing or arm;" from PIE *aks- "axis" (see axis).
"wing-like," 1839; "of or pertaining to wings," 1847, from Latin alaris, from ala "wing, armpit, wing of an army" (source of Spanish ala, French aile), from *axla, originally "joint of the wing or arm;" from PIE *aks- "axis" (see axis).
"square stone for building or paving," mid-14c., from Old French aisseler, Medieval Latin arsella "a little board or shingle," diminutive of Latin assis "a board, plank," also spelled axis, which is perhaps not the same axis that means "axle." De Vaan regards the Latin spelling axis as a hyper-correction. The stone sense is peculiar to English. The meaning "thin slab of stone used as facing on a wall" is from 1823.
"of uncertain outcome, depending on a contingent event," literally "depending on the throw of a die," 1690s, from Latin aleatorius "pertaining to a gamester," from aleator "a dice player," from alea "a game with dice; chance, hazard, risk; a die, the dice;" perhaps literally "a joint-bone" (marked knuckle-bones used as early dice), "a pivot-bone," and related to axis. Aleatoric "incorporating chance and randomness" was used as a term in the arts from 1961.
"pole or pin upon which a wheel revolves" (properly, the round ends of the axle-tree which are inserted in the hubs or naves of the wheels), 1630s, from Middle English axel-, from some combination of Old English eax and Old Norse öxull "axis," both from Proto-Germanic *akhsulaz (source also of Old English eaxl "shoulder," oxta, ohsta "armpit," which survived as dialectal oxter; also Old Saxon ahsla, Old High German ahsala, German Achsel "shoulder"), from PIE *aks- "axis" (see axis, which is from the Latin cognate of this Germanic word). Before 14c. it was found only in the compound axle-tree.