"bottom of anything considered as its support, foundation, pedestal," early 14c., from Old French bas "depth" (12c.), from Latin basis "foundation," from Greek basis "a stepping, a step, that on which one steps or stands, pedestal," from bainein "to go, walk, step," from PIE root *gwa- "to go, come."
The military sense "secure ground from which operations proceed" is from 1860. The chemical sense "compound substance which unites with an acid to form a salt" (1810) was introduced in French 1754 by French chemist Guillaume-François Rouelle (1703-1770). Sporting sense of "starting point" is from 1690s, also "destination of a runner" (1812). As a "safe" spot in a tag-like or ball game, suggested from mid-15c. (as the name of the game later called prisoner's base). Hence base-runner (1867), base-hit (1874), etc. Meaning "resources on which something draws for operation" (as in power-base, database, etc.) is by 1959.