"art of computation, the most elementary branch of mathematics," mid-13c., arsmetike, from Old French arsmetique (12c.), from Latin arithmetica, from Greek arithmetike (tekhnē) "(the) counting (art)," fem. of arithmetikos "of or for reckoning, arithmetical," from arithmos "number, counting, amount," from PIE *erei-dhmo-, suffixed variant form of root *re- "to reason, count."
The form arsmetrik was based on folk-etymology derivation from Medieval Latin ars metrica; the spelling was corrected early 16c. in English (though arsmetry is attested from 1590s) and French. The native formation in Old English was tælcræft, literally "tell-craft."
1530s, "writing in secret code or occult characters," verbal noun from cipher (v.). Meaning "action of using figures in arithmetic" is from 1610s.
late 15c., "one who or that which multiplies or increases in number," agent noun from multiply. In arithmetic, "the number by which another is multiplied," 1540s.
"manifold, multiple, multiplicate," 1550s, from Latin multiplex "having many folds; many times as great in number; of many parts" (see multiply). As a noun, late 14c. in arithmetic, "a multiple."
"of, pertaining to, or of the nature of mathematics," early 15c., from Medieval Latin mathematicus "of or belonging to mathematics," from Latin mathematica (see mathematic) + -al (1). Also, by 1765, "pertaining to the quadrivium," comprising arithmetic, geometry, astronomy, and music. It also could include optics. Related: Mathematically.
The four mathematical arts are arithmetic, geometry, music, and astronomy; these anciently were termed the quadrivium, or fourfold way of knowledge. [Sir John Hawkins, "A General History of the Science and Practice of Music," Sir John Hawkins, 1776]