"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."
*rē-, Proto-Indo-European root meaning "to reason, count;" a variant of PIE root *ar-, also arə-, "to fit together."
It forms all or part of: Alfred; arraign; arithmetic; Conrad; dread; Eldred; Ethelred; hatred; hundred; kindred; logarithm; Ralph; rate (n.) "estimated value or worth;" rathskeller; ratify; ratio; ration; read; reason; rede; rhyme; riddle (n.1) "word-game;" rite; ritual.
It is the hypothetical source of/evidence for its existence is provided by: Sanskrit radh- "to succeed, accomplish;" Greek arithmos "number, amount;" Latin reri "to consider, confirm, ratify," ritus "rite, religious custom;" Old Church Slavonic raditi "to take thought, attend to;" Old Irish im-radim "to deliberate, consider;" Old English rædan "to advise, counsel, persuade; read;" Old English, Old High German rim "number;" Old Irish rim "number," dorimu "I count."
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."