subtraction (n.)

word-forming element meaning "under, beneath; behind; from under; resulting from further division," from Latin preposition sub "under, below, beneath, at the foot of," also "close to, up to, towards;" of time, "within, during;" figuratively "subject to, in the power of;" also "a little, somewhat" (as in sub-horridus "somewhat rough"), from PIE *(s)up- (perhaps representing *ex-upo-), a variant form of the root *upo "under," also "up from under." The Latin word also was used as a prefix and in various combinations.

In Latin assimilated to following -c-, -f-, -g-, -p-, and often -r- and -m-. In Old French the prefix appears in the full Latin form only "in learned adoptions of old Latin compounds" [OED], and in popular use it was represented by sous-, sou-; as in French souvenir from Latin subvenire, souscrire (Old French souzescrire) from subscribere, etc.

The original meaning is now obscured in many words from Latin (suggest, suspect, subject, etc.). The prefix is active in Modern English, sometimes meaning "subordinate" (as in subcontractor); "inferior" (17c., as in subhuman); "smaller" (18c.); "a part or division of" (c. 1800, as in subcontinent).

"area," mid-15c., "period or lapse of time," from Latin tractus "track, course, space, duration," lit, "a drawing out or pulling," from stem of trahere "to pull, draw," from PIE root *tragh- "to draw, drag, move" (source also of Slovenian trag "trace, track," Middle Irish tragud "ebb;" perhaps with a variant form *dhragh-; see drag (v.)). The meaning "stretch of land or water" is first recorded 1550s. Specific U.S. sense of "plot of land for development" is recorded from 1912; tract housing attested from 1953.