late 14c., divisioun, "act of separating into parts, portions, or shares; a part separated or distinguished from the rest; state of being at variance in sentiment or interest," from Old French division and directly from Latin divisionem (nominative divisio), noun of action from past-participle stem of dividere "to divide" (see divide (v.)).
Military sense "portion of an army, fleet, or ship's company" is from 1590s. Mathematical sense of "operation inverse to multiplication" is from late 14c. The mathematical division sign supposedly was invented by British mathematician John Pell (1611-1685) who taught at Cambridge and Amsterdam.
1520s, in part a shortening of across, in part from the adverb (see cross (adv.)). Earliest sense is "falling athwart, lying athwart the main direction, passing from side to side." Meaning "intersecting, lying athwart each other" is from c. 1600.
Sense of "adverse, opposed, obstructing, contrary, opposite" is from 1560s; of persons, "peevish, ill-tempered," from 1630s, probably from the earlier senses of "contrary, athwart," especially with reference to winds and sailing ships. A 19c. emphatic form was cross as two sticks (1807), punning on the verb. Cross-grained is from 1670s of wood; as "opposed in nature or temper" from 1640s.
word-forming element typically representing cross as a noun, adverb (cross-examine), adjective (crossbar), and in many words a confluence of them. "There is no distinct line of division between cross as an adjective and cross as a prefix. As a prefix, it often represents the adv. cross, or the prep. cross, across." [Century Dictionary]
Old English cros "instrument of Christ's crucifixion; symbol of Christianity" (mid-10c.), probably from Old Norse or another Scandinavian source, picked up by the Norse from Old Irish cros, from Latin crux (accusative crucem, genitive crucis) "stake, cross" on which criminals were impaled or hanged (originally a tall, round pole); hence, figuratively, "torture, trouble, misery;" see crux. Also from Latin crux are Italian croce, French croix, Spanish and Portuguese cruz, Dutch kruis, German Kreuz.
The modern word is the northern England form and has predominated. Middle English also had two other forms of the same word, arriving from the continent by different paths: cruche, crouche (c. 1200) was from Medieval Latin, with pronunciation as in Italian croce (compare Crouchmas "festival of the Invention of the Cross," late 14c.). Later, especially in southern England, the form crois, croice, from Old French, was the common one (compare croisade, the older form of crusade). The Old English word was rood.
By c. 1200 as "ornamental likeness of the cross, something resembling or in the form of a cross; sign of the cross made with the right hand or with fingers." From mid-14c. as "small cross with a human figure attached; a crucifix;" late 14c. as "outdoor structure or monument in the form of a cross." Also late 14c. as "a cross formed by two lines drawn or cut on a surface; two lines intersecting at right angles; the shape of a cross without regard to religious signification." From late 12c. as a surname.
From c. 1200 in English in the figurative sense "the burden of a Christian; any suffering voluntarily borne for Christ's sake; a trial or affliction; penance in Christ's name," from Matthew x.38, xvi.24, etc. Theological sense "crucifixion and death of Christ as a necessary part of his mission" is from late 14c.
As "a mixing of breeds in the production of animals" from 1760, hence broadly "a mixture of the characteristics of two different things" (1796). In pugilism, 1906, from the motion of the blow, crossing over the opponent's lead (1880s as a verb; cross-counter (n.) is from 1883). As "accidental contact of two wires belonging to different circuits," 1870.
c. 1200, "make the sign of a cross as an act of devotion," from cross (n.) and in part from French croiser. Sense of "to go across, pass from side to side of, pass over" is from c. 1400; that of "to cancel by drawing a line over or crossed lines over" is from mid-15c.
From late 14c. as "lie across; intersect;" also "place (two things) crosswise of each other; lay one thing across another." From early 15c. as "mark a cross on." Meaning "thwart, obstruct, hinder, oppose" is from 1550s. Meaning "to draw or run a line athwart or across" is from 1703. Also in Middle English in now-archaic sense "crucify" (mid-14c.), hence, figuratively, crossed "carrying a cross of affliction or penance."
Sense of "cause to interbreed" is from 1754. In telegraphy, electricity, etc., in reference to accidental contact of two wires on different circuits or different parts of a circuit that allows part of the current to flow from one to the other, from 1884. Meaning "to cheat" is by 1823.
Cross my heart as a vow is from 1898. To cross over as euphemistic for "to die" is from 1930. To cross (someone's) path "thwart, obstruct, oppose" is from 1818. Of ideas, etc., to cross (someone's) mind "enter into" (of an idea, etc.) is from 1768; the notion is of something entering the mind as if passing athwart it.