"section of something made by a plane passing through it at a right angle to one of its axes," 1748, originally in engineering sketches, from cross (adj.) + section (n.). Figurative sense of "representative sample" is by 1903.
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.
late 14c., "intersection of two straight lines; division of a scale;" from Old French section or directly from Latin sectionem (nominative sectio) "a cutting, cutting off, division," noun of action from past participle stem of secare "to cut," from PIE root *sek- "to cut." From 1550s as "act of cutting or dividing." Meaning "subdivision of a written work, statute, etc." is from 1570s. Meaning "a part cut off from the rest" is from early 15c.
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Harper, D. (n.d.). Etymology of cross-section. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/cross-section