cross-section (n.)

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., seccioun, in astronomy, "the intersection of two straight lines; a division of a scale;" from Old French section and 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").

 The meaning "a part cut off or separated from the rest" is from early 15c. That of "a drawing representing something as if cut through" is from 1660s. From 1550s in English in the meaning "act of cutting or dividing," a sense now rare or archaic and preserved in some medical phrases, most notably Caesarian section. The meaning "a subdivision of a written work, statute, etc." is from 1570s.

Books are commonly divided into Chapters, Chapters into Sections, and Sections into Paragraphs or Breaks, as Printers call them .... [Blount, "Glossigraphia," 1656]

In music, "a group of similar instruments in a band or orchestra" (1880). In U.S. history, a square of 640 acres into which public lands were divided (1785). In World War II U.S. military slang, section eight was a reference to the passage in an Army Regulations act that referred to discharge on grounds of insanity.