Etymology
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intersection (n.)

1550s, "act or fact of crossing," from French intersection (14c.) and directly from Latin intersectionem (nominative intersectio) "a cutting asunder, intersection," noun of action from past-participle stem of intersecare "intersect, cut asunder," from inter- "between" (see inter-) + secare "to cut" (from PIE root *sek- "to cut"). In English originally a term in geometry; meaning "crossroads, a place of crossing" is from 1864. Related: Intersectional.

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intersect (v.)
1610s (trans.), back-formation from intersection, or else from Latin intersectus, past participle of intersecare "intersect, cut asunder," from inter "between" (see inter-) + secare "to cut" (from PIE root *sek- "to cut"). Intransitive sense is from 1847. Related: Intersected; intersecting.
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guide-post (n.)
also guidepost, 1761, from guide (v.) + post (n.1). Placed at a fork or intersection, with signs to guide travelers on their way.
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intersect (n.)
"point of intersection," 1850, from intersect (v.) or from Latin intersectum, neuter past pasticiple of intersecare. Earlier (1650s) it was used for "an insect."
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node (n.)

early 15c., "a knot or lump," from Latin nodus "knot" (from PIE root *ned- "to bind, tie"). Originally borrowed c. 1400 in Latin form, meaning "lump in the flesh." Meaning "point of intersection" (originally in astronomy, of planetary orbits with the ecliptic) is recorded from 1660s.

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chiasma (n.)

in anatomy, "a crossing, an intersection," 1832, medical Latin, from Greek khiasma "two things placed crosswise," which is related to khiasmos (see chi, and compare chiasmus). In cytology from 1911. Related: Chiasmal.

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hyperbola (n.)
curve formed by the intersection of a plane with a double cone, 1660s, from Latinized form of Greek hyperbole "extravagance," literally "a throwing beyond (others);" see hyperbole, which in English is the same word in its Greek garb. Perhaps so called because the inclination of the plane to the base of the cone exceeds that of the side of the cone.
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crossing (n.)

mid-15c., "a making of the sign of a cross;" 1530s, "a marking with a cross," verbal noun from cross (v.). From early 15c. as "place or action of passing across;" 1630s as "place where (a river, a road, etc.) is crossed;" from 1690s as "intersection" (originally of streets). Meaning "action of crossing out by drawing crossed lines through" is from 1650s. Crossing-gate is from 1876.

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section (n.)
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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groin (n.)
"oblique depression of the body between the abdomen and thighs," 1590s, earlier grine (1530s), from Middle English grynde "groin" (c. 1400), originally "depression in the ground," from Old English grynde "abyss," perhaps also "depression, hollow," from Proto-Germanic *grundus (see ground (n.)). Altered 16c. by influence of loin or obsolete groin "snout of a pig." The architectural groin "curving edge formed by the intersection of two vaults" is from 1725.
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