"point of intersection," 1850, from intersect (v.) or from Latin intersectum, neuter past pasticiple of intersecare. Earlier (1650s) it was used for "an insect."
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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