An Etymological Dictionary of Astronomy and Astrophysics

To cut or divide by passing through or across: a comet intersecting Earth’s orbit.
Geometry: Of lines, to meet and cross at a point.

Etymology (EN): From L. intersectus, p.p. of intersecarer, from → inter- + secare “to cut.”

Etymology (PE): Andarboridan, from andar-, → inter-, + boridan “to cut,” from Mid.Pers. britan, brinitan “to cut off;” Av. brāy-, present tense brin-, only with suffix pairi-, “to cut off;” cf. Skt. bhri- “to hurt, injure,” bhrinanti “they hurt.”
Andarsekanjidan, from andar-, → inter-, + sekanjidan [Dehxodâ] “to cut, scrape, pare;” Mid.Pers. škastan, škenn- “to break,” Mod.Pers. šekastan “to beak, split,” present stem šekan-; Av. scind-, scand “to beak, cleave;”
Proto-Iranian *skand- “to beak, cleave;” PIE sken- “to cut off.”