"going in four directions," 1820, from Latin quadrivius "of the crossroads," literally "going four ways," from quadrivium "crossroads" (see quadrivium).
Entries linking to quadrivious
quadrivium n.
"arithmetic, music, geometry, astronomy" (the four branches of mathematics, according to the Pythagoreans), by 1751, from Latin quadrivium, which meant "place where four roads meet, crossroads," from quadri- "four" (from PIE root *kwetwer- "four") + via "way, road, channel, course" (see via). Compare liberal arts, and also see trivium.
The adjective quadrivial is attested from mid-15c. in English with the sense of "belonging to the quadrivium," late 15c. with the sense of "having four roads, having four ways meeting in a point."