"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."