late 15c., perpendiculer, of a line, "lying at right angles to the horizon" (in astronomy, navigation, etc.), from an earlier adverb (late 14c.), "at right angles to the horizon," from Old French perpendiculer, from Late Latin perpendicularis "vertical, as a plumb line," from Latin perpendiculum "plumb line," from perpendere "balance carefully," from per "thoroughly" (see per) + pendere "to hang, cause to hang; weigh" (from PIE root *(s)pen- "to draw, stretch, spin").
The meaning "perfectly vertical" is by 1590s. As a noun, "a line that meets another line or plane at right angles," from 1570s. The earlier noun was perpendicle (c. 1400). Related: Perpendicularly; perpendicularity.