perpendiculum

Latin perpendiculum was the plumb line — a cord with a heavy weight (plumbum, lead) at the bottom, used by builders and surveyors to establish a perfectly vertical line. The plumb line always hangs at 90 degrees to the horizontal because gravity always points straight down. From per (through, thoroughly) and pendere (to hang). Perpendiculum → perpendicular: the direction established by hanging.

The Romans used plumb lines throughout their construction: checking walls for vertical accuracy, setting columns, aligning foundations. Roman surveying instruments (the groma) used perpendicular plumb lines to establish right angles and grid lines. The military camps they built across Europe used perpendicular grids — which is why so many European cities built on Roman foundations have perpendicular street grids.

In mathematics, perpendicular acquired its precise geometric meaning: two lines meeting at exactly 90 degrees. Euclid's Elements defined perpendicular lines and proved their properties in Book I. The right angle — the perpendicular meeting — became the fundamental unit of geometric measurement. Degrees themselves are defined relative to the right angle: 90 degrees is perpendicular.

Gothic architecture developed the Perpendicular Style in England from the late 14th century — characterized by vertical emphasis, large windows with perpendicular tracery, and fan vaulting. King's College Chapel, Cambridge (completed 1515), is the definitive example. The architectural style borrowed its name from the mathematical property of its vertical tracery lines.