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.
word-forming element making abstract nouns from adjectives and meaning "condition or quality of being ______," from Middle English -ite, from Old French -ete (Modern French -ité) and directly from Latin -itatem (nominative -itas), suffix denoting state or condition, composed of -i- (from the stem or else a connective) + the common abstract suffix -tas (see -ty (2)).
Roughly, the word in -ity usually means the quality of being what the adjective describes, or concretely an instance of the quality, or collectively all the instances; & the word in -ism means the disposition, or collectively all those who feel it. [Fowler]