Etymology
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perpendicular (adj.)

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.

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perpensity (n.)

"consideration, a pondering, careful attention," 1704 (Swift), from Latin perpens-, past-participle stem of perpendere "to balance carefully" (see perpendicular) + -ity. Noted as obsolete by late 19c.

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*(s)pen- 

Proto-Indo-European root meaning "to draw, stretch, spin."

It forms all or part of: append; appendix; avoirdupois; compendium; compensate; compensation; counterpoise; depend; dispense; equipoise; expend; expense; expensive; hydroponics; impend; painter (n.2) "rope or chain that holds an anchor to a ship's side;" pansy; penchant; pend; pendant; pendentive; pending; pendular; pendulous; pendulum; pension; pensive; penthouse; perpendicular; peso; poise; ponder; ponderous; pound (n.1) "measure of weight;" prepend; prepense; preponderate; propensity; recompense; span (n.1) "distance between two objects;" span (n.2) "two animals driven together;" spangle; spanner; spend; spider; spin; spindle; spinner; spinster; stipend; suspend; suspension.

It is the hypothetical source of/evidence for its existence is provided by: Latin pendere "to hang, to cause to hang," pondus "weight" (perhaps the notion is the weight of a thing measured by how much it stretches a cord), pensare "to weigh, consider;" Greek ponos "toil," ponein "to toil;" Lithuanian spendžiu, spęsti "lay a snare;" Old Church Slavonic peti "stretch, strain," pato "fetter," pina "I span;" Old English spinnan "to spin," spannan "to join, fasten; stretch, span;" Armenian henum "I weave;" Greek patos "garment," literally "that which is spun;" Lithuanian pinu "I plait, braid," spandau "I spin;" Middle Welsh cy-ffiniden "spider;" Old English spinnan "draw out and twist fibers into thread," spiðra "spider," literally "spinner."

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*per- (1)

Proto-Indo-European root forming prepositions, etc., meaning "forward," and, by extension, "in front of, before, first, chief, toward, near, against," etc.

It forms all or part of: afford; approach; appropriate; approve; approximate; barbican; before; deprive; expropriate; far; first; for; for-; fore; fore-; forefather; foremost; former (adj.); forth; frame; frau; fret; Freya; fro; froward; from; furnish; furniture; further; galore; hysteron-proteron; impervious; improbity; impromptu; improve; palfrey; par (prep.); para- (1) "alongside, beyond; altered; contrary; irregular, abnormal;" paradise; pardon; paramount; paramour; parvenu; pellucid; per; per-; percent; percussion; perennial; perestroika; perfect; perfidy; perform; perfume; perfunctory; perhaps; peri-; perish; perjury; permanent; permeate; permit; pernicious; perpendicular; perpetual; perplex; persecute; persevere; perspective; perspire; persuasion; pertain; peruse; pervade; pervert; pierce; portray; postprandial; prae-; Prakrit; pre-; premier; presbyter; Presbyterian; preterite; pride; priest; primal; primary; primate; primavera; prime; primeval; primitive; primo; primogenitor; primogeniture; primordial; primus; prince; principal; principle; prior; pristine; private; privilege; privy; pro (n.2) "a consideration or argument in favor;" pro-; probably; probe; probity; problem; proceed; proclaim; prodigal; produce; profane; profess; profile; profit; profound; profuse; project; promise; prompt; prone; proof; proper; property; propinquity; prophet; prose; prostate; prosthesis; protagonist; Protean; protect; protein; Proterozoic; protest; proto-; protocol; proton; protoplasm; Protozoa; proud; prove; proverb; provide; provoke; prow; prowess; proximate; Purana; purchase; purdah; reciprocal; rapprochement; reproach; reprove; veneer.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit pari "around, about, through," parah "farther, remote, ulterior," pura "formerly, before," pra- "before, forward, forth;" Avestan pairi- "around," paro "before;" Hittite para "outside of," Greek peri "around, about, near, beyond," pera "across, beyond," paros "before," para "from beside, beyond," pro "before;" Latin pro "before, for, on behalf of, instead of," porro "forward," prae "before," per "through;" Old Church Slavonic pra-dedu "great-grandfather;" Russian pere- "through;" Lithuanian per "through;" Old Irish ire "farther," roar "enough;" Gothic faura "before," Old English fore (prep.) "before, in front of," (adv.) "before, previously," fram "forward, from," feor "to a great distance, long ago;" German vor "before, in front of;" Old Irish air- Gothic fair-, German ver-, Old English fer-, intensive prefixes.

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aweigh (adv., adj.)

of an anchor, "raised, perpendicular," 1620s, nautical, from a- (1) + weigh.

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aslant (adv.)

"in a sloping direction, not perpendicular or at right angles," early 14c., o-slant, literally "on slant," from a- (1) "on" + slant (v.). As a preposition from c. 1600.

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normal (adj.)

c. 1500, "typical, common;" 1640s, in geometry, "standing at a right angle, perpendicular," from Late Latin normalis "in conformity with rule, normal," in classical Latin "made according to a carpenter's square," from norma "rule, pattern," literally "carpenter's square," a word of unknown origin (see norm). Meaning "conforming to common standards or established order or usage, regular, usual" is attested from 1828 but probably is older than the record [Barnhart].

Meaning "heterosexual" is by 1914. As a noun meaning "usual state or condition," from 1890 (in geometry as "a perpendicular" from 1727). Sense of "a normal person or thing" is attested by 1894. Normal school "training college for teachers" (1835) is a translation of French école normale (1794), a creation of the French Republic; the notion is of "serving to set a standard." The U.S. city of Normal, Illinois, was named 1857 for the normal school established there.

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plumb (adj.)

"perpendicular, vertical, true according to a plumb-line," mid-15c., plom, from plumb (n.). As an adverb, "in a vertical direction, straight down," c. 1400. The notion of "exact measurement" led to the extended adverbial sense of "completely, downright" (1748), sometimes spelled plump, plum, or plunk.

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precipice (n.)

1630s, "very steep or perpendicular face of rock," from French précipice, from Latin praecipitium "a steep place," literally "a fall or leap, a falling down or headlong," from praeceps (genitive praecipitis) "steep, headlong, headfirst," from prae "before, forth" (see pre-) + caput "head" (from PIE root *kaput- "head"). Figuratively, "a perilous position," by 1650s. Earlier in English as a verb (1590s) meaning "fall to great depth."

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martingale (n.)

1580s, "strap passing between the forelegs of a horse as part of the harness," from French martingale (16c.), of uncertain origin, perhaps from Old Provençal martegalo, fem. of martegal "inhabitant of Martigue," a commune northwest of Marseilles, making the etymological sense "worn in the manner of the people of Martigue;" or perhaps it is from Spanish almartaga, a word for a sort of halter or rein, from Arabic almartak, in which case it might have been influenced in form by the Provençal word. The nautical sense of  "short, perpendicular spar under the bowsprit-end" is by 1794.

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