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hypotenuse: hypotenuse: [16] The hypotenuse is etymologically a line that is ‘stretched under’ the right angle of a triangle. The word comes via Latin hypotēnūsa from Greek hupoteínousa, a derivative of hupoteínein. This was a compound verb formed from the prefix hupo- ‘under’ and teínein ‘stretch’ (a relative of English tend, tense, etc).
=> tend, tense
normal: normal: [17] Latin norma originally denoted a sort of set square used by carpenters, masons, etc for measuring right angles. It was extended metaphorically to a ‘rule, pattern, precept’, but English originally took over its derivative normālis as a mathematical term, in the fairly literal sense ‘perpendicular’. The more familiar modern sense ‘standard, usual’ did not emerge until the 19th century, at about the same time as normality, normalcy, and norm itself began to appear on the scene.
abeam (adv.): "at right angles to the mainmast," 1826, nautical, literally "on beam;" see a- (1) + beam (n.).
cross (n.): Old English cros "instrument of Christ's crucifixion; symbol of Christianity" (mid-10c.), from Old Irish cros, probably via Scandinavian, from Latin crux (accusative crucem, genitive crucis) "stake, cross" on which criminals were impaled or hanged (originally a tall, round pole); hence, figuratively, "torture, trouble, misery." The word is possibly of Phoenician origin. Replaced Old English rood.

Also from Latin crux are Italian croce, French croix, Spanish and Portuguese cruz, Dutch kruis, German Kreuz.

By c. 1200 as "ornamental likeness of the cross, something resembling or in the form of a cross; sign of the cross made with the right hand or with fingers." From mid-14c. as "small cross with a human figure attached; a crucifix;" late 14c. as "outdoor structure or monument in the form of a cross." Also late 14c. as "a cross formed by two lines drawn or cut on a surface; two lines intersecting at right angles; the shape of a cross without regard to religious signification." From late 12c. as a surname.

From c. 1200 in the figurative sense "the burden of a Christian; suffering; a trial or affliction; penance in Christ's name," from Matt. x.38, xvi.24, etc. Theological sense "crucifixion and death of Christ as a necessary part of his mission" is from late 14c.

As "a mixing of breeds in the production of animals" from 1760, hence broadly "a mixture of the characteristics of two different things." In pugilism, 1906, from the motion of the blow (1880s as a verb; cross-counter (n.) is from 1883).
hypotenuse (n.): 1570s, from Late Latin hypotenusa, from Greek hypoteinousa "stretching under" (the right angle), fem. present participle of hypoteinein, from hypo- "under" (see sub-) + teinein "to stretch" (see tenet). Formerly often erroneously hypothenuse.
normal (adj.): c. 1500, "typical, common;" 1640s, "standing at a right angle," from Late Latin normalis "in conformity with rule, normal," from Latin normalis "made according to a carpenter's square," from norma "rule, pattern," literally "carpenter's square" (see norm). Meaning "conforming to common standards, usual" is from 1828, but probably older than the record [Barnhart].

As a noun meaning "usual state or condition," from 1890. Sense of "normal person or thing" is from 1894. Normal school (1834) is from French école normale (1794), a republican foundation. The city of Normal, Illinois, U.S., was named 1857 for the normal school established there.
normalcy (n.): 1857, "mathematical condition of being at right angles," from normal + -cy. Associated since c. 1920 with U.S. president Warren G. Harding and derided as an example of his incompetent speaking style. Previously used mostly in the mathematical sense. The word prefered by purists for "a normal situation" is normality (1849).
plywood (n.): 1907, from ply (n.) + wood (n.). So called because the layers are arranged so that the grain of one runs at right angles to that of the next.
rectangle (n.): 1570s, from Middle French rectangle (16c.) and directly from Late Latin rectangulum, from rect-, comb. form of Latin rectus "right" (see right (adj.1)) + Old French angle (see angle (n.)). Medieval Latin rectangulum meant "a triangle having a right angle."
right (adj.1): "morally correct," Old English riht "just, good, fair; proper, fitting; straight, not bent, direct, erect," from Proto-Germanic *rekhtaz (cognates: Old Frisian riucht "right," Old Saxon reht, Middle Dutch and Dutch recht, Old High German reht, German recht, Old Norse rettr, Gothic raihts), from PIE root *reg- "move in a straight line," also "to rule, to lead straight, to put right" (see regal; cognates: Greek orektos "stretched out, upright;" Latin rectus "straight, right;" Old Persian rasta- "straight, right," aršta- "rectitude;" Old Irish recht "law;" Welsh rhaith, Breton reiz "just, righteous, wise").

Compare slang straight (adj.1) "honest, morally upright," and Latin rectus "right," literally "straight," Lithuanian teisus "right, true," literally "straight." Greek dikaios "just" (in the moral and legal sense) is from dike "custom." As an emphatic, meaning "you are right," it is recorded from 1580s; use as a question meaning "am I not right?" is from 1961. The sense in right whale is "justly entitled to the name." Right stuff "best human ingredients" is from 1848, popularized by Tom Wolfe's 1979 book about the first astronauts. Right of way is attested from 1767. Right angle is from late 14c.
square (n.): mid-13c., "tool for measuring right angles, carpenter's square," from Old French esquire "a square, squareness," from Vulgar Latin *exquadra, back-formation from *exquadrare "to square," from Latin ex- "out" (see ex-) + quadrare "make square, set in order, complete," from quadrus "a square" (see quadrant).

Meaning "square shape or area" is recorded by late 14c. (Old English used feower-scyte). Geometric sense "four-sided rectilinear figure" is from 1550s; mathematical sense of "a number multiplied by itself" is first recorded 1550s. Sense of "open space in a town or park" is from 1680s; that of "area bounded by four streets in a city" is from c. 1700. As short for square meal, from 1882. Square one "the very beginning" (often what one must go back to) is from 1960, probably a figure from board games.
square (adj.): early 14c., "containing four equal sides and right angles," from square (n.), or from Old French esquarre, past participle of esquarrer. Meaning "honest, fair," is first attested 1560s; that of "straight, direct" is from 1804. Of meals, from 1868.

Sense of "old-fashioned" is 1944, U.S. jazz slang, said to be from shape of a conductor's hand gestures in a regular four-beat rhythm. Square-toes meant nearly the same thing late 18c.: "precise, formal, old-fashioned person," from the style of men's shoes worn early 18c. and then fallen from fashion. Squaresville is attested from 1956. Square dance attested by 1831; originally one in which the couples faced inward from four sides; later of country dances generally.
[T]he old square dance is an abortive attempt at conversation while engaged in walking certain mathematical figures over a limited area. [March 1868]
swastika (n.): Greek cross with arms bent at right angles, 1871 (in English specifically as emblem of the Nazi party from 1932), from Sanskrit svastika-s, literally "being fortunate," from svasti-s "well-being, luck," from su- "well" (from PIE *(e)su- "good") + as-, root of asti "(he) is," which is from the same PIE root as Latin esse "to be" (see essence).

Also known as gammadion (Byzantine), cross cramponnee (heraldry), Thor's hammer, and, perhaps, fylfot. Originally an ancient cosmic or religious symbol thought to bring good luck. Use in reference to the Nazi emblem first recorded in English in 1932. The German word was Hakenkreuz, literally "hook-cross."
rectangulate (2): "To place at right angles; to divide into rectangles; to give a rectangular form to; to arrange or set out in a rectangular form", Mid 19th cent.; earliest use found in John Phillips. From post-classical Latin rectangulum rectangle + -ate.
rectangulometer: "An instrument used to determine whether an angle is a right angle", Mid 19th cent.; earliest use found in Charles Holtzapffel (1806–1847), mechanical engineer and technical writer. From post-classical Latin rectangulum rectangle + -ometer.