Origins of Mathematical Words: A Comprehensive Dictionary of Latin, Greek, and Arabic Roots

Q

264 Florence. The volume of the pyramid is [nr2 sin (2π/n)]a, and its centroid is a/4 up the axis, the same as in the case of a cone. Pythagorean This is the English adjective formed from the name of the Greek mathematician PuqagÒraj on the analogy of Latin adjectives ending in -eanus, -a, -um. The correct Latin adjective is Pythagoreus, -a, -um. A Pythagorean triplet is a triplet a, b, c of positive integers such that a2 + b2 = c2 . The triplet is primitive if a, b, and c have no common factor. The primitive Pythagorean triplets were studied by the Babylonians, as we know from the Plimpton cuneiform tablet number 322 in the collection of Columbia University. They are given by c2 = p2 + q2 , b2 = p2 – q2 , and a = 2pq, where p and q are relatively prime positive integers such that p > q and exactly one of p and q is odd. Q Q.E.D. This is the abbreviation for the Latin Quod erat demonstrandum, which was a Latin translation of the way Euclid ended the proofs of his theorems, Ö œdei de‹xai, “This is what it was necessary to prove.” Constructions ended with Ö œdei poiÁsai, “This is what it was necessary to do,” which became Quod erat faciendum or Q.E.F. The earliest translators, however, did not use Q.E.D. or Q.E.F. Instead, we find such phrases as Quod oportebat facere (Boëthius), Et hoc est quod proposuimus (Adelard of Bath), Et hoc est quod demonstrare voluimus (Gerard of Cremona), and Quod proposuimus (Johannes de Tinamue). Q.E.F. See the previous entry. quadri- or quadr- The Latin noun quadra, -ae (also quadrum, -i) means a square. It is related to the adjective quattuor, which means four. This prefix is therefore correctly attached to other words of Latin origin to convey the idea of four. 265 quadrangle This word is derived from the Latin quadrangulus, a plane figure having four angles. See the entries quadri- and angle. quadrant This is the stem of the Latin noun quadrans, quadrantis, which means a fourth part. quadratic The Latin verb quadro, quadrare, quadravi, quadratus means to make a square (quadrum). The past participle quadratus means made into a square or squared. The correct English adjective should therefore be quadrate. Quadratic is a mistake produced by adding the Greek adjectival suffix -ic to the stem of a Latin participle. quadratrix This word means squarer, that which squares, and is the name of a curve used by Hippias (fifth century B.C.) to square the circle, from the Latin quadro, to square. The feminine form quadratrix is preferred over the masculine form quadrator since the name is supposed to be in apposition to linea curva (curved line) understood. The quadratrix may be defined in the following manner: Consider the square ABCD in the first quadrant, whose side AB is on the y-axis, whose side AD is on the x-axis, and whose sides each have length a. The vertical line segment BC descends at uniform speed to the base AD at the same time that the side AB revolves at uniform angular speed about A to the same base AD. The locus of intersection of the two moving lines is the quadratrix of Hippias. The polar equation of the quadratrix is r = 2aq/psin q. quadrature This is derived from the future active participle quadraturus, -a, -um of the verb quadro, quadrare, to make into a square. quadric This word is a mistake, the result of adding a Greek suffix to the root of a Latin noun. The mistake comes from the analogy of cubic, but cube is of Greek origin. quadrifolium This well-formed word is the composition of the Latin prefix quadri- (from quattuor, four) and the noun folium, leaf. 266 quadrilateral This word is composed of the Latin prefix quadri- (from quattuor, four) and the adjective lateralis, which means pertaining to a side (latus). quadrivium This word is derived from the numeral quattuor, four, and the noun via, road. It is the Latin name for an intersection of four roads. The quadrivium consisted of the four mathematical subjects of the seven liberal arts, geometry, arithmetic (number theory), astronomy, and music. quadruple The Latin adjectives quadruplex, quadruplicis and quadruplus both mean fourfold. The second is the parent of quadruple. The neuter quadruplum as a noun means four times the...