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LEFT Q, q, the 17th letter and the 13th con- QUADRAGESIMA ("fortieth"), thr sonant of the English alphabet, a conso- Latin name for the whole season of Lent, nant having only one sound, that of k with its 40 days, but the name is com- or c. The name of the letter is said to be from French queue=a tail, the form being that of an O with a tail to it. As an initial, Q represents the Latin Quintus in inscriptions or literature; in geometry, etc., it represents the Latin quod (=which), as Q. E. D.=quod erat de7nonstrandtim^=vfhich was to be shown or proved; Q. E. F.=quod erat facien- dwm=which was to be done. monly assigned to the first Sunday in Lent. QUADRANGLE, a square or four- sided court or space surrounded by build- ings, as often seen in the buildings of a college, school, etc. In geometry, a fig- ure having four angles, and consequently four sides. QUADRANT, in architecture, the As a symbol, Q was formerly used for same as Quadrangle (q. v.). In geom 500, and with a dash over it, for 500,000. QUACKENBOS, JOHN DUNCAN, an American physician; bom in New York, N. Y., April 22, 1848; was graduated at Columbia College in 1868 and at the Col- lege of Physicians and Surgeons in 1871; began practice in New York; became Ad- etry, the fourth part of a circle. Nauti- cally, an instrument for making angular measurements. It is now superseded by the Sextant (g. v.) QUADRATE BONE, in comparative anatomy, a bone by means of which the rami are articulated with the skull in junct Professor of the English Language birds, reptiles, and fishes (often called and Literature at Columbia College in the hypotympanic bone). 1884; Professor of Rhetoric in Barnard College in 1891-1893. He then became a specialist in mental diseases and lec- tured extensively on scientific and liter- ary topics. He wrote "History of the World"; "History of Ancient Litera- ture"; ''Tuberculosis"; "Magnhild" (1919), etc. A specialist in mental dis- eases. QUACKENBUSH, STEPHEN PLATT, an American naval officer; bom in Al- bany, N. Y., Jan. 23, 1823; joined the navy in 1840; promoted lieutenant-com- mander in 1862; had charge of various vessels in blockading fleets during the Civil War; participated in the action at Elizabeth City and Newbem, N. C, cap- tured the "Princess Royal" and won dis- tinction in other operations. He was retired with the rank of rear-admiral in 1885. He died in Washington, D. C, Feb. 4, 1890. QUADER SANDSTONE, a siliceous QUADRATURE, the state of being quadrate or square^ a square space. In astronomy, the position of one heavenly body with respect to another 90° dis- tant, as the moon when midway between the points of opposition and conjunction. In geometry, the act of squaring; the reducing of a figure to a square. The quadrature of the circle is a famous problem, which has probably been the subject of more discussion and research than any other problem within the whole range of mathematical science. QUADRATURES, METHODS OF, any arithmetical method of determining the area of a curve. When the exact area is known a square whose area is equal to it can be found — hence the term "quadratures." It has been shown (see Calculus) that the area of a curve whose equation is ?/=/ (x) is fydx, and can therefore be found when the integral can be evaluated. Hence the approxi- sandstone of Cretaceous age, with many mate determination of the value of a ^ssil shells identical with those of the definite integral is obtainable by the ^.nglish Chalk. method of quadratures. 392