QUADRAT 



Quadrat. In typography, piece 

 of metal cast lower than the letters 

 and used for spaces between them, 

 and for filling out blank lines. It is 

 usually abbreviated as quad. 



Quadratic Equation. In 

 mathematics, equations which in- 

 volve the second power of the un- 

 known quantity. Every quadratic 

 equation can be reduced to the 

 form x--{-ax-\-b=0 where x is the 

 unknown quantity, and a and 6 

 the terms in which its value may be 

 expressed. See Equation. 



Quadratics i Lit. guadrare, to 

 square). In mathematics, name 

 given to a type of curves the ordin- 

 ates of which are a measure of the 

 areas of other curves. One of the 

 most famous of these curves is that 

 called the quadratrix of Dino- 

 stratus. It is the plane locus of 

 the intersection of a straight line 

 revolving uniformly about a point 

 and another straight line moving 

 uniformly parallel to a given direc- 

 tion. It was realized that the con- 

 struction of such a curve, one of 

 the most ancient of transcendental 

 curves, would enable the squaring 

 of the circle, the duplicating of the 

 cube, and the trisection of an angle 

 to be accomplished, the three most 

 famous geometrical problems of 

 the ancients. The quadratrix of 

 Tschirnhausen is a curve with 

 similar properties. 



Quadrature. In astronomy, 

 the relative position of two heaven- 

 ly bodies when their difference of 

 longitude is 90. The first quarter 

 of the moon is its eastern quad- 

 rature, the last its western quad- 

 rature. Quadrature of an inferior 

 planet with the sun is impossible, 

 since its maximum elongation is 

 less than 90. 



In mathematics quadrature is 

 the finding of an area equal to a 

 given area. It is usually restricted 

 to the finding of a square equal in 

 area to a given area. The squaring 

 of the circle (q.v. ) was one of the 

 three famous problems of anti- 

 quity. The area of any figure 

 bounded by straight lines is easily 

 found, since the figure may be 

 divided into triangles, the areas of 

 which were first demonstrated by 

 Euclid. The areas of figures 

 bounded by curves cannot in 

 general be found. Where the 

 equations of the curves can be 

 stated in algebraic functions, how- 

 ever, the areas can be obtained by 

 the calculus. See Mensuration. 



Quadrilateral. Four-sided 

 polygon. Particular kinds of quad- 

 rilateral are the square, parallelo- 

 gram, rhombus, and trapezium. 

 The word usually indicates a 

 figure in one plane, a quadri- 

 lateral not in one plane being 

 known as a gauche quadrilateral. 



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Quadrilateral (Lat. quatuor, 

 four ; ll a*, side). Name used for 

 four fortresses grouped for stra- 

 tegic purposes. Perhaps the most 

 famous quadrilateral is the one in 

 N. Italy, composed of the fortified 

 towns of Peschiera, Mantua, Leg- 

 nago, and Verona, which enabled 

 the Austrians to maintain their 

 hold on N. Italy. Verona, com- 

 manding the Adige valley, allowed 

 supplies to come from Austria, and 

 Mantua was so strongly situated 

 and fortified that it was long 

 deemed impregnable. In 1848, 

 Peschiera fell to the Italians, who 

 then besieged Mantua, but they 

 met with a reverse at Custozza and 

 retreated. After the battle of 

 Solferino, the French and Italians 

 were bombarding Peschiera, when 

 the peace of Villaf ranca terminated 

 hostilities. In 1866 the Italians 

 again attempted to capture the 

 quadrilateral, but without success. 

 Quadrilateral was also the name 

 given to a redoubt in France, J m. 

 E. of Ginchy, in a ravine adjoining 

 the Morval Road prominent in 

 the Great War. It was strongly 

 fortified by the Germans to cover 

 Morval, and was captured by the 

 British 6th Division on Sept. 18, 

 1916. Another quadrilateral was 

 the strongly defended series of 

 trenches held by the Turks east of 

 Kereves Dere on the Gallipoli 

 peninsula in the Great War. It was 

 stormed by the French in June, 

 1915. Other quadrilaterals were 

 those of N.E. Germany, whose 

 fortresses were Konigsberg, Danzig, 

 Posen, and Thorn, and of Poland 

 consisting of Brest-Litovsk, Ivan- 

 gorod, Novo-Georgievsk and War- 

 saw. See Gallipoli, Campaign in; 

 Somme, Battles of the. 



Quadrille (It. squadra, a square). 

 Dance which originated in the 

 French ballets of the 18th century, 

 and was later transferred to the 

 ballroom. It is danced by four 

 couples who stand in a square. The 

 music consists of five parts : Le 

 Pantalon, L'Ete, La Poule, La 

 Trenise, and Finale, the names 

 being taken from old contre-danses. 

 See Dancing. 



Quadrille. Obsolete or almost 

 obsolete card game. It is an off- 

 shoot of Ombre (q-v.), and is 

 played by four persons with 40 

 cards, the 8, 9, and 10 of each suit 

 being eliminated from the pack. 



Qua dr ire me. Ancient war 

 vessel. It was propelled by four 

 banks of oars, one above the other. 

 See Trireme. 



Quadroon (Span, cuarteron ; 

 from Lat. quartus, fourth). Term 

 applied generally to one who has 

 one-fourth negro blood the off- 

 spring of a white and a mulatto. 

 It is sometimes applied to a person 



QUAGGA 



who is fourth in descent from a 

 negro ancestor, provided that one 

 the parents in each generation has 

 been white ; the person who is 

 third in descent is known as a 

 terceron. The Spaniards early used 

 the word for the offspring of a white 

 and an Indian half-breed, and it is 

 sometimes applied to similar 

 crossings in other races, and also to 

 animals and plants. See Negro. 



Quadruplane. Name for an 

 aeroplane whose main lifting sur- 

 faces take the form of four sets of 

 superimposed wings. 



Quadruple Alliance (Lat. 

 quadruplus, fourfold). Alliance of 

 four countries. Such was the 

 treaty of 1718 by which Great 

 Britain, the Netherlands, France, 

 and the Empire, signed an agree- 

 ment to uphold the treaty of 

 Utrecht against the aggressive pol- 

 icy then pursued by Spain. An- 

 other quadruple alliance was signed 

 in 1834 by Great Britain, France, 

 Spain, and Portugal, with the object 

 of keeping the Dom Miguel from the 

 throne of Portugal. See Treaty ; 

 Triple Alliance. 



Quadruplet. Musical term for 

 an abnormal group of four equal 

 notes. It is performed in the time 

 of three or six of the same nominal 

 value. 



Quaestor (from Lat. quaerere, 

 to ask, inquire). Magistrate of 

 ancient Rome. Their number was 

 originally two, but by the last period 

 of the Republic it had increased 

 to 40. Under the empire the num- 

 ber was reduced to 20. At the 

 inception of the office in the early 

 republic the quaestors had certain 

 legal duties in connexion with in- 

 quisition into murder charges, but 

 this function soon passed to the 

 aediles and tribunes. Latterly, the 

 quaestors were financial and ad- 

 ministrative officers entirely, e.g. 

 quaestores classici, who looked after 

 the financial administration of the 

 fleet, and quaestores urbani, who 

 had charge of the treasury. The 

 quaestorship was the lowest of the 

 higher magistracies, whose holders 

 were entitled to a seat in the senate 

 after their year of office. The 

 quaestorship was thus the first 

 step in a public career. 



Quagga. Name formerly ap- 

 plied to a dark variety of zebra, 

 once common in Cape Colony. It 

 became extinct about 1870. The 

 name was onomatopoeic, being the 

 natives' reproduction (qua-ha) 

 of the animal's barklike neigli 

 " qua-ha-ha " ; it was applied by 

 them to zebras in general. It is now 

 believed that the supposed Equtis 



