# Quadrature Sentence Examples

Among his later poems may be mentioned La Divine Tragedie (1916) and La

**Quadrature**de l'Amour (1920).The intercept on the axis of y is 2a/7r; therefore, if it were possible to accurately construct the curve, the

**quadrature**of the circle would be effected.On the other hand, it is worth noticing that the words "

**quadrature**" and " cubature " are originally due to geometrical rather than numerical considerations; the former implying the construction of a square whose area shall be equal to that of a given surface, and the latter the construction of a cube whose volume shall be equal to that of a given solid.He extended the "law of continuity" as stated by Johannes Kepler; regarded the denominators of fractions as powers with negative exponents; and deduced from the

**quadrature**of the parabola y=xm, where m is a positive integer, the area of the curves when m is negative or fractional.In the same work Wallis obtained an expression for the length of the element of a curve, which reduced the problem of rectification to that of

**quadrature**.AdvertisementA relation which is of historical interest connects the logarithmic function with the

**quadrature**of the hyperbola, for, by considering the equation of the hyperbola in the form xy=const., it is evident that the area included between the arc of a hyperbola, its nearest asymptote, and two ordinates drawn parallel to the other asymptote from points on the first asymptote distant a and b from their point of intersection, is proportional to log bla.Essentially, therefore, Descartes's process is that known later as the process of isoperimeters, and often attributed wholly to Schwab.2 In 16J5 appeared the Arithmetica Infinitorum of John Wallis, where numerous problems of

**quadrature**are dealt with, the curves being now represented in Cartesian co-ordinates, and algebra playing an important part.Montucla, successful attempt to show that

**quadrature**of the circle by a Euclidean construction was impossible.'A much less wise class than the 7r-computers of modern times are the pseudo-circle-squarers, or circle-squarers technically so called, that is to say, persons who, having obtained by illegitimate means a Euclidean construction for the

**quadrature**or a finitely expressible value for 7r, insist on using faulty reasoning and defective mathematics to establish their assertions.The area of the surface included between this curve and its base is found - the first known instance of a

**quadrature**of a curved surface.AdvertisementPascal solved the hitherto refractory problem of the general

**quadrature**of the cycloid, and proposed and solved a variety of others relating to the centre of gravity of the curve and its segments, and to the volume and centre of gravity of solids of revolution generated in various ways by means of it.In 1 754 he published an anonymous treatise entitled Histoire des recherches sur la

**quadrature**du cercle, and in 1758 the first part of his great work, Histoire des mathdmatiques, the first history of mathematics worthy of the name.The first contains an explanation of the doctrine of fluxions, and of its application to the

**quadrature**of curves; the second, a classification of seventy-two curves of the third order, with an account of their properties.When the satellite is in

**quadrature**the convergence of the lines of attraction toward the centre of the sun tends to bring the two bodies together.P. de Roberval, who accused him of plagiarizing his earlier solution of the problem of its

**quadrature**.AdvertisementHe studied the properties of the cycloid, and attempted the problem of its

**quadrature**; and in the "infinitesimals," which he was one of the first to introduce into geometrical demonstrations, was contained the fruitful germ of the differential calculus.The second includes a "Method for the

**Quadrature**of Parabolas," and a treatise "on Maxima and Minima, on Tangents, and on Centres of Gravity," containing the same solutions of a variety of problems as were afterwards incorporated into the more extensive method of fluxions by Newton and Leibnitz.This modulation technique is called

**quadrature**amplitude modulation (QAM ).Areas covered include linear algebra, optimization,

**quadrature**, differential equations, regression analysis, and time series analysis.Projection steps in the EP iteration that cannot be done analytically are done using Gaussian

**quadrature**.AdvertisementGaussian

**quadrature**is used to obtain a 2-D expression covering all points on the tooth face.The currents are arranged to be in phase

**quadrature**.During the seventeenth century it was becoming clear that fluxions and

**quadrature**were intimately related in fact, that they are inverse processes.A Latin version of them was published by Isaac Barrow in 1675 (London, 4to); Nicolas Tartaglia published in Latin the treatises on Centres of Gravity, on the

**Quadrature**of the Parabola, on the Measurement of the Circle, and on Floating Bodies, i.In mensuration, "cubature" is sometimes used to denote the volume of a solid; the word is parallel with "

**quadrature**," to determine the area of a surface (see Mensuration; Infinitesimal Calculus) .AdvertisementThe Arithmetica infinitorum relates chiefly to the

**quadrature**of curves by the so-called method of indivisibles established by Bonaventura Cavalieri in 1629 (see Infinitesimal Calculus).He attempted the

**quadrature**of the circle by interpolation, and arrived at the remarkable expression known as Wallis's Theorem (see Circle, Squaring Of).Rectification and

**quadrature**of the circle have thus been, since the time of Archimedes at least, practically identical problems. Again, since the circumferences of circles are proportional to their diameters - a proposition assumed to be true from the dawn almost of practical geometry - the rectification of the circle is seen to be transformable into finding the ratio of the circumference to the diameter.He is described as the first to treat theology on mathematical principles and he also wrote on the

**quadrature**of the circle.In the

**Quadrature**of the parabola Archimedes finds the area of a segment of a parabola cut off by any chord.An ideal

**quadrature**encoder should provide square-wave signals that are 90 degrees out of phase with each other.The total charge on a surface is obtained by integration, using Simpson 's

**quadrature**rule.Near the convergence criterion the full

**quadrature**grid as input will be applied.