quadrature

From the Table I., or by quadrature of the curve in fig.

20Under the general heading "Geometry" occur the subheadings "Foundations," with the topics principles of geometry, non-Euclidean geometries, hyperspace, methods of analytical geometry; "Elementary Geometry," with the topics planimetry, stereometry, trigonometry, descriptive geometry; "Geometry of Conics and Quadrics," with the implied topics; "Algebraic Curves and Surfaces of Degree higher than the Second," with the implied topics; "Transformations and General Methods for Algebraic Configurations," with the topics collineation, duality, transformations, correspondence, groups of points on algebraic curves and surfaces, genus of curves and surfaces, enumerative geometry, connexes, complexes, congruences, higher elements in space, algebraic configurations in hyperspace; "Infinitesimal Geometry: applications of Differential and Integral Calculus to Geometry," with the topics kinematic geometry, curvature, rectification and quadrature, special transcendental curves and surfaces; "Differential Geometry: applications of Differential Equations to Geometry," with the topics curves on surfaces, minimal surfaces, surfaces determined by differential properties, conformal and other representation of surfaces on others, deformation of surfaces, orthogonal and isothermic surfaces.

00Among his later poems may be mentioned La Divine Tragedie (1916) and La Quadrature de l'Amour (1920).

00If a fourth integral is obtainable, the solution is reducible to quadrature, but this is not possible except in a limited series of cases, investigated by H.

00quadrator, squarer), in mathematics, a curve having ordinates which are a measure of the area (or quadrature) of another curve.

00The 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.

00Quadrature >>

00His chief works are: Astronomical History of Observations of Heavenly Motions and Appearances (1634); Ecliptica prognostica (1634); Controversy with Longomontanus concerning the Quadrature of the Circle (1646?); An Idea of the Mathematics, 12m0 (1650); A Table of Ten Thousand Square Numbers (fol.; 1672).

00On 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.

00He 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.

00In 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.

00A 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.

00The first attempts to solve the purely geometrical problem appear to have been made by the Greeks (Anaxagoras, &c.) 2, one of whom, Hippocrates, doubtless raised hopes of a solution by his quadrature of the so-called meniscoi or lune.3 [The Greeks were in possession of several relations pertaining to the quadrature of the lune.

00" Quadrature of the Circle, '"in' English Cyclop.; Glaisher, Mess.

005 For minute and lengthy details regarding the quadrature of the circle in the Low Countries, see de Haan, " Bouwstoffen voor de geschiedenis, &c.," in Versl.

00Essentially, 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.

00Montucla, successful attempt to show that quadrature of the circle by a Euclidean construction was impossible.'

00A 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.

00The area of the surface included between this curve and its base is found - the first known instance of a quadrature of a curved surface.

00i.) to appear in 1656, take care to remove some of the worst mistakes exposed by Wallis, and, while leaving out all the references to Vindex, now profess to make, in altered form, a series of mere " attempts " at quadrature; but he was far from yielding the ground to the enemy.

00Pascal 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.

00In 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.

00The 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.

00When 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.

00equation of the centre and evection are, at quadrature 6.29° sin g+I 27° sin g= 7.56° sin g.

00P. de Roberval, who accused him of plagiarizing his earlier solution of the problem of its quadrature.

00He 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.

00The 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.

00This modulation technique is called quadrature amplitude modulation (QAM ).

00Areas covered include linear algebra, optimization, quadrature, differential equations, regression analysis, and time series analysis.

00quadrature of the circle.

00quadrature of the parabola Archimedes finds the area of a segment of a parabola cut off by any chord.

00Projection steps in the EP iteration that cannot be done analytically are done using Gaussian quadrature.

00Gaussian quadrature is used to obtain a 2-D expression covering all points on the tooth face.

00Solution method: Recurrence relations, power series expansion, numerical quadrature.

00Solution method: The program solves the Cauchy principal value integrals numerically using adaptive Gaussian quadrature.

00quadrature encoder should provide square-wave signals that are 90 degrees out of phase with each other.

00quadrature rule.

00quadrature points used.

00quadrature grid as input will be applied.

00quadrature routine requires full recursivity qualities from the Fortran compiler.

00quadrature amplitude modulation (QAM ).

00The currents are arranged to be in phase quadrature.

00During the seventeenth century it was becoming clear that fluxions and quadrature were intimately related in fact, that they are inverse processes.

00(6) The Quadrature of the Parabola (Tetragonismos paraboles) is a book in twenty-four propositions, containing two demonstrations that the area of any segment of a parabola is a of the triangle which has the same base as the segment and equal height.

00A 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.

00In 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) .

00The 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).

00He attempted the quadrature of the circle by interpolation, and arrived at the remarkable expression known as Wallis's Theorem (see Circle, Squaring Of).

00Rectification 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.

00equation of the centre and evection are, at quadrature 6.29Ã‚° sin g+I 27Ã‚° sin g= 7.56Ã‚° sin g.

00He is described as the first to treat theology on mathematical principles and he also wrote on the quadrature of the circle.

00In the Quadrature of the parabola Archimedes finds the area of a segment of a parabola cut off by any chord.

00An ideal quadrature encoder should provide square-wave signals that are 90 degrees out of phase with each other.

00The total charge on a surface is obtained by integration, using Simpson 's quadrature rule.

00Running time: The execution time depends strongly on the number of quadrature points used.

00Near the convergence criterion the full quadrature grid as input will be applied.

00Unusual features: The adaptive quadrature routine requires full recursivity qualities from the Fortran compiler.

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