## A Treatise on Infinitesimal Calculus: Containing Differential and Integral Calculus, Calculus of Variations, Applications to Algebra and Geometry, and Analytical Mechanics, Volume 2University Press, 1865 - Calculus |

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### Contents

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### Common terms and phrases

angle application axis Beta-function calculus of variations consequently constant contained convergent convergent series corresponding curvature cycloid d.bx d.by deduced definite integral denominator denoted derived functions determined differential Differential Calculus divergent double integral dy dx dydx element-function ellipse ellipsoid equal equivalent evaluation expressed f dx finite and continuous formula fraction Gamma-function geodesic geometrical given Hence inferior limit infinitesimal element Integral Calculus intrinsic equation investigation involute involves left-hand member length Let the equation let us suppose limits of integration maxima and minima means method multiple integral ordinates perpendicular plane curve polar coordinates positive probability problem radius vector range of integration replaced respectively result revolution right-hand member Section shew shewn similar sphere subject-variable substituting superior limit surface surface-element symbols tangent theorem tion values variables variation volume y-integration

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Page 721 - Ovid. Selections for the use of Schools. With Introductions and Notes, and an Appendix on the Roman Calendar. By W. Ramsay, MA Edited by GG Ramsay, MA, Professor of Humanity, Glasgow. Ext. fcap. 8vo. cloth, 5«.

Page 721 - An Elementary Treatise on Quaternions. By PG Tait, MA, Professor of Natural Philosophy in the University of Edinburgh ; formerly Fellow of St. Peter's College, Cambridge. Demy 8vo.

Page 727 - Librarian of Trinity College, Cambridge. I. The Merchant of Venice. Extra fcap. 8vo. stiff covers, is. II. Richard the Second. Extra fcap. 8vo. stiff covers, is.

Page 726 - Oxford, and Professor of English Literature at King's College, London. It is especially hoped that this Series may prove useful to Ladies' Schools and Middle Class Schools; in which English Literature must always be a leading subject of instruction. A General Introduction to the Series. By Professor Brewer, MA I. Chaucer. The Prologue to the Canterbury Tales; The Kniehtes Tale; The Nonne Prestes Tale.

Page 589 - Find the curve in which the perpendicular from the origin upon the tangent is equal to the abscissa of the point of contact.

Page 726 - A Treatise on Harmony. By Sir FA Gore Ouseley, Bart., MA, Mus. Doc., Professor of Music in the University of Oxford. 410. cloth, los. A Treatise on Counterpoint, Canon, and Fugue, based upon that of Cherubim.

Page 722 - W. Ward, MA, Fellow of St. Peter's College, Cambridge. Professor of istory, Owens College, Manchester. A History of British India. By SJ Owen, MA, Reader in History, Christ Church, and Teacher of Indian Law and History in the University of Oxford. A History of Greece. By EA Freeman, MA, formerly Fellow of Trinity College, Oxford.

Page 486 - A point moves on an ellipsoid so that its direction of motion always passes through the perpendicular from the centre of the ellipsoid on the tangent plane at any point ; shew that the curve traced out by the point is given by the intersection of the ellipsoid with the surface xm~" yn~l zl~m = constant, I, m, n being inversely proportional to the squares of the semiaxes of the ellipsoid.

Page 476 - F3 are proportional to the directioncosines of the normal to the surface at the point (x...

Page 269 - Y will be identical, and all points will lie on a line passing through the origin and making an angle of 45° with the two axes.