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A TREATISE

ON

INFINITESIMAL CALCULUS;

CONTAINING

DIFFERENTIAL AND INTEGRAL CALCULUS, CALCULUS OF VARIA-
TIONS, APPLICATIONS TO ALGEBRA AND GEOMETRY,
AND ANALYTICAL MECHANICS.

BY

BARTHOLOMEW PRICE, M.A., F.R.S., F.R.A.S.,

FELLOW AND TUTOR OF PEMBROKE COLLEGE, AND
SEDLEIAN PROFESSOR OF NATURAL PHILOSOPHY, OXFORD.

VOL. I.

DIFFERENTIAL CALCULUS.

SECOND EDITION.

** Les progres de la science ne sont vraiment fructueux, que quand ils amenent
aussi le progres des Trails elementaires."—Ch. Dupin.

OXFORD:
AT THE UNIVERSITY PRESS.

M.DCCC.LVIl.

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The character of Infinitesimal Calculus as a progressive science has been so well sustained during the last few years, that in preparing for the press this second edition of my first volume I have found it necessary to make more alterations than might otherwise have been desirable. In Great Britain, no less than in other parts of the world, and especially in Germany and France, have the boundaries of our science been advanced: new methods and new processes have been devised, new theorems have been discovered, and to new forms of subject-matter the principles of the Calculus have been applied. Every one who has watched the progress of the science will hardly need to be told of Sir W. R. Hamilton, Cayley, Boole, Donkin, Spottiswoode, Sylvester, Salmon, Hargreave, any more than of Jacobi, Dirichlet, Joachimsthal, Hesse, Pliicker, Steiner, Sturm, Liouville. To all these in their several degrees is due the credit of having brought the subject to a state of perfection never heretofore attained; and a treatise pretending to be didactic and educational would ill deserve those epithets if the discoveries of such eminent mathematicians were not noticed in it.

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