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State of the Sciences among the Christians in the West, to the end of the thirteenth Century

CHAP. X.

State of the Sciences among the Christians in the West, continued through the fourteenth and fifteenth Centuries

PERIOD THE THIRD.

PROGRESS OF THE MATHEMATICS, FROM THE END
OF THE FIFTEENTH CENTURY TO THE INVENTION
OF THE METHOD OF FLUXIONS.

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The Discovery of the Analysis of Infinites: Leibnitz first published it's Elements; Newton employed a similar Method in his PRINCIPIA MATHEMATICA

CHAP, II.

Leibnitz continues to extend his new Analysis, seconded by the two Bernoullis. Various problems proposed and resolved. The Marquis de l'Hopital's Analysis of Infinites

CHAP. III.

308

310

- 316

Extraordinary progress in the theory of maxima and minima. Dispute between the two Bernoullis on the problem of isoperimetrical figures

CHAP. IV.

Solutions of various problems. Leibnitz invents the method of differencing de curva in curvam. Justi fication of the marquis de l'Hopital.

331

Newton's

345

works. Account of some other geometricians

CHAP. V.

An Examination of the Claims of Leibnitz and Newton to the Invention of the Analysis of Infinites

CHAP. VI.

Continuation of the dispute. War of problems between John Bernoulli and the english. Miscellaneous articles

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CHAP

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Problem of isochronous curves in resisting mediums. General reflections on problems of pure theory. Al gebra of sines and cosines. Utility of methods of approximation, and in particular of infinite series

CHAP. IX.

Continuation. Progress of the methods for resolving differential equations. New step in the problem of isoperimetrical figures. The integral calculus with partial differences

CHAP. X.

Of some works on analysis

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406

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HISTORY

OF

MATHEMATICS.

INTRODUCTION.

A general view of the mathematical sciences. Nations by whom they have been cultivated.

THE term mathematics, implying from it's etymology discipline, science, represents with justice and precision the high idea that we ought to form of what is signified by it. In fact mathematics are á methodical concatenation of principles, reasonings, and conclusions, always accompanied by certainty, as their truth is always evident: an advantage that particularly characterises accurate knowledge, and the true sciences, with which we must be careful not to associate metaphysical notions, conjectures, or even the strongest probabilities.

The subjects of mathematics are the mensuration and comparison of magnitudes; for instance, numbers, distances, velocities, &c. They are divided into pure and mixed; what is understood by mixed mathematics being sometimes called the physico-mathematical sciences.

Pure

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