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 170 172 176 177 179 185 191 204 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 CHAP 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 400 406 - 415 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 |