—Anonymous.
CHAPTER XIX
THE CALCULUS AND ALLIED TOPICS
[1901]. It may be said that the conceptions of differential quotient and integral, which in their origin certainly go back to Archimedes, were introduced into science by the investigations of Kepler, Descartes, Cavalieri, Fermat and Wallis.... The capital discovery that differentiation and integration are inverse operations belongs to Newton and Leibnitz.—Lie, Sophus.
Leipziger Berichte, 47 (1895), Math.-phys. Classe, p. 53.
[1902]. It appears that Fermat, the true inventor of the differential calculus, considered that calculus as derived from the calculus of finite differences by neglecting infinitesimals of higher orders as compared with those of a lower order.... Newton, through his method of fluxions, has since rendered the calculus more analytical, he also simplified and generalized the method by the invention of his binomial theorem. Leibnitz has enriched the differential calculus by a very happy notation.—Laplace.
Lés Intégrales Définies, etc.; Oeuvres, t. 12 (Paris, 1898), p. 359.
[1903]. Professor Peacock’s Algebra, and Mr. Whewell’s Doctrine of Limits should be studied by every one who desires to comprehend the evidence of mathematical truths, and the meaning of the obscure processes of the calculus; while, even after mastering these treatises, the student will have much to learn on the subject from M. Comte, of whose admirable work one of the most admirable portions is that in which he may truly be said to have created the philosophy of the higher mathematics.—Mill, J. S.
System of Logic, Bk. 3, chap. 24, sect. 6.