"The depictions of Newton and Leibniz in today's textbooks gain deeper meaning when one compares them to texts written closer to the episode in question. To discover how the celebrities appear in 17th- and 18th-century mathematical texts, I examined 17 texts from 1694 to 1768, published in Holland, England and France. I looked mostly at prefaces, though in some cases I looked more extensively at the body of the text. In the first text, which was published in two subsequent editions in the 1690s by Niewentijdt in Holland, Leibniz is generally mentioned in the preface more frequently than Newton. L'Hôpital--who is familiar to calculus students for the eponymous rule for finding the limit of a quotient of two functions by differentiation--was tutored directly by Johann Bernoulli. His 1696 text (not surprisingly) also clearly favors Leibniz over Newton, where he mentioned Leibniz 6 times, Newton only once:"'I must yet give due recognition to the learned Mr. Newton, who has been recognized [in this capacity] by Mr. Leibniz himself: for he has also found something similar to differential calculus...But Mr. Leibniz characteristic [triangle] renders his [calculus] much easier and more expedient (pp. 12-13).'"
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"In the seventeenth century came Newton and Leibniz, the two founders of infinitesimal calculus. Although their results were the same, their motivations and interpretations were quite different. This is a very natural occurrence in mathematics: the same ideas are treated in a different manner because they are used for different purposes. Leibniz developed his calculus based on differential quantities, their ratios (derivatives), and their infinite sums (integrals). ..."
Nonstandard Analysis and the Hyperreals
This is immaterial. Anyone who suggests that Newton is unnecessary is a simple fool. His contribution to science is greater than any other.
"The Principia is pre-eminent above any other production of human genius." Laplace