Leibniz’s ﬁrst publication of his calculus, 1684ĥ THE MATHEMATICS OF NATURE: NEWTON’S PRINCIPIA 5.1 Newton’s Principia, Book I 5.1.1 5.1.2 5.1.3 5.1.4 5.1.5 5.1.6 The chronology of Newton’s calculus Newton’s treatise on ﬂuxions and series, 1671 Newton’s ﬁrst publication of his calculus, 1704 1655 Wallis’ use of indivisibles, 1656 Mercator and the rectangular hyperbola, 1668Ī method of cubature Torricelli’s inﬁnite solid, 1644 Viète’s introduction to the analytic art, 1591 Fermat and analytic geometry, 1636 Descartes and analytic geometry, 1637Ĭavalieri’s theory of indivisibles, 1635 Wallis and Hobbes on indivisibles, 1656ģ FORESHADOWINGS OF CALCULUS 3.1 Methods for tangents 3.1.1 3.1.2įermat’s quadrature of higher hyperbolas, early 1640s Brouncker and the rectangular hyperbola, c. Stevin’s decimal fractions, 1585 Napier’s logarithms, 1614 825 adĢ FRESH IDEAS 2.1 Improvements in calculation 2.2 250 bc The Arithmetica of Diophantus, (after 150 ad)Ĭompleting the square, c. 250 bc Euclid’s proof of the inﬁnity of primes, c. 250 bc Archimedes on circle measurement, c. 250 bc Euclid’s construction of proportionals, c.

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