By Bloch S. (ed.)
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Additional info for Algebraic Geometry - Bowdoin 1985, Part 1
This finally yields the power-series expansion of the sine function: sinx = x − x 3 / 3! + x 5 / 5! − … . It takes one’s breath away! This formal, algebraic style of analysis, used so brilliantly by Euler and practiced by most eighteenth-century mathematicians, is astonishing. 5 • A Look Ahead: Foundations 45 5 power series. Mathematicians put their trust in such broad principles because for the most part they yielded correct results. 5 A Look Ahead: Foundations Mathematicians of the seventeenth and eighteenth centuries realized that the subject they were creating was not on firm ground.
Viii], entitled The Book on Games of Chance . His most influential work, The Great Art, dealing with the solution of the cubic and quartic equations by radicals, was a fundamental contribution to mathematics (see 7 Chapter 2). The Division Problem presents a much greater challenge. Among the first to introduce it was the Italian mathematician Luca Pacioli, in his 1494 book Everything About Arithmetic, Geometry, and Proportions, better known as Suma. 489]: »» Two players are playing a fair game [the players are equally capable] that was to continue until one player had won six rounds.
Math. Mag. 56, 307–314 (1983) References 47 5 Further Reading 12. : Cavalieri’s method of indivisibles. Arch. Hist. Exact Sci. 31, 291–367 (1985) 13. : The Origins of the Infi nitesimal Calculus. : Differentials, higher-order differentials and the derivative in the Leibnizian calculus. Arch. Hist. Exact Sci. 14, 1–90 (1974) 15. : Cavalieri, limits and discarded infinitesimals. Scr. Math. 8, 79–91 (1941) 16. : The History of the Calculus and Its Conceptual Development. Dover, New York (1959) 17.