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When first published in 1963, more than two decades after Otto Toeplitz's death, this book presented a radically different approach to the teaching of calculus. In sharp contrast to the methods of his time, Toeplitz did not teach calculus as a static system of techniques and facts to be memorized. Instead, he drew on his knowledge of the history of mathematics and presented calculus as an organic evolution of ideas beginning with the discoveries of Greek scholars, such as Archimedes, Pythagoras, and Euclid, and developing through the centuries in the work of Kepler, Galileo, Fermat, Newton, and Leibniz. Through this unique approach, Toeplitz summarized and elucidated the major mathematical advances that contributed to modern calculus. Reissued for the first time since 1981 and updated with a new foreword, this classic text is experiencing a resurgence of interest among students and teachers of calculus today.