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CONTENTS Preface viii Acknowledgments x Introduction xii 1. Ghiyth al-D+n Jamsh+d Mas kd al-Ksh+ (ca. 1380-1429): Accurate Decimal Approximations 1 Early Astronomical Writings 2 Determining the Value of À 5 Roots, Decimals, and Domes 8 Estimating EMBED Equation.3 11 Minor Works 13 Conclusion 14 2. François Viète (1540-1603): Father of Modern Algebra 16 Lawyer, Tutor, Government Official, and Code-Breaker 16 Early Writings on Mathematics and Science 17 Modern Algebra Introduced as the Analytic Art 19 Theory of Equations Provides Diverse Methods of Solution 23 Further Advances in Geometry, Trigonometry, and Algebra 25 Conclusion 29 3. John Napier (1550-1617): Coinventor of Logarithms 32 Inventor and Theologian 32 Rumored to Be a Magician 34 Napier¿s Bones Aid in Multiplication 36 Logarithms Simplify Computation 38 Logarithms Receive International Acclaim 40 Additional Mathematical Contributions 42 Conclusion 43 4. Pierre de Fermat (1601-1665): Father of Modern Number Theory 47 Professional Life Leaves Time for Mathematical Investigations 47 Origins of Analytic Geometry 49 Essential Ideas in Calculus 51 Fundamentals of the Theory of Probability 54 Questions about Primes and Divisibility Define Modern Number Theory 55 Writing Numbers as Sums of Powers 57 Conclusion 60 5. Blaise Pascal (1623-1662): Coinventor of Probability Theory 63 Discoveries in Projective Geometry 63 Calculating Machine Performs Addition and Subtraction 65 Experiments on Vacuums and Air Pressure 66 Foundations of Probability Theory and the Arithmetic Triangle 68 Study of the Cycloid Reinvigorates Pascal¿s Interest in Mathematics 70 Conclusion 73 6. Sir Isaac Newton (1642-1727): Calculus, Optics, and Gravity 76 Education and Early Life 76 Infinite Series and the General Binomial Theorem 78 Method of Fluxions Introduces the Formal Theory of Calculus 80 Additional Mathematical Treatises 83 A New Theory of Light 85 Laws of Motion and the Principle of Universal Gravitation 87 Activities beyond Mathematics and Physics 90 Conclusion 91 7. Gottfried Leibniz (1646-1716): Coinventor of Calculus 94 Family and Education 94 Service to Royal Patrons 95 General Theory of Calculus 98 Additional Mathematical Discoveries 102 Philosophy, Dynamics, and Theology 105 Conclusion 106 8. Leonhard Euler (1707-1783): Leading Mathematician of the 18th Century 109 Student Years, 1707-1726 109 Early Years at St. Petersburg Academy, 1727-1741 111 Middle Years at Berlin Academy, 1741-1766 116 Return to St. Petersburg Academy, 1766-1783 119 Conclusion 121 9. Maria Agnesi (1718-1799): Mathematical Linguist 124 Early Family Life 124 Instituzioni analitiche (Analytical Institutions) 126 Reactions to the Book 128 ¿The Witch of Agnesi¿ 130 Second Career after Mathematics 131 Conclusion 133 10. Benjamin Banneker (1731-1806): Early African-American Scientist 136 Tobacco Farmer 136 Wooden Clock 137 Diverse Interests 138 Astronomer 139 Surveying the District of Columbia 141 1792 Almanac 143 Professional Almanac-Maker 145 Honors and Memorials 147 Conclusion 149 Glossary 151 Further Reading 164 Associations 171 Index 172

Library of Congress Subject Headings for this publication:

Mathematicians -- Biography.

Mathematics, Medieval.