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The European Mathematical Awakening A Journey Through the History of Mathematics from 1000 to 1800



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Dover Publications
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A global survey of the history of mathematics, this collection of 32 articles traces the subject from AD 1000 to 1800. Newly corrected and updated, the highly readable essays by such distinguished educators as Carl Boyer and Morris Kline introduce fascinating studies by Fibonacci, Descartes, Cardano, Kepler, Galileo, Pascal, Newton, Euler, and others. Suitable for readers with no background in math.

Table of Contents

Perspective: The European Mathematical Awakening
Historical Exhibit 1: The Growth of Mathematical Knowledge
1. Counters: Computing if You Can Count to Five
Historical Exhibit 2: Bede's Finger Mathematics
2. Gerbert's Letter to Adelbold
Historical Exhibit 3: The Geometry of Gothic Church Windows
3. The Arithmetic of Medieval Universities
4. The Craft of Nimbryng
Historical Exhibit 4: Algorist versus the Abacist
5. Leonardo Fibonacci
6. Leonardo of Pisa and his Liber quadratorum
7. Some Uses of Graphing before Decartes
8. Adam Riese
9. Tangible Arithmetic: Finger Reckoning and Other Devices
10. The Cardano-Tartaglia Dispute
Historical Exhibit 5: Cardano's Technique for the Solution of a Reduced Cube Equation
11. Complex Numbers: An Example of Recurring Themes in the Development of  Mathematiocs.
12. Robert Recorde's Whetstone of Witte, 1557
13. The Teaching of Arithmetic in England from 1550 until1880 as Influenced by Social Change
14. Tangible Arithmetic: Napier's and Genaille's Rods
15. The Life and Times of Johann Kepler
Historical Exhibit 6: Multiplication Algorithm of the Fifteenth and Sixteenth Centuries
16. Simon Steven and Decimal Fractions
Historical Exhibit 7: Mathematical Considerations on the Trajectory of a Cannon Ball
17. Viete's Use of Decimal Fractions
18. John Napier and His Logarithims
Historical Exhibit 8: The Evolution of Algebraic Symbolism
19. Projective Geometry
20. Pisa, Galileo, Rome
Historical Exhibit 9: Torricelli's Wine Glass
21. Analytic Geometry: The Discovery of Fermat and Descartes
22. The Young Pascal
Historical Exhibit 10: Roberval's Quadrature of the Cycloid
23. Isaac Newton: Man, Myth, Mathematics
Historical Exhibit 11: Newton's Method of Fluxions
24. The Newton-Leibniz Controversy Concerning the Discovery of Calculus
Historical Exhibit 12: Mengoli's Proof for the Divergence of the Harmonic Series
25. The Bernoulli Family
26. The Bernoullis and the Harmonic Series
27. The First Calculus Textbooks
28. The Origin of L'Hopital's Rule
29. Euler, the Master Calculator
30. Gaspard Monge and the Descriptive Geometry
31. Mathematicians of  the French Revolution
32. The Ladies Diary...Circa 1700
Historical Exhibit 13: Women in Mathematics
Epilogue: The Process Continues
Suggested Readings

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