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

**by**Swetz, Frank J.

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### 9780486498058

0486498050

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4/17/2013

Dover Publications

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## Summary

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

Preface

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

Index