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

Frank J. Swetz

Dover Publications | 2013 - Reprint edition | 224 páginas | rar - epub | 18,5 Mb

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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. Reprint of selected material from From Five Fingers to Infinity: A Journey Through the History of Mathematics, Open Court Publishing Company, Chicago, 1994.

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
VERA SANFORD
HISTORICAL EXHIBIT 2 Bede’s Finger Mathematics
2.Gerbert’s Letter to Adelbold
G. A. MILLER
HISTORICAL EXHIBIT 3 The Geometry of Gothic Church Windows
3.The Arithmetic of Medieval Universities
DOROTHY V. SCHRADER
4.The Craft of Nombryng
E. R. SLEIGHT
5.Leonardo Fibonacci
CHARLES KING
6.Leonardo of Pisa and his Liber quadratorum
R. B. McCLENON
7.Some Uses of Graphing before Descartes
THOMAS M. SMITH
8.Adam Riese
DOROTHY I. CARPENTER
9.Tangible Arithmetic: Finger Reckoning and Other Devices
PHILLIP S. JONES
10.The Cardano-Tartaglia Dispute
RICHARD W. FELDMANN
HISTORICAL EXHIBIT 5 Cardano’s Technique for the Solution of a Reduced Cubic Equation
11.Complex Numbers: An Example of Recurring Themes in the Development of Mathematics—I
PHILLIP S.JONES
12.Robert Recorde’s Whetstone of Witte, 1557
VERA SANFORD
13.The Teaching of Arithmetic in England from 1550 until 1800 as Influenced by Social Change
JAMES KING BIDWELL
14.Tangible Arithmetic: Napier’s and Genaille’s Rods
ILLIP S. JONES
15.The Life and Times of Johann Kepler
BERNARD H. TUCK
HISTORICAL EXHIBIT 6 Multiplication Algorithms of the Fifteenth and Sixteenth Centuries
16.Simon Steven and the Decimal Fractions
D. J. STRUIK
HISTORICAL EXHIBIT 7 Mathematical Considerations on the Trajectory of a Cannon Ball
17.Viète’s Use of Decimal Fractions
CARL B. BOYER
18.John Napier and His Logarithms
C. B. READ
HISTORICAL EXHIBIT 8 The Evolution of Algebraic Symbolism
19.Projective Geometry
MORRIS KLINE
20.Pisa, Galileo, Rome
EDMOND R. KIELY
HISTORICAL EXHIBIT 9 Torricelli’s Wine Glass
21.Analytic Geometry: The Discovery of Fermat and Descartes
CARL B. BOYER
22.The Young Pascal
HAROLD MAILE BACON
HISTORICAL EXHIBIT 10 Roberval’s Quadrature of the Cycloid
23.Isaac Newton: Man, Myth, and Mathematics
V. FREDERICK RICKEY
HISTORICAL EXHIBIT 11 Newton’s Method of Fluxions
24.The Newton-Leibniz Controversy Concerning the Discovery of the Calculus
DOROTHY V. SCHRADER
HISTORICAL EXHIBIT 12 Mengoli’s Proof for the Divergence of the Harmonic Series
25.The Bernoulli Family
HOWARD EVES
26.The Bernoullis and the Harmonic Series
WILLIAM DUNHAM
27.The First Calculus Textbooks
CARL B. BOYER
28.The Origin of L’Hopital’s Rule
D. J. STRUIK
29.Euler, the Master Calculator
JERRY D. TAYLOR
0.Gaspard Monge and Descriptive Geometry
LEO GAFNEY
31.Mathematicians of the French Revolution
CARL B. BOYER
32.The Ladies Diary… Circa 1700
TERI PERL
HISTORICAL EXHIBIT 13 Women in Mathematics
Epilogue: The Process Continues
Suggested Readings

Revisão: MAA