The History Of Mathematics

710 Pages·70.976 MB·English

by  David M. Burton

The
History of
MATHEMATICS
AN INTRODUCTION
SECOND EDITION
David M. Burton
Some Important Historical Names, Dates* and Events
Mathematical General
Early Beginnings (Before the 6th Century B.C.)
B.C. 30000 Notched wolf bone B.C. 3300 Menes unites Egypt
8000 Ishango bone 2600 Great Pyramid at Gizeh
2500 Table tablets from Nippur 2100 Code of Hammurabi
1900 Plimpton 322 500 Phoenician alphabet
1
1850 Moscow Papyrus 200 Trojan War
1
1650 Rhind Papyrus 700 Homer: The Odyssey
Classical Period (6th Century B.C. to 5th Century)
B.C. 622-547 Thales of Miletus B.C. 558-486 Darius the Great
585-501 Pythagoras of Samos 485-430 Herodotus
ca. 470 Theodorus of Cyrene 480 Battle of Thermopylae
460-380 Hippocrates of Chios 469-399 Socrates
ca. 420 Hippias of Elis 431 Peloponnesian War
408-355 Eudoxus of Cnidos 388 Plato founds Academy
323-285 Euclid 356-323 Alexander the Great
287-212 Archimedes ca. 370 Eudemus of Rhodes
262 -190 Apollonius of Perga 331 Foundation of Alexandria
ca. 240 Nicomedes 213 Books burned in China
ca. 230 Eratosthenes of Cyrene 212 Fall of Syracuse to Romans
A.D. ca. 75 Heron of Alexandria 195 Rosetta Stone engraved
ca. 100 Nicomachus of Gerasa 106 Cicero
85 160 Claudius Ptolemy 44 Assassination of Caesar
ca. 250 Diophantus 27 Beginning of Roman Empire
ca. 260 Liu Hui AD 100 Paper made in China
ca. 300 Pappus of Alexandria 272 337 Constantine the Great
365 395 Theon of Alexandria 286 Division of the Empire
d. 415 Hypatia 324 Constantinople founded
410 4X> Proclus 455 Vandals sack Rome
*Most dates before 600 B.< are only approximate.
'1293
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Mathematical General
Medieval and Renaissance Periods (6th Century to 16th Century)
ca. 475-524 Boethius 636 Death of the Prophet
Mohammed
ca. 476-550 Aryabhata 641 Library at Alexandria burned
ca. 625 Brahmagupta 732 Arabs defeated at Tours
ca. 826-901 Thabit-ibn-Korra 787 Start of Viking Invasions
735-804 Alcuin of York 800 Charlemagne crowned
Emperor
ca. 850-930 Abu Kamil ca. 1000 Leif Eriksson sails to
America
ca. 1050-1130 Omar Khayyam 1066 Battle of Hastings
b. 1114 Bhaskara 1096-1099 The First Crusade
1114-1187 Gerard of Cremona 1200 University of Paris chartered
ca. 1120 Adelhard of Bath 1209 Cambridge University
founded
ca. 1175-1250 Leonardo of Pisa 1215 Magna Carta signed
1436-1476 Regiomontanus 1258 Oxford University founded
1445-1514 Luca Pacioli 1271 -1295 Travels of Marco Polo
1473-1543 Nicolas Copernicus 1293 Paper produced in Bologna
1494-1575 Francesco Maurolico 1337--1453 Hundred Years' War
1495-1552 Peter Apian 1348 Black Death in Europe
1500-1557 Niccolo Tartaglia 1440 Invention of Printing
1501-1576 Girolamo Cardan 1447 Founding of Vatican Library
1510-1558 Robert Recorde 1451 Death of Joan of Arc
1522-1565 Ludovico Ferrari 1453 Turks capture Constantinople
1526-1572 Raphael Bombelli 1472--1514 Leonardo da Vinci
1540-1603 Francois Vieta 1478 Treviso Arithmetic
1546-1601 Tycho Brahe 1492 Columbus reaches West
Indies
1548-1626 Pietro Cataldi 1513 Balboa discovers the Pacific
1550-1617 John Napier 1517 Luther's 95 Theses
1564-1642 Galileo Galilei 1564-1616 William Shakespeare
1571-1630 Johannes Kepler 1588 Defeat of Spanish Armada

The
History
of
Mathematics
An
Introduction
Second Edition
David M. Burton
Universityof New Hampshire
ffuD
Wm.C.Brown Publishers
BookTeam
Editor Earl McPeek
Developmental Editor Theresa Gruiz
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M
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Copyright© 1985 by Allyn and Bacon. Inc
Copyright© 1988. 1991 by Wm. C. Brown Publishers. All rights
reserved
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ISBN 697 11196 2
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10
All these were honored in their generations, and were the glory oftheir times.
There be ofthem, that have left a name behind them, that their praises might be reported.
And some there be, which have no memorial; who are perished, as though they had never been; and
are become as though they had never been born; and their children after them.
Ecclesiasticus 44:7-9

Contents
Preface, Chapter
ix 3
The Beginnings of Greek
Chapter
1 Mathematics, 83
Early Number Systems and
Symbols, 3.1 The Geometrical Discoveries of
1
Thales, 83
1.1 Primitive Counting, 1
3.2 Pythagorean Mathematics, 90
1.2 Number Recording of the Egyptians
3.3 The Pythagorean Problem, 105
and Greeks, 7
1.3 Number Recording of the 3.4 Three Construction Problems of
Antiquity, 120
Babylonians, 19
3.5 The Quadratrix of Hippias, 130
Chapter
2
Mathematics in Early Chapter 4
Civilizations, 32
The First Alexandrian School:
Euclid, 140
2.1 The Rhind Papyrus, 32
4.1 Euclid and the Elements, 140
2.2 Egyptian Arithmetic, 36
4.2 Euclidean Geometry, 144
2.3 Three Problems from the Rhind
Papyrus, 45
4.3 The Quadratic Equation, 165
2.4 Egyptian Geometry, 52
4.4 Euclid's Number Theory, 180
2.5 Babylonian Mathematics, 62
4.5 Eratosthenes, the Wise Man of
Alexandria, 193
2.6 Plimpton 322, 73
4.6 Archimedes, 204
Contents
VI
Chapter Chapter
5 8
The Second Alexandrian School: The Mechanical World: Descartes
Diophantus, 221 and Newton, 310
5.1 The Decline of Alexandrian 8.1 The Dawn of Modern
Mathematics, 221 Mathematics, 310
5.2 The Arithmetica, 226 8.2 Descartes: The Discours de la
Methode, 326
5.3 Diophantine Equations, 231
8.3 Newton: The Principia
5.4 The Later Commentators, 240 Mathematica, 343
Chapter 8.4 Gottfried Leibniz: The Calculus
6
Controversy, 366
The First Awakening:
Fibonacci, 247
Chapter
9
6.1 The Decline and Revival of The Development of Probability
Learning, 247 theory: pascal, bernoulli, and
Laplace, 394
6.2 The Liber Abaci and Liber
Quadratorum, 256 9.1 The Origins of Probability
Theory, 394
6.3 The Fibonacci Sequence, 263
9.2 Pascal's Arithmetic Triangle, 411
6.4 Fibonacci and the Pythagorean
Problem, 270 9.3 The Bernoullis and Laplace, 424
Chapter Chapter
7 10
The Cubk Controversy: Cardan The Renaissance of Number
andTartaglia. 276 Theory: Fermat, Euler, and
Gauss, 449
7.1 Europe in the Fourteenth and
Fifteenth Centuries, 276 10.1 Marin Mersenne and the Search for
Perfect Numbers, 449
7.2 The Battle of the Scholars, 287
10.2 From Fermat to Euler, 464
7.3 Cardan's Ars Magna, 294
10.3 The Prince of Mathematicians: Karl
7.4 Ferrari's Solution of the Quartic Friedrich Gauss, 488
Kquation, 302