Table of contents for The birth of mathematics : ancient times to 1300 / Michael J. Bradley.

Bibliographic record and links to related information available from the Library of Congress catalog.

Note: Contents data are machine generated based on pre-publication provided by the publisher. Contents may have variations from the printed book or be incomplete or contain other coding.


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CONTENTS
Preface												ix
Acknowledgments										xi
Introduction											xii
1. Thales of Miletus (ca. 625 B.C.E.-ca. 547 B.C.E.): Earliest Proofs of Geometrical Theorems											1
	Early Years										1
	Natural Philosopher									2
	First Proofs of Theorems in Mathematics						3
	Discoveries in Astronomy								5
	Ingenious Solutions to Practical Problems						6
	Legends About Thales								8
	Conclusion										10
	Further Reading									12
2. Pythagoras of Samos (ca. 560 B.C.E.-ca. 480 B.C.E.): Ancient Greek Proves Theorem about Right Triangles									14
	First Student Is Paid To Learn							14
	Pythagorean Society Blends Mysticism with Mathematics				15
	Early Research in Number Theory 							17
	Ratios in Music and Astronomy							19
	Pythagorean Theorem									20
	Irrational Numbers									21
	Five Regular Solids									23
	Conclusion 										25
	Further Reading									26
3. Euclid of Alexandria (ca. 325 B.C.E.-ca. 270 B.C.E.): Geometer Who Organized Mathematics											27
	Professor of Mathematics								27
	Elements 										29	
	Original Results in Elements								31	
	Criticisms of Euclid's Methods							32	
	Parallel Postulate									33
	Euclid's Additional Writings								35
	Conclusion										38
	Further Reading									39
4. Archimedes of Syracuse (ca. 287 B.C.E.-212 B.C.E.): Innovator of Techniques in Geometry											41
	Inventor of Practical Machines 							41
	Approximation of Pi Using Inscribed and Circumscribed Polygons			43	
	Method of Exhaustion to Estimate Areas and Volumes				45
	Creative Problem Solver								48
	Investigations of Large Numbers							51
	Conclusion										53
	Further Reading									55
5. Hypatia of Alexandria (ca. 370-415): First Woman of Mathematics			57
	The "Perfect" Human Being								57
	Commentaries on Classical Mathematics Books 					59	
	Famous Teacher, Philosopher, and Scientist						62	
	Brutally Murdered									63
	Conclusion										64
	Further Reading									66	
6. Aryabhata I (476-550): From Alphabetical Numbers to the Rotation of the Earth	68	
	Aryabhatiya (Aryabhata's treatise)							69
	Arithmetical Methods									70	
	Geometric Techniques								72	
	Tables of Sines									74	
	Algebraic Advances									75	
	Astronomical Theories								76	
	Second Astronomical Treatise							78	
	Conclusion										79		Further Reading									80	
7. Brahmagupta (598-668): Father of Numerical Analysis				81	
	Brahmasphutasiddhanta (Improved astronomical system of Brahma)		82		Arithmetical Innovations								84	
	New Geometrical Techniques								86	
	Algebraic Methods									87	
	Second Astronomical Treatise							90	
	Conclusion										92	
	Further Reading									94	
8. Abu Ja?far Muhammad ibn Musa al-Khwarizmi (ca. 800-ca. 847): Father of 
Algebra 											95
	Early Years										95	
	Text on Algebra									96	
	Text on Arithmetic									100	
	Astronomical Tables									101
	Geographical Work									103
	Minor Works										104	
	Conclusion										105
	Further Reading									406
9. Omar Khayy m (ca. 1048-ca. 1131): Mathematician, Astronomer, Philosopher, 
and Poet											107
	Early Years										107
	Early Writings on Arithmetic, Algebra, and Music					108	
	Geometrical Solutions of Cubic Equations						111	
	Calendar Reform									112	
	Parallel Lines and Ratios								113	
	Philosophical Writings								114	
	Rub iy t (Quatrains)									115
	Conclusion										117
	Further Reading									118
10. Leonardo Fibonacci (ca. 1175-ca. 1250): Hindu-Arabic Numerals in Europe	120	
	Early Years										120	
	Hindu-Arabic Numbering System							121	
	Liber abaci (Book of computation)							123
	Fibonacci Series									125
	Mathematical Tournament								126
	Liber quadratorum (Book of the square)						128
	Other Works										129
	Conclusion										130	
	Further Reading									132	
Glossary											133	
Further Reading										145	
Associations											153	
Index												154													

Library of Congress Subject Headings for this publication:

Mathematicians -- Biography.
Mathematics, Ancient.
Mathematics -- History -- To 1500.