The Ambitious Horse - Ancient Chinese Mathematics Problems

Lawrence Swienciki

Key Curriculum | 2000 | 135 páginas | pdf | 7,94 Mb

online: math.utep.edu


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• Numbers and Arithmetic includes subjects such as Chinese writing; The Calculating Rods of Ancient China: and ancient Chinese multiplication.

• Geometry and Dissection problems includes subjects such as tangrams, the Measure of Heaven and Ancient Chinese Philosophy.

• Algebra Integrated with Geometry includes subjects such as Square Roots; Quadratic Equations; and mathematical treats such as the "Pillar of Delightful Contemplation", the "Exalted Treasure of Jade" and the "Precious Golden Rope".

On the one hand this book is far beyond what many 7th and 8th grader students are capable of. On the other hand, it is so interesting and so well done that it might just be that this is the book that helps transforms your child from a grudging math student to an enthusiastic one!

Filled with stories, puzzles and plenty of hands-on problems, this book is a treasure. It is divided into three sections:

Answers and solutions included.

Note: The problems get more difficult as the book progresses and so can be used for several years. Suitable for a very math-able 7th grader, a solid 8th grader and to enthuse and inspire high school students

Mathematics and Measurement

 Oswald Ashton Wentworth Dilke

University of California Press | 1987 | 66 páginas

online: google books

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This fully illustrated book outlines the ancient systems of mathematics and measurement and describes how they were used in mapping, surveying, telling time, trade and commerce, as well as in leisure pursuits such as games and puzzles, and in the occult.

Contents
The Background 
2 Numbering by Letters 
1 Mathematical Education in the Greek World 
4. Measurement
5 Mathematics (or the Surveyor and Architect)
6 Mapping and the Concept of Scale 
7 Telling the Time
8. Calculatioos for Trade and Commerce
9. Mathematics in Leisure Pursuits and the Occult 
10 The Sequel 
Bibliography 62
Index 

Diophantos of Alexandria: A Study in the History of Greek Algebra

Thomas Little Heath

Cambridge, University press | 1985 | 298 páginas

online: ualberta.ca
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The Greek mathematician Diophantos of Alexandria lived during the third century CE. Apart from his age (he reached eighty-four), very little else is known about his life. Even the exact form of his name is uncertain, and only a few incomplete manuscripts of his greatest work, Arithmetica, have survived. In this impressive scholarly investigation, first published in 1885, Thomas Little Heath (1861-1940) meticulously presents what can be gleaned from Greek, Latin and Arabic sources, and guides the reader through the algebraist's idiosyncratic style of mathematics, discussing his notation and originality. This was the first thorough survey of Diophantos' work to appear in English. Also reissued in this series are Heath's two-volume History of Greek Mathematics, his treatment of Greek astronomy through the work of Aristarchus of Samos, and his edition in modern notation of the Treatise on Conic Sections by Apollonius of Perga.

A history of astronomy

Walter William Bryant

London Methuen 1907

online: archive.org

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A History of Astronomy, first published in 1907, offers a comprehensive introduction to the steady development of the science since its inception in the ancient world up to the momentous progress of the nineteenth century. It includes biographical material relating to the most famous names in the study of astronomy – Copernicus, Galileo, Newton, Herschel – and their contributions, clear and accessible discussions of key discoveries, as well as detailing the incremental steps in technology with which many of the turning points in astronomy were intimately bound up.

CONTENTS
CHAP. PAGE
I. EARLY NOTIONS
II. THE EASTERN NATIONS OF ANTIQUITY 8
III. THE GREEKS 14
IV. THE ARABS 25
V. THE REVIVAL-COPERNICUS-TYCHO BRAHE 28
VI. KEPLER-GALl LEO 39
'VII. NEWTON 47
VIII. NEWTON'S SUCCESSORS: LAPLACE 53
IX. FLAMSTEED-HALLEy-BRADLEy-HERSCHEL 63
X. THE EARLY NINETEENTH CENTURy-NEPTUNE 73
XI. HERSCHEL-BESSEL-STRUVE • 83
XII. COMETS • 96
XIII. THE SUN-EcLIPSES-PARALLAX 103
XIV. GENERAL ASTRONOMY AND CELESTIAL MECHANICS 118
XV. OBSERVATORIES AND INSTRUMENTS • 132
XVI. ADJUSTMENT OF OBSERVATIONS. PERSONAL ERRORS 141
XVII. THE SUN 146
XVIII. SOLAR SPECTROSCOPY 159
XIX. SOLAR ECLIPSES-SPECTROSCOPY 169
XX. THE MOON 183
XXI. THE EARTH 192
XXII. THE INTERIOR PLANETS 201
XXIII. MARS 209
XXIV. MINOR PLANETS 219
XXV. THE MAJOR PLANETS 226
XXVI. THE SOLAR SYSTEM • 24I
XXVII. COMETS, METEORS, ZODIACAL LIGHT 247
XXVIII. THE STARS-CATALOGUES-PROPER MOTION-PARALLAX-MAGNITUDE 27I
XXIX. DOUBLE STARS 292
XXX. VARIABLE STARS 303
XXXI. CLUSTERS-NEBULIE-MILKY WAY. 318
XXXII. STELLAR SPECTROSCOPY 327
XXXIII. CONCLUSION • 340

Mathematics in Western Culture

Morris Kline

Oxford University Press | 1964 | 512 páginas |

online : archive.org

This book gives a remarkably fine account of the influences mathematics has exerted on the development of philosophy, the physical sciences, religion, and the arts in Western life.

Table of Contents
I Introduction. True and False Conceptions, 3
II The Rule of Thumb in Mathematics, 13
III The Birth of the Mathematical Spirit, 24
IV The Elements oi Euclid, 40
V Placing a Yardstick to the Stars, 60
VI Nature Acquires Reason, 74
VII Interlude, 89
VIII Renewal of the Mathematical Spirit, 99
IX The Harmony of the World, no
X Painting arid Perspective, 126
XI Science Born of Art: Projective Geometry, 144
XII A Discourse on Method, 159
XIII The Quantitative Approach to Nature, 182
XIV The Deduction of Universal Laws, 196
XV Grasping the Fleeting Instant: The Calculus, 214
XVI The Newtonian Influence: Science and Philosophy, 234
XVII The Newtonian Influence: Religion, 257
XVIII The Newtonian Influence: Literature and Aesthetics, 272
XIX The Sine of G Major, 287
XX Mastery of the Ether Waves, 304
XXI The Science of Human Nature, 322
XXII The Mathematical Theory of Ignorance: The Statistical Approach
to the Study of Man, 340
XXIII Prediction and Probability, 359
XXIV Our Disorderly Universe: The Statistical View of Nature, 376
XXV The Paradoxes of the Infinite, 395
XXVI New Geometries, New Worlds, 410
XXVII The Theory of Relativity, 432
XXVIII Mathematics: Method and Art, 453

A History of Mathematics

Carl B. Boyer

 John Wiley & Sons Inc; International Ed edition | 1968 | 738 páginas

online: archive.org

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Contents

Chapter I. Primitive Origins 

Chapter II. Egypt 

Chapter III. Mesopotamia 

Chapter IV. Ionia and the Pythagoreans

Chapter V. The Heroic Age

Chapter VI. The Age of Plato and Aristotle 

Chapter VII. Euclid of Alexandria

Chapter VIII. Archimedes of Syracuse

Chapter IX. Apollonius of Perga

Chapter X. Greek Trigonometry and Mensuration

Chapter XI. Revival and Decline of Greek Mathematics

Chapter XII. China and India

Chapter XIII. The Arabic Hegemony

Chapter XIV. Europe in the Middle Ages

Chapter XV. The Renaissance

Chapter XVI. Prelude to Modern Mathematics

Chapter XVII. The Time of Fermat and Descartes

Chapter XVIII. A Transitional Period

Chapter XIX. Newton and Leibniz 

Chapter XX. The Bernoulli Era 

Chapter XXI. The Age of Euler

Chapter XXII. Mathematicians of the French Revolution

Chapter XXIII. The Time of Gauss and Cauchy

Chapter XXIV. The Heroic Age in Geometry

Chapter XXV. The Arithmetization of Analysis

Chapter XXVI. The Rise of Abstract Algebra

Chapter XXVII. Aspects of the Twentieth Century

General Bibliography 679

Appendix: Chronological Table 683

Index 697

The exact sciences in antiquity

Otto Neugebauer

Copenhagen | 1957 - 2.ª edição

online: hathitrust.org

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Based on a series of lectures delivered at Cornell University in the fall of 1949, and since revised, this is the standard non-technical coverage of Egyptian and Babylonian mathematics and astronomy, and their transmission to the Hellenistic world. Entirely modern in its data and conclusions, it reveals the surprising sophistication of certain areas of early science, particularly Babylonian mathematics.
After a discussion of the number systems used in the ancient Near East (contrasting the Egyptian method of additive computations with unit fractions and Babylonian place values), Dr. Neugebauer covers Babylonian tables for numerical computation, approximations of the square root of 2 (with implications that the Pythagorean Theorem was known more than a thousand years before Pythagoras), Pythagorean numbers, quadratic equations with two unknowns, special cases of logarithms and various other algebraic and geometric cases. Babylonian strength in algebraic and numerical work reveals a level of mathematical development in many aspects comparable to the mathematics of the early Renaissance in Europe. This is in contrast to the relatively primitive Egyptian mathematics. In the realm of astronomy, too, Dr. Neugebauer describes an unexpected sophistication, which is interpreted less as the result of millennia of observations (as used to be the interpretation) than as a competent mathematical apparatus. The transmission of this early science and its further development in Hellenistic times is also described. An Appendix discusses certain aspects of Greek astronomy and the indebtedness of the Copernican system to Ptolemaic and Islamic methods.
Dr. Neugebauer has long enjoyed an international reputation as one of the foremost workers in the area of premodern science. Many of his discoveries have revolutionized earlier understandings. In this volume he presents a non-technical survey, with much material unique on this level, which can be read with great profit by all interested in the history of science or history of culture. 14 plates. 52 figures.

Famous geometrical theorems and problems, with their history

William Whitehead Rupert

Boston, D.C. Heath & Co. | 1900

online: 
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The author, having derived much pleasure and inspiration from the brief historical notes in some of the mathematical text-books that he studied when a student in college, has thought that, by giving the history of a few of the most celebrated geometrical theorems and problems, he might place a light in the window which may throw a cheerful ray adown the long and sometimes dusty pathway that leads to geometrical truth. In the preparation of this little book most valuable assistance has been derived from Florian Cajori sHistory of Mathematics, James Gows History of Greek Mathematics, and G, J. Allmans Greek Geometry from Thales to Euclid, It is, however, toW. W.Rourse Balls reniarkably interesting Short History of Mathematics that Famous Geometrical Theorems and Problems owes the largest debt. To Professor A, D. Eisenhower, Principal of the Norristown High School, George Q.Sheppard, Professor of Mathematics, Hill School, Pottstown, Pa., Dr. George M.Philips, Principal West Chester State Normal School, and Daniel Carhart, Ce., Dean and Professor of Civil Engineering, Western University of Pennsylvania, who have read this book in manuscript, the author is indebted for valuable, suggestions and many kind words of encouragement.

Ancient Egyptian Mathematics

Ancient Egyptian Science, A Source Book.
Volume Three: Ancient Egyptian MathematicsMarshall Clagett

DIANE Publishing | 1999 | 462 páginas

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Descrição: This volume continues Marshall Clagett's studies of the various aspects of the science of Ancient Egypt. The volume gives a discourse on the nature and accomplishments of Egyptian mathematics and also informs the reader as to how our knowledge of Egyptian mathematics has grown since the publication of the Rhind Mathematical Papyrus toward the end of the 19th century. The author quotes and discusses interpretations of such authors as Eisenlohr, Griffith, Hultsch, Peet, Struce, Neugebauer, Chace, Glanville, van der Waerden, Bruins, Gillings, and others. He also also considers studies of more recent authors such as Couchoud, Caveing, and Guillemot.

Ancient Egyptian Science: Calendars, clocks, and astronomy

Ancient Egyptian Science: Calendars, clocks, and astronomy, Volume II
Marshall Clagett

DIANE Publishing | 1995 | 575 páginas

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Descrição: This volume is part of Marshall Clagett's three-volume study of the various aspects of science of Ancient Egypt. Volume Two covers calendars, clocks, and astonomical monuments. Within each area of treatment there is a fair chronology evident as benefits a historical work covering three millenia of activity. Includes more than 100 illustrations of documents and scientific objects.

Non-Euclidean Geometry: A Critical And Historical Study Of Its Development

Roberto Bonola

Chicago Open Court Pub. Co | 1912

online: archive.org

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Examines various attempts to prove Euclid's parallel postulate — by the Greeks, Arabs and Renaissance mathematicians. Ranging through the 17th, 18th, and 19th centuries, it considers forerunners and founders such as Saccheri, Lambert, Legendre, W. Bolyai, Gauss, Schweikart, Taurinus, J. Bolyai and Lobachewsky. Includes 181 diagrams.

Table of Contents

Chapter I. The Attempts to prove Euclid's Parallel Postulate.

1-5. The Greek Geometers and the Parallel Postulate

6. The Arabs and the Parallel Postulate

7-10. The Parallel Postulate during the Renaissance and the 17th Century

Chapter II. The Forerunners on Non-Euclidean Geometry.

11-17. GEROLAMO SACCHERI (1667-1733)

18-22. JOHANN HEINRICH LAMBERT (1728-1777)

23-26. The French Geometers towards the End of the 18th Century

27-28. ADRIEN MARIE LEGENDRE (1752-1833)

29. WOLFGANG BOLYAI (1775-1856)

30. FRIEDRICH LUDWIG WACHTER (1792-1817)

30. (bis) BERNHARD FRIEDRICH THIBAUT (1776-1832)

Chapter III. The Founders of Non-Euclidean Geometry.

31-34. KARL FRIEDRICH GAUSS (1777-1855)

35. FERDINAND KARL SCHWEIKART (1780-1859)

36-38. FRANZ ADOLF TAURINUS (1794-1874)

Chapter IV. The Founders of Non-Euclidean Geometry (Cont.).

39-45. NICOLAI IVANOVITSCH LOBATSCHEWSKY (1793-1856)

46-55. JOHANN BOLYAI (1802-1860)

56-58. The Absolute Trigonometry

59. Hypotheses equivalent to Euclid's Postulate

60-65. The Spread of Non-Euclidean Geometry

Chapter V. The Later Development of Non-Euclidean Geometry.

66. Introduction

Differential Geometry and Non-Euclidean Geometry

67-69. Geometry upon a Surface

70-76. Principles of Plane Geometry on the Ideas of RIEMANN

77. Principles of RIEMANN'S Solid Geometry

78. The Work of HELMHOLTZ and the Investigations of LIE

Projective Geometry and Non-Euclidean Geometry

79-83. Subordination of Metrical Geometry to Projective Geometry

84-91. Representation of the Geometry of LOBATSCHEWSKY-BOLYAI on the Euclidean Plane

92. Representation of RIEMANN'S Elliptic Geometry in Euclidean Space

93. Foundation of Geometry upon Descriptive Properties

94. The Impossibility of proving Euclid's Postulate

Appendix I. The Fundamental Principles of Statistics and Euclid's Postulate.

1-3. On the Principle of the Lever

4-8. On the Composition of Forces acting at a Point

9-10. Non-Euclidean Statics

11-12. Deduction of Plane Trigonometry from Statics

Appendix II. CLIFFORD'S Parallels and Surface. Sketch of CLIFFFORD-KLEIN'S Problems.

1-4. CLIFFORD'S Parallels

5-8. CLIFFORD'S Surface

9-11. Sketch of CLIFFORD-KLEIN'S Problem

Appendix III. The Non-Euclidean Parallel Construction and other Allied Constructions.

1-3. The Non-Euclidean Parallel Construction

4. Construction of the Common Perpendicular to two non-intersecting Straight Lines

5. Construction of the Common Parallel to the Straight Lines which bound an Angle

6. Construction of the Straight Line which is perpendicular to one of the lines bounding an acute Angle and Parallel to the other

7. The Absolute and the Parallel Construction

Appendix IV. The Independence of Projective Geometry from Euclid's Postu

1. Statement of the Problem

2. Improper Points and the Complete Projective Plane

3. The Complete Projective Line

4. Combination of Elements

5. Improper Lines

6. Complete Projective Space

7. Indirect Proof of the Independence of Projective Geometry from the Fifth Postulate

8. BELTRAMI'S Direct Proof of this Independence

Appendix V. The Impossibility of proving Euclid's Postulate. An Elementary Demonstration of this Impossibility founded upon the Properties of the System of Circles orthogonal to a Fixed Circle.

1. Introduction

2-7. The System of Circles passing through a Fixed Point

8-12. The System of Circles orthogonal to a Fixed Circle

Index of Authors

The Science of Absolute Space and the Theory of Parallels

A source book in mathematics

David Eugene Smith

New York : McGraw-Hill Book Co. | 1929

online: archive.org

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Vol. 1

Dover Publications Inc. | 1993 | 324 páginas | djvu | 10,87 Mb

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The writings of Newton, Liebniz, Pascal, Riemann, Bernoulli, and others in a comprehensive selection of 125 treatises, articles from the Renaissance to end of the 19th century—most unavailable elsewhere. Grouped in five sections: Number; Algebra; Geometry; Probability; and Calculus, Functions, and Quaternions. Index. 83 illustrations.

Vol. 2

Dover Publications Inc. | 1993 | 418 páginas | djvu | 12,53Mb

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A Long Way from Euclid

Constance Reid

 Thomas Y. Crowell Company | 1834

online: archive.org

Dover Publications | 2004 | 304 páginas

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This lively guide by a prominent historian focuses on the role of Euclid's Elements in mathematical developments of the last 2,000 years. No mathematical background beyond elementary algebra and plane geometry is necessary to appreciate the clear and simple explanations, which are augmented by more than 80 drawings. 1963 edition. 

A short account of the history of mathematics

W. W. Rouse Ball

The Macmillan Company | 1901

online: archive.org

online: gutenberg.org

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This is the classic resource on the history of mathematics providing a deeper understanding of the subject and how it has impacted our culture, all in one essential volume. From the early Greek influences to the middle ages and the renaissance to the end of the 19th-century, trace the fascinating foundation of mathematics as it developed through the ages.

The Copernicus of Antiquity - Aristarchus of Samos

Thomas L. Heath

online: archive.org

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Apollonius of Perga Treatise on Conic Sections 1896

Thomas L. Heath

online: archive.org

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Índice

Introduction: pt. I. The earlier history of conic sections among the Greeks. 1. The discovery of conic sections; Menaechmus. 2. Aristaeus and Euclid. 3. Archimedes. pt. II. Introduction to the conics of Apollonius. 1. The author and his own account of the conics. 2. General characteristics. 3. The methods of Apollonius. 4. The construction of a conic by means of tangents. 5. The three-line and four-line locus. 6. The construction of a conic through five points.-Appendix: Notes on the terminology of Greek geometry.--The conics of Apollonius

The Works of Archimedes

Thomas L. Heath

PDF| 18,45 MB
on-line: archive.org

Diophantus of Alexandria: A Study in the History of Greek Algebra

Second Edition.
Thomas L. Heath
Cambridge, University Press | 1910| 387 páginas | PDF| 39,47 MB

online: archive.org

Robert Of Chester's Latin Translation Of The Algebra Of Al-Khowarizmi

Robert Of Chester's Latin Translation Of The Algebra Of Al-Khowarizmi
Al-Khowarizmi

Kessinger Publishing, LLC | 2009 | 194 páginas | rar - pdf | 4,34 Mb

on-line: archive.org

The History of the Calculus and Its Conceptual Development

Carl B. Boyer

Dover Publications | 1949 | 368 páginas |

online: archive.org

Fluent description of the development of both the integral and differential calculus. Early beginnings in antiquity, Medieval contributions and a century of anticipation lead up to a consideration of Newton and Leibniz, the period of indecison that followed them, and the final rigorous formulation that we know today.