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Other titles in the Dover Books on Mathematics series:
A Short Account of the History of Mathematicsby Walter W. Rouse Ball
Synopses & Reviews
This text remains one of the clearest, most authoritative and most accurate works in the field. The standard history treats hundreds of figures and schools instrumental in the development of mathematics, from the Phoenicians to such 19th-century giants as Grassman, Galois, and Riemann.
Exceptionally clear, authoritative survey--from the Egyptians and Phoenicians through 19th-century figures such as Grassman, Galois, Riemann. Fourth edition.
This standard text treats hundreds of figures and schools instrumental in the development of mathematics, from the Phoenicians to such 19th-century giants as Grassman, Galois, and Riemann.
Table of Contents
TABLE OF CONTENTS
CHAPTER I. EGYPTIAN AND PHOENICIAN MATHEMATICS.
The history of mathematics begins with that of the Ionian Greeks
Greek indebtedness to Egyptians and Phoenicians
Knowledge of the science of numbers possessed by the Phoenicians
Knowledge of the science of numbers possessed by the Egyptians
Knowledge of the science of geometry possessed by Egyptians
Note on ignorance of mathematics shewn by the Chinese
First Period. Mathematics under Greek Influence.
CHAPTER II. THE IONIAN AND PYTHAGOREAN SCHOOLS.
The Ionian School
"THALES, 640-550 B.C."
His geometrical discoveries
His astronomical teaching
Anaximander. Anaximenes. Mamercus. Mandryatus
The Pythagorean School
"PYTHAGORAS, 569-500 B.C."
The Pythagorean teaching
The Pythagorean geometry
The Pythagorean theory of numbers
Epicharmus. Hippasus. Phiololaus. Archippus. Lysis
"ARCHYTAS, circ. 400 B.C."
His solution of the duplication of a cube
Theodorus. Timaeus. Bryso
Other Greek Mathematical Schools in the Fifth Century B.C.
Oenopides of Chios
Zeno of Elea. Democritus of Abdera
CHAPTER III. THE SCHOOLS OF ATHENS AND CYZICUS.
Mathematical teachers at Athens prior to 420 B.C.
Anaxogoras. The Sophists. Hippias (The quadratrix)
Three problems in which these schools were specially interested
"HIPPOCRATES of Chios, circ. 420 B.C."
Letters used to describe geometrical diagrams
Introduction in geometry of the method of reduction
The quadrature of certain lunes
The problem of the duplication of the cube
"Plato, 429-348 B.C."
Introduction in geometry of the method of analysis
Theorem on the duplication of the cube
"EUDOXUS, 408-355 B.C."
Theorems on the golden section
Introduction of the method of exhaustions
Pupils of Plato and Eudoxus
"MENAECHMUS, circ. 340 B.C."
Discussion of the conic selections
His two solutions of the duplication of the cube
"Aristotle, 384-322 B.C."
Questions on mechanics. Letters used to indicate magnitudes
CHAPTER IV. THE FIRST ALEXANDRIAN SCHOOL
Foundation of Alexandria
The Third Century before Christ
"EUCLID, circ. 330-275 B.C."
The Elements as a text-book of geometry
The Elements as a text-book of the theory of numbers
Euclid's other works
"Aristarchus, circ. 310-250 B.C."
Method of determining the distance of the sun
Conon. Dositheus. Zeuxippus. Nicoteles
"ARCHIMEDES, 287-212 B.C."
His works on plane geometry
His works on geometry of three dimensions
"His two papers on arithmetic, and the "cattle problem"
His works on the statistics of solids and fluids
The principles of geometry and that of Archimedes
"APOLLONIUS, circ. 260-200 B.C."
His conic sections
His other works
His solution of the duplication of a cube
Contrast between his geometry and that of Archimedes
"Erathosthenes, 275-194 B.C."
The Sieve of Eratosthenes
The Second Century before Christ
"Hypsicles (Euclid, book XIV). Nicomedes. Diocles"
"HIPPARCHUS, circ. 130 B.C."
Foundation of scientific astronomy
Foundation of trigonometry
"HERO of Alexandria, circ. 125 B.C."
Foundation of scientific engineering and of land-surveying
Area of a triangle determined in terms of its sides
Features of Hero's works
The First Century before Christ
End of the First Alexandrian School
Egypt constituted a Roman province
CHAPTER V. THE SECOND ALEXANDRIAN SCHOOL
The First Century after Christ
Introduction of the arithmetic current in medieval Europe
The Second Century after Christ
Theon of Smyran. Thymaridas
"PTOLEMY, died in 168"
The Third Century after Christ
"Pappus, circ. 280"
"The Suagwg?, a synopsis of Greek mathematics"
The Fourth Century after Christ
Metrodorus. Elementary problems in arithmetic and algebra
Three stages in the development of algebra
"DIOPHANTUS, circ. 320 (?)"
Introduction of syncopated algebra in his Arithmetic
"The notation, methods, and subject-matter of the work"
Subsequent neglect of his discoveries
Theon of Alexandria. Hypatia
Hostility of the Eastern Church to Greek science
The Athenian School (in the Fifth Century)
"Proclus, 412-485. Damascius. Eutocius"
Nature and extent of the mathematics read at Rome
Contrast between the conditions at Rome and at Alexandria
End of the Second Alexandrian School
"The capture of Alexandria, and end of the Alexandrian Schools"
CHAPTER VI. THE BYZANTINE SCHOOL.
Preservation of works of the great Greek Mathematicians
Hero of Constantinople. Psellus. Planudes. Barlaam. Argyrus
Nicholas Rhabdas. Pachymeres. Moschopulus (Magic Squares)
"Capture of Constantinople, and dispersal of Greek Mathematicians"
CHAPTER VII. SYSTEMS OF NUMERATION AND PRIMITIVE ARITHMETIC.
Methods of counting and indicating numbers amoung primitive races
Use of the abacus or swan-pan for practical calculation
Methods of representing nu
The Lilavati or arithmetic ; decimal numeration used
The Bija Ganita or algebra
Development of Mathematics in Arabia
"ALKARISMI or AL-KHWARIZMI, circ. 830"
His Al-gebr we 'l mukabala
His solution of a quadratic equation
Introduction of Arabic or Indian system of numeration
"TABIT IBN KORRA, 836-901 ; solution of a cubic equation"
Alkayami. Alkarki. Development of algebra
Albategni. Albuzjani. Development of trigonometry
Alhazen. Abd-al-gehl. Development of geometry
Characteristics of the Arabian School
CHAPTER X. INTRODUCTION OF ARABIAN WORKS INTO EUROPE.
The Eleventh Century
Moorish Teachers. Geber ibn Aphla. Arzachel
The Twelfth Century
Adelhard of Bath
Ben-Ezra. Gerad. John Hispalensis
The Thirteenth Century
"LEONARDO OF PISA, circ. 1175-1230"
"The Liber Abaci, 1202"
The introduction of the Arabic numerals into commerce
The introduction of the Arabic numerals into science
The mathematic tournament
"Frederick II., 1194-1250"
"JORDANUS, circ. 1220"
His De Numeris Datis ; syncopated algebra
"ROGER BACON, 1214-1294"
The Fourteenth Century
The reform of the university curriculum
The Fifteenth Century
CHAPTER XI. THE DEVELOPMENT OF ARITHMETIC.
The Boethian arithmetic
Algorism or modern arithmetic
The Arabic (or Indian) symbols : history of
"Introduction into Europe by science, commerce, and calendars"
Improvements introduced in algoristic arithmetic
(I) Simplification of the fundemental processe
(ii) Introduction of signs for addition and subtraction
(iii) "Invention of logarithms, 1614"
(iv) "Use of decimals, 1619"
CHAPTER XII. THE MATHEMATICS OF THE RENAISSANCE.
Effect of invention of printing. The renaissance
Development of Syncopated Algebra and Trigonometry
His De Triangulis (printed in 1496)
"Purbach, 1423-1461. Cusa, 1401-1464. Chuquet, circ. 1484"
Introduction and origin of symbols + and -
"Pacioli or Lucas di Burgo, circ. 1500"
"His arithmetic and geometry, 1494"
"Leonardo da Vinci, 1452-1519"
"Dürer, 1471-1528. Copernicus, 1473-1543"
"Record, 1510-1588 ; introduction of symbol for equality"
"Rudolff, circ. 1525. Riese, 1489-1559"
"His Arithmetica Integra, 1544"
"His solution of a cubic equation, 1535"
"His arithmetic, 1556-1560"
"Hid Ars Magna, 1545 ; the third work printed on algebra"
His solution of a cubic equation
"Ferrari, 1522-1565 ; solution of a biquadratic equation"
"Rheticus, 1514-1576. Maurolycus. Borrel. Xylander"
"Commandino. Peletier. Romanus. Pitiscus. Ramus, 1515-1572"
"Bombelli, circ. 1570"
Development of Symbolic Algebra
"The In Artem ; introduction of symbolic algebra, 1591"
Vieta's other works
"Girard, 1590-1633 ; development of trigonometry and algebra"
"NAPIER, 1550-1617 ; development of trigonometry and algebra"
"Briggs, 1556-1631 ; calculations of tables of logarithms"
"HARRIOT, 1560-1621 ; development of analysis in algebra"
The Origin of the more Common Symbols in Algebra
CHAPTER XIII. THE CLOSE OF THE RENAISSANCE.
Development of Mechanics and Experimental Methods
"Commencement of the modern treatment of statistics, 1586"
Commencement of the science of dynamics
"Francis Bacon, 1561-1626"
Revival of Interest in Pure Geometry
"His Paralipomena, 1604 ; principle of continuity"
"His Stereometria, 1615 ; use of infinitesimals"
"Kepler's laws of planetary motion, 1609 and 1619"
His Brouillon project ; use of projective geometry
Mathematical Knowledge at the Close of the Renaissance
Third Period. Modern Mathematics
CHAPTER XIV. THE HISTORY OF MODERN MATHEMATICS.
Treatment of the subject
Invention of analytical geometry and the method of indivisibles
Invention of the calculus
Development of mechanics
Application of mathematics to physics
Recent development of pure mathematics
CHAPTER XV. HISTORY OF MATHEMATICS FROM DESCARTES TO HUYGENS.
His views on philosophy
"His invention of analytical geometry, 1637"
"His algebra, optics, and theory of vortices"
The method of indivisibles
His geometrical conics
The arthmetical triangle
"Foundation of the theory of probabilities, 1654"
His discussion of the cycloid
"The Arithmetica Infinitorum, 1656"
Law of indices in algebra
Use of series in quadratures
"Earliest rectification of curves, 1657"
His investigation on the theory of numbers
His use in geometry of analysis and of infinitesimals
"Foundation of the theory of probabilities, 1654"
"The Horologium Oscillatorium, 1673"
The undulatory theory of light
Other Mathematicians of this Time
Marsenne ; theorem on primes and perfect numbers
Roberval. Van Schooten. Saint-Vincent
Torricelli. Hudde. Frénicle
De Laloubère. Mercator. Barrow ; the differential triangle
Brouncker ; continued fractions
James Gregory ; distinction between convergent and divergent series
Sir Christopher Wren
Pell. Sluze. Viviani
Tschirnhausen. De la Hire. Roemer. Rolle.
CHAPTER XVI. THE LIFE AND WORKS OF NEWTON.
Newton's school and undergraduate life
"Investigations in 1665-1666 on fluxions, optics, and gravitation"
"His views on gravitation, 1666"
Researches in 1667-1669
"Elected Lucasian professor, 1669"
"Optical lectures and discoveries, 1669-1671"
"Emission theory of light, 1675"
"The Leibnitz Letters, 1676"
"Discoveries and lectures on algebra, 1673-1683"
"Discoveries and lectures on gravitation, 1684"
"The Principia, 1685-1686"
The subject-matter of the Principia
Publication of the Principia
Investigations and work from 1686 to 1696
"Appointment at the Mint, and removal to London, 1696"
"Publication of the Optics, 1704"
Appendix on classification of cubic curves
Appendix on quadrature by
The controversy as to the
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