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A Short Account of the History of Mathematics

by

A Short Account of the History of Mathematics Cover

 

Synopses & Reviews

Synopsis:

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.

Synopsis:

Exceptionally clear, authoritative survey--from the Egyptians and Phoenicians through 19th-century figures such as Grassman, Galois, Riemann. Fourth edition.

Synopsis:

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

PREFACE

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.

    Authorities

    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.

    Authorities

    Mathematical teachers at Athens prior to 420 B.C.

      Anaxogoras. The Sophists. Hippias (The quadratrix)

      Antipho

    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

    Aristaeus. Theaetetus

    "Aristotle, 384-322 B.C."

    Questions on mechanics. Letters used to indicate magnitudes

  CHAPTER IV. THE FIRST ALEXANDRIAN SCHOOL

    Authorities

    Foundation of Alexandria

    The Third Century before Christ

    "EUCLID, circ. 330-275 B.C."

      Euclid's Elements

      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

      His astronomy

      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"

      Perseus. Zejodorus

    "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

    Theodosius

    Dionysodorus

    End of the First Alexandrian School

    Egypt constituted a Roman province

  CHAPTER V. THE SECOND ALEXANDRIAN SCHOOL

    Authorities

    The First Century after Christ

    Serenus. Menelaus

    Nicomachus

      Introduction of the arithmetic current in medieval Europe

    The Second Century after Christ

    Theon of Smyran. Thymaridas

    "PTOLEMY, died in 168"

      The Almagest

      Ptolemy's astronomy

      Ptolemy's geometry

    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"

      His Porisms

      Subsequent neglect of his discoveries

    Iamblichus

    Theon of Alexandria. Hypatia

    Hostility of the Eastern Church to Greek science

    The Athenian School (in the Fifth Century)

    "Proclus, 412-485. Damascius. Eutocius"

    Roman Mathematics

    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.

    Authorities

    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

  Holywood

  "ROGER BACON, 1214-1294"

  Campanus

  The Fourteenth Century

  Bradwardine

  Oresmus

  The reform of the university curriculum

  The Fifteenth Century

  Beldomandi

CHAPTER XI. THE DEVELOPMENT OF ARITHMETIC.

  Authorities

  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.

  Authorities

  Effect of invention of printing. The renaissance

  Development of Syncopated Algebra and Trigonometry

  "REGIOMONTANUS, 1436-1476"

    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"

  "STIFEL, 1486-1567"

    "His Arithmetica Integra, 1544"

  "TARTAGLIA, 1500-1559"

    "His solution of a cubic equation, 1535"

    "His arithmetic, 1556-1560"

  "CARDAN, 1501-1576"

    "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

  "VIETA, 1540-1603"

    "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"

  "Oughtred, 1574-1660"

  The Origin of the more Common Symbols in Algebra

CHAPTER XIII. THE CLOSE OF THE RENAISSANCE.

  Authorities

  Development of Mechanics and Experimental Methods

  "STEVINUS, 1548-1620"

    "Commencement of the modern treatment of statistics, 1586"

  "GALILEO, 1564-1642"

    Commencement of the science of dynamics

    Galileo's astronomy

  "Francis Bacon, 1561-1626"

  Revival of Interest in Pure Geometry

  "KEPLER, 1571-1630"

    "His Paralipomena, 1604 ; principle of continuity"

    "His Stereometria, 1615 ; use of infinitesimals"

    "Kepler's laws of planetary motion, 1609 and 1619"

  "Desargues, 1593-1662"

    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.

  Authorities

  "DESCARTES, 1596-1650"

    His views on philosophy

    "His invention of analytical geometry, 1637"

    "His algebra, optics, and theory of vortices"

  "CAVALIERI, 1598-1647"

    The method of indivisibles

  "PASCAL, 1623-1662"

    His geometrical conics

    The arthmetical triangle

    "Foundation of the theory of probabilities, 1654"

    His discussion of the cycloid

  "WALLIS, 1616-1703"

    "The Arithmetica Infinitorum, 1656"

    Law of indices in algebra

    Use of series in quadratures

    "Earliest rectification of curves, 1657"

    Wallis's algebra

  "FERMAT, 1601-1665"

    His investigation on the theory of numbers

    His use in geometry of analysis and of infinitesimals

    "Foundation of the theory of probabilities, 1654"

  "HUYGENS, 1629-1695"

    "The Horologium Oscillatorium, 1673"

    The undulatory theory of light

  Other Mathematicians of this Time

  Bachet

  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

  Hooke. Collins

  Pell. Sluze. Viviani

  Tschirnhausen. De la Hire. Roemer. Rolle.

CHAPTER XVI. THE LIFE AND WORKS OF NEWTON.

  Authorities

  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

Product Details

ISBN:
9780486206301
Author:
Ball, W. W. Rouse
Publisher:
Dover Publications
Author:
Ball, W. W. Rouse
Author:
Mathematics
Location:
New York
Subject:
General
Subject:
General science
Subject:
History
Subject:
Mathematics
Subject:
Matemâatica
Subject:
General Mathematics
Subject:
Mathematics -- History.
Subject:
Science Reference-General
Edition Number:
4
Edition Description:
Trade Paper
Series:
Dover Books on Mathematics
Series Volume:
no. 113
Publication Date:
20100931
Binding:
TRADE PAPER
Language:
English
Pages:
522
Dimensions:
8.5 x 5.38 in 1.31 lb

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Product details 522 pages Dover Publications - English 9780486206301 Reviews:
"Synopsis" by ,
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.
"Synopsis" by , Exceptionally clear, authoritative survey--from the Egyptians and Phoenicians through 19th-century figures such as Grassman, Galois, Riemann. Fourth edition.

"Synopsis" by ,
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.
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