A history of mathematics / Carl B. Boyer.

Author
Edition
  • 2nd ed.
Published
  • New York : Wiley ©1989
Physical description
xviii, 762 pages : illustrations ; 25 cm
ISBN
  • 0471097632
  • 9780471097631
  • 0471503576
  • 9780471503576
Notes
  • Includes bibliographical references (pages 713-723) and index.
  • Previous ed.: 1968
Contents
  • 1. Origins. The concept of number -- Early number bases -- Number language and the origin of counting -- Origin of geometry. 2. Egypt. Early records -- Hieroglyphic notation -- Ahmes papyrus -- Unit fractions -- Arithmetic operations -- Algebraic problems -- Geometric problems -- A trigonometric ratio -- Moscow papyrus -- Mathemetical weaknesses. 3. Mesopotamia. Cuneiform records -- Positional numeration -- Sexagesimal fractions -- Fundamental operations -- Algebraic problems -- Quadratic equations -- Cubic equations -- Pythagorean triads -- Polygonal areas -- Geometry as applied arithmetic -- Mathematical weaknesses.
  • 4. Ionia and the Pythagoreans. Greek origins -- Thales of Miletus -- Pythagoras of Samos -- The Pythagorean pentagram -- Number mysticism -- Arithmetic and cosmology -- Figurate numbers -- Proportions -- Attic numeration -- Ionian numeration -- Arithmetic and logistic. 5. The heroic age. Centers of activity -- Anaxagoras of Clazomenae -- Three famous problems -- Quadrature of lunes -- Continued proportions -- Hippias of Elis -- Philolaus and Archytas of Tarentum -- Duplication of the cube -- Incommensurability -- The golden section -- Paradoxes of Zeno -- Deductive reasoning -- Geometric algebra -- Democritus of Abdura.
  • 6. The age of Plato and Aristotle. The seven liberal arts -- Socrates -- Platonic solids -- Theodorus of Cyrene -- Platonic arithmetic and geometry -- Origin of analysis -- Eudoxus of Cnidus -- Method of exhaustion -- Mathematical astronomy -- Menaechmus -- Duplication of the cube -- Dinostratus and the squaring of the circle -- Autolycus of Pitane -- Aristotle -- End of the Hellenic period. 7. Euclid of Alexandria. Author of the Elements -- Other works -- Purpose of the Elements -- Definitions and postulates -- Scope of the Book I -- Geometric algebra -- Books III and IV -- Theory of the proportion -- Theory of numbers -- Prime and perfect numbers -- Incommensurability -- Solid geometry -- Apocrypha -- Influence of the Elements.
  • 8. Archimedes of Syracuse. The siege of Syracuse -- Law of the lever -- The hydrostatic principle -- The Sand-reckoner -- Measurement of the circle -- Angle trisection -- Area of a parabolic segment -- Volume of a paraboloidal segment -- Segment of a sphere -- On the sphere and cylinder -- Book of Lemmas -- Semiregular solids and trigonometry -- The method -- Volume of a sphere -- Recovery of the Method. 9. Apollonius of Perga. Lost works -- Restoration of lost works -- The problem of Apollonius -- Cycles and epicycles -- The Conics -- Names of the conic sections -- The double-napped cone -- Fundamental properties -- Conjugate diameters -- Tangents and harmonic division -- The 3- and 4- line locus -- Intersecting conics -- Foci of conics -- Use of coordinates.
  • 10. Greek trigonometry and mensuration. Early trigonometry -- Aristarchus of Samos -- Eratosthenes of Cyrene -- Hipparchus of Nicaea -- Menelaus of Alexandria -- Ptolemy's Almagest -- The 360-degree circle -- Construction of tables -- Ptolemaic astronomy -- Other works by Ptolemy -- Optics and astrology -- Heron of Alexandria -- Principle of least distance -- Decline of Greek mathematics. 11. Revival and decline of Greek mathematics. Applied mathematics -- Diophantus of Alexandria -- Nicomachus of Gerasa -- The Arithmetica of Diophantus -- Diophantine problems -- The place of Diophantus in algebra -- Pappus of Alexandria -- The Collection -- Theorems of Pappus -- The Pappus problem -- The Treasury of analysis -- The Pappus-Guldin theorems -- Proclus of Alexandria -- Boethius -- End of the Alexandrian period -- The Greek anthology -- Byzantine mathematicians of the sixth century.
  • 12. China and India. The oldest documents -- The nine chapters -- Magic squares -- Rod numerals -- The abacus and decimal fractions -- Values of pi -- Algebra and Horner's method -- Thirteenth-century mathematicians -- The arithmetic triangle -- Early mathematics in India -- The Sulvasūtras -- The Siddhāntas -- Aryabhata -- Hindu numerals -- The symbol for zero -- Hindu trigonometry -- Hindu multiplication -- Long division -- Brahmagupta -- Brahmagupta's formula -- Indeterminate equations -- Bhaskara -- The Lilavati -- Ramanujan.
  • 13. The Arabic hegemony. Arabic conquests -- The House of wisdom -- Al-jabr -- Quadratic equations -- The father of algebra -- Geometric foundation -- Algebraic problems -- A problem from Heron -- 'Abd al-Hamid ibn-Turk -- Thabit ibn-Qurra -- Arabic numerals -- Arabic trigonometry -- Abu'l-Wefa and al-Karkhi -- Al-Biruni and Alhazen -- Omar Khayyam -- The parallel postulate -- Nasir Eddin -- Al-Kashi. 14. Europe in the Middle Ages. From Asia to Europe -- Byzantine mathematics -- The Dark Ages -- Alcuin and Gerbert -- The century of translation -- The spread of Hindu-Arabic numerals -- The Liber abaci -- The Fibonacci sequence -- A solution of a cubic equation -- Theory of numbers and geometry -- Jordanus Nemorarius -- Campanus of Novara -- Learning in the thirteenth century
  • Medieval kinematics -- Thomas Bradwardine -- Nicole Oresme -- The latitude of forms -- Infinite series -- Decline of medieval learning. 15. The Renaissance. Humanism -- Nicholas of Cusa -- Regiomontanus -- Application of algebra to geometry -- A transitional figure -- Nicolas Chuguet's Triparty -- Luca Pacioli's Summa -- Leonardo da Vinci -- Germanic algebras -- Cardan's Ars magna -- Solution of the cubic equation -- Ferrari's solution of the quartic equation -- Irreducible cubics and complex numbers -- Robert Recorde -- Nicholas Copernicus -- Georg Joachim Rheticus -- Pierre de la Ramée -- Bombelli's Algebra -- Johannes Werner -- Theory of perspective -- Cartography.
  • Prelude to modern mathematics. Francois Vi`ete -- Concept of a parameter -- The analytic art -- Relations between roots and coefficients -- Thomas Harriot and William Oughtred -- Horner's method again -- Trigonometry and prosthaphaeresis -- Trigonometric solution of equations -- John Napier -- Invention of logarithms -- Henry Briggs -- Jobst Bürgi -- Applied mathematics and decimal fractions -- Algebraic notations -- Galileo Galilei -- Values of pi -- Reconstruction of Apollonius' On tangencies -- Infinitesimal analysis -- Johannes Kepler -- Galileo's Two new sciences -- Galileo and the infinite -- Bonaventura Cavalieri -- The spiral and the parabola.
  • 17. The time of Fermat and Descartes. Leading mathematicians of the time -- The Discours de la methode -- Invention of analytic geometry -- Arithmetization of geometry -- Geometric algebra -- Classificaition of curves -- Rectification of curves -- Identification of conics -- Normals and tangents -- Descartes' geometric concepts -- Fermat's loci -- Higher-dimensional analytic geometry -- Fermat's differentiations -- Fermat's integrations -- Gregory of St. Vincent -- Theory of numbers -- Theorems of Fermat -- Gilles Persone de Roberval -- Evangelista Torricelli -- New curves -- Girard Desargues -- Projective geometry -- Blaise Pascal -- Probability -- The cycloid.
  • 18. A transitional period. Phillippe de Lahire -- George Mohr -- Pietro Mengoli -- Frans van Schooten -- Jan De Witt -- Johann Hudde -- René Franc̦ois de Sluse -- The pendulum clock -- Involutes and evolutes -- John Wallis -- On conic sections -- Arithmetica infinitorum -- Christopher Wren -- Wallis' formulas -- James Gregory -- Gregory's series -- Nicolaus Mercator and William Brouncker -- Barrow's method of tangents. 19. Newton and Leibniz. Newton's early work -- The binomial theorem -- Infinite series -- The Method of fluxions -- The Principia -- Leibniz and the harmonic triangle -- The differential triangle and infinite series -- The differential calculus -- Determinants, notations, and imaginary numbers
  • The algebra of logic -- The inverse square law -- Theorems on conics -- Optics and curves -- Polar and other coordinates -- Newton's method and Newton's parallelogram -- The Arithmetica universalis -- Later years. 20. The Bernoulli era. The Bernoulli family -- The logarithmic spiral -- Probability and infinite series -- L'Hospital's rule -- Exponential calculus -- Logarithms of negataive numbers -- Petersburg paradox -- Abraham De Moivre -- De Moivre's theorem -- Roger Cotes -- James Stirling -- Colin Maclaurin -- Taylor's series -- The Analyst controversy -- Cramer's rule -- Tschirnhaus transformations -- Solid analytic geometry -- Michel Rolle and Pierre Varignon -- Mathematics in Italy -- The parallel postulate -- Divergent series.
  • 21. The age of Euler. Life of Euler -- Notation -- Foundation of analysis -- Infinite series -- Convergent and divergent series -- Life of d'Alembert -- The Euler identities -- D'Alembert and limits -- Differential equations -- The Clairauts -- The Riccatis -- Probability -- Theory of numbers -- Synthetic geometry -- Solid analytic geometry -- Lambert and the parallel postulate -- Bézout and elimination. 22. Mathematicians of the French Revolution. The age of revolution -- Leading mathematicians -- Publications before 1789 -- Lagrange and determinants -- Committee on weights and measures -- Condorcet on education -- Monge as administrator and teacher -- Descriptive geometry and analytic geometry -- Lacroix on analytic geometry -- The organizer of victory -- Metaphysics of the calculus and geometry -- Géométrie de position -- Transversals
  • Legendre's Geometry -- Elliptic integrals -- Theory of numbers -- Theory of functions -- Calculus of variations -- Lagrange multipliers -- Laplace and probabililty -- Celestial mechanics and operators -- Political changes. 23. The time of Gauss and Cauchy. Nineteenth-century overview -- Gauss: early work -- Number theory -- Reception of the Disquisitiones arithmeticae -- Gauss's contributions to astronomy -- Gauss's middle years -- The beginnings of differential geometry -- Gauss's later work -- Paris in the 1820s -- Cauchy -- Gauss and Cauchy compared -- Non-Euclidean geometry -- Abel and Jacobi -- Galois -- Diffusion -- Reforms in England and Prussia.
  • 24. Geometry. The school of Monge -- Projective geometry: Poncelet and Chasles -- Synthetic metric geometry: Steiner -- Synthetic nonmetric geometry: von Staudt -- Analytic geometry -- Riemannian geometry -- Spaces of higher dimensions -- Felix Klein -- Post-Riemannian algebraic geometry. 25. Analysis. Berlin and Göttingen at mid-century -- Riemann in Göttingen -- Mathematical physics in Germany -- Mathematical physics in the English-speaking countries -- Weierstrass and students -- Arithmetization of analysis -- Cantor and Dedekind -- Analysis in France.
  • 26. Algebra. British algebra and the operational calculus of functions -- Boole and the algebra of logic -- De Morgan -- Hamilton -- Grassmann and Ausdehnungslehre -- Cayley and Sylvester -- Linear associative algebras -- Algebraic geometry -- Algebraic and arithmetic integers -- Axioms of arithmetic. 27. Poincaré and Hilbert. Turn-of-the-century overview -- Poincare -- Mathematical physics and other applications -- Topology -- Other fields and legacy -- Hilbert -- Invariant theory -- Hilbert's Zahlbericht -- The foundations of geometry -- The Hilbert problems -- Hilbert and analysis -- Waring's problem and Hilbert's work after 1909.
  • 28. Aspects of the twentieth century. General overview -- Integration and measure -- Functional analysis and general topology -- Algebra -- Diffential geometry and tensor analysis -- The 1930s and World War II -- Probability -- Homological algebra and category theory -- Bourbaki -- Logic and computing -- Future outlook.
Other names
Related item
  • Online version:: Boyer, Carl B. (Carl Benjamin), 1906-1976. History of mathematics. 2nd ed. New York : Wiley, ©1989
  • http://catdir.loc.gov/catdir/description/wiley032/89005325.html
  • http://www.loc.gov/catdir/description/wiley032/89005325.html
Genre
  • Bibliography
  • History.
  • Illustrated
  • text
Language
  • English

Summary

  • Develops world contributions to mathematics, from the inception of numbers and geometry to modern probability and Bourbaki's mathematics.

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Aberystwyth University Library: External Store QA21.B7 (N1.44)
Bangor University Library: Deiniol Library QA21 .B767 1989
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