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A history of mathematics

Author: Carl B Boyer; Uta C Merzbach
Publisher: New York : Wiley, ©1991.
Edition/Format:   eBook : Document : English : 2nd ed. [rev.]View all editions and formats
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Genre/Form: History
Additional Physical Format: Print version:
Boyer, Carl B. (Carl Benjamin), 1906-1976.
History of mathematics.
New York : Wiley, ©1991
(DLC) 89005325
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Carl B Boyer; Uta C Merzbach
OCLC Number: 1035607906
Notes: "The initial revision [i.e. 2nd ed.], which appeared two years ago, was designed for classroom use. The exercises found there, and in the original edition, have been dropped in this edition"--Page ix.
Description: 1 online resource (xx, 715 pages : illustrations
Contents: Origins --
Egypt --
Mesopotamia --
Ionia and the Pythagoreans --
Heroic age --
Age of Plato and Aristotle --
Euclid of Alexandria --
Archimedes of Syracuse --
Apollonius of Perga --
Greek trigonometry and mensuration --
Revival and decline of Greek mathematics --
China and India --
Arabic hegemony --
Europe in the Middle Ages --
Renaissance --
Prelude to modern mathematics --
Time of Fermat and Descartes --
Transitional period --
Newton and Leibniz --
Bernoulli era --
Age of Euler --
Mathematicians of the French Revolution --
Time of Gauss and Cauchy --
Geometry --
Analysis --
Algebra --
Poincare and Hilbert --
Aspects of the twentieth century --
References --
General bibliography --
Appendix: Chronological table --
Index. 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 --
Mathematical 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 as 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 Abdera --
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 Book I --
Geometric algebra --
Books III and IV --
Theory of 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 --
Books 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 three- and four-line locus --
Intersecting conics --
Maxima and minima, tangents and normals --
Similar conics --
Foci of conics --
Use of coordinates --
10. Greek trigonometry and mensuration --
Early trigonometry --
Aristarchus of Samos --
Eratosthenes of Cyrene --
Hipparchus of Necaea --
Menelaus of Alexandria --
Ptolemy's Almagest --
The 360-degree circle --
Construction of tables --
Ptolemaic astronomy --
Other works by Ptolemy --
Optics and astronomy --
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 Sulvasåutras --
The Siddhåantas --
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 latitute 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 Chuquet'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 Ramâee --
Bombelli's Algebra --
Johannes Werner --
Theory of perspective --
Cartography --
16. Prelude to modern mathematics --
Franðcois Viáete --
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 Bèurgi --
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 --
Bonaventure Cavalieri --
The spiral the and parabola. 17. The time of Fermat and Descartes --
Leading mathematicians of the time --
The Discours de la mâethode --
Invention of analytic geometry --
Arithmetization of geometry --
Geometric algebra --
Classification 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 --
Philippe de Lahire --
Georg Mohr --
Pietro Mengoli --
Frans van Schooten --
Jan De Witt --
Johann Hudde --
Renâe Franðcois 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 negative 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 --
Textbooks --
Synthetic geometry --
Solid analytic geometry --
Lambert and the parallel postulate --
Bâezout and elimination --
22. Mathematicians of the French Revolution --
The age of revolutions --
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 --
Textbooks --
Lacroix on analytic geometry --
The organizer of victory --
Metaphysics of the calculus and geometry --
Gâeomâetrie de position --
Transversals --
Legendre's Geometry --
Elliptic integrals --
Theory of numbers --
Theory of functions --
Calculus of variations --
Lagrange multipliers --
Laplace and probability --
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 Gèottingen at mid-century --
Riemann in Gèottingen --
Mathematical physics in Germany --
Mathematical physics in the English-speaking countries --
Weierstrass and students --
The arithmetization of analysis --
Cantor and Dedekind --
Analysis in France. 26. Algebra --
Introduction --
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. Poincarâe and Hilbert --
Turn-of-the-century overview --
Poincarâe --
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 --
Differential geometry and tensor analysis --
The 1930s and World War II --
Probability --
Homological algebra and category theory --
Bourbaki --
Logic and computing --
Future outlook --
References --
General bibliography --
Appendix : Chronological table --
Index.
Responsibility: Carl B. Boyer ; revised by Uta C. Merzbach ; [foreword by Isaac Asimov].
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