Catálogo de la biblioteca Antonio Monteiro - INMABB

Incluye referencias bibliográficas e índice.

Chapter I. Primitive Origins [1] --
l The concept of number. --
2 Early number bases. --
3 Number language and the origin of counting. --
4 Origin of geometry. --
Chapter II. Egypt [9] --
1 Early records. --
2 Hieroglyphic notation. --
3 Ahmes papyrus. --
4 Unit fractions. --
5 Arithmetic operations. --
6 Algebraic problems. --
7 Geometrical problems. --
8 A trigonometric ratio. --
9 Moscow papyrus. --
10 Mathematical weaknesses. --
Chapter III. Mesopotamia [26] --
1 Cuneiform records. --
2 Positional numeration. --
3 Sexagesimal fractions. --
4 Fundamental operations. --
5 Algebraic problems. --
6 Quadratic equations. --
7 Cubic equations. --
8 Pythagorean triads. --
9 Polygonal areas. --
10 Geometry as applied arithmetic. --
11 Mathematical weaknesses. --
Chapter IV. Ionia and the Pythagoreans [48] --
1 Greek origins. --
2 Thales of Miletus. --
3 Pythagoras of Samos. --
4 The Pythagorean pentagram. --
5 Number mysticism. --
6 Arithmetic and cosmology. --
7 Figurate numbers. --
8 Proportions. --
9 Attic numeration. --
10 Ionian numeration. --
11 Arithmetic and logistic. --
Chapter V. The Heroic Age [69] --
1 Centers of activity. --
2 Anaxagoras of Clazomenae. --
3 Three famous problems. --
4 Quadrature of lunes. --
5 Continued proportions. --
6 Hippias of Ellis. --
7 Philolaus and Archytas of Tarentum. --
8 Duplication of the cube. --
9 Incommensurability. --
10 The golden section. --
11 Paradoxes of Zeno. --
12 Deductive reasoning. --
13 Geometrical algebra. --
14 Democritus of Abdera. --
Chapter VI. The Age of Plato and Aristotle [91] --
1 The seven liberal arts. --
2 Socrates. --
3 Platonic solids. --
4 Theodorus of Cyrene. --
5 Platonic arithmetic and geometry. --
6 Origin of analysis. --
7 Eudoxus of Cnidus. --
8 Method of exhaustion. --
9 Mathematical astronomy. --
10 Menaech-mus. --
11 Duplication of the cube. --
12 Dinostratus and the squaring of the circle. --
13 Autolycus of Pitane. --
14 Aristotle. --
15 End of the Hellenic period. --
Chapter VII. Euclid of Alexandria [111] --
1 Author of the Elements. --
2 Other works. --
3 Purpose of the Elements. --
4 Definitions and postulates. --
5 Scope of Book I. --
6 Geometrical algebra. --
7 Books III and IV. --
8 Theory of proportion. --
9 Theory of numbers. --
10 Prime and perfect numbers. --
11 Incommensurability. --
12 Solid geometry. --
13 Apocrypha. --
14 Influence of the Elements. --
Chapter VIII. Archimedes of Syracuse [134] --
1 The siege of Syracuse. --
2 Law of the lever. --
3 The hydrostatic principle. --
4 The Sand-Reckoner. --
5 Measurement of the circle. --
6 Angle trisection. --
7 Area of a parabolic segment. --
8 Volume of a paraboloidal segment. --
9 Segment of a sphere. --
10 On the Sphere and Cylinder. --
11 Book of Lemmas. --
12 Semiregular solids and trigonometry. --
13 The Method. --
14 Volume of a sphere. --
15 Recovery of the Method. --
Chapter IX. Apollonius of Perga [157] --
1 Lost works. --
2 Restorations of lost works. --
3 The problem of Apollonius. --
4 Cycles and epicycles. --
5 The Conics. --
6 Names of the conic sections. --
7 The double-napped cone. --
8 Fundamental properties. --
9 Conjugate diameters. --
10 Tangents and harmonic division. --
11 The three-and-four-line locus. --
12 Intersecting conics. --
13 Maxima and minima, tangents and normals. --
14 Similar conics. --
15 Foci of conics. --
16 Use of coordinates. --
Chapter X. Greek Trigonometry and Mensuration [176] --
1 Early trigonometry. --
2 Aristarchus of Samos. --
3 Eratosthenes of Cyrene. --
4 Hipparchus of Nicaea. --
5 Menelaus of Alexandria. --
6 Ptolemy’s Almagest. --
7 The 360 degree circle. --
8 Construction of tables. --
9 Ptolemaic astronomy. --
10 Other works by Ptolemy. --
11 Optics and astrology. --
12 Heron of Alexandria. --
13 Principle of least distance. --
14 Decline of Greek mathematics. --
Chapter XI. Revival and Decline of Greek Mathematics [196] --
1 Applied mathematics. --
2 Diophantus of Alexandria. --
3 Nicomachus of Gerasa. --
4 The Arithmetica of Diophantus. --
5 Diophantine problems. --
6 The place of Diophantus in algebra. --
7 Pappus of Alexandria. --
8 The Collection. --
9 Theorems of Pappus. --
10 The Pappus problem. --
11 The Treasury of Analysis. --
12 The Pappus-Guldin theorems. --
13 Proclus of Alexandria. --
14 Boethius. --
15 End of the Alexandrian period. --
16 The Greek Anthology. --
17 Byzantine mathematicians of the sixth century. --

Chapter XII. China and India [217] --
1 The oldest documents. --
2 The Nine Chapters. --
3 Magic squares. --
4 Rod numerals. --
5 The abacus and decimal fractions. --
6 Values of pi. --
7 Algebra and Horner’s method. --
8 Thirteenth-century mathematicians. --
9 The arithmetic triangle. --
10 Early mathematics in India. --
11 The Sulvasutras. --
12 The Siddhǡntas. --
13 Aryabhata. --
14 Hindu numerals. --
15 The symbol for zero. --
16 Hindu trigonometry. --
17 Hindu multiplication. --
18 Long division. --
19 Brahmagupta. --
20 Brahmagupta’s formula. --
21 Indeterminate equations. --
22 Bhaskara. --
23 The Lilavati. --
24 Ramanujan. --
Chapter XIII. The Arabic Hegemony [249] --
1 Arabic conquests. --
2 The House of Wisdom. --
3 Al-jabr. --
4 Quadratic equations. --
5 The father of algebra. --
6 Geometric foundation. --
7 Algebraic problems. --
8 A problem from Heron. --
9 Abd al-Hamid ibn-Turk. --
10 Thabit ibn-Qurra. --
11 Arabic numerals. --
12 Arabic trigonometry. --
13 Abu’l-Wefa and al-Karkhi. --
14 Al-Biruni and Alhazen. --
15 Omar Khayyam. --
16 The parallel postulate. --
17 Nasir Eddin. --
18 Al-Kashi. --
Chapter XIV. Europe in the Middle Ages [272] --
1 From Asia to Europe. --
2 Byzantine mathematics. --
3 The Dark Ages. --
4 Alcuin and Gerbert. --
5 The century of translation. --
6 The spread of Hindu-Arabic numerals. --
7 The Liber abaci. --
8 The Fibonacci sequence. --
9 A solution of a cubic equation. --
10 Theory of numbers and geometry. --
11 Jordanus Nemor-arius. --
12 Campanus of Novara. --
13 Learning in the thirteenth century. --
14 Medieval kinematics. --
15 Thomas Bradwardine. --
16 Nicole Oresme. --
17 The latitude of forms. --
18 Infinite series. --
19 Decline of medieval learning. --
Chapter XV. The Renaissance [297] --
1 Humanism. --
2 Nicholas of Cusa. --
3 Regiomontanus. --
4 Application of algebra to geometry. --
5 A transitional figure. --
6 Nicolas Chuquet’s Triparty. --
7 Luca Pacioli’s Summa. --
8 Leonardo da Vinci. --
9 Germanic algebras. --
10 Cardan’s Ars magna. --
11 Solution of the cubic equation. --
12 Ferrari’s solution of the quartic equation. --
13 Irreducible cubics and complex numbers. --
14 Robert Recorde. --
15 Nicholas Copernicus. --
16 Georg Joachim Rheticus. --
17 Pierre de la Ramée. --
18 Bombelli’s Algebra. --
19 Johannes Werner. --
20 Theory of perspective. --
21 Cartography. --
Chapter XVI. Prelude to Modern Mathematics [333] --
1 Francois Viete. --
2 Concept of a parameter. --
3 The analytic art. --
4 Relations between roots and coefficients. --
5 Thomas Harriot and William Oughtred. --
6 Horner's method again. --
7 Trigonometry and prosthaphaeresis. --
8 Trigonometric solution of equations. --
9 John Napier. --
10 Invention of logarithms. --
11 Henry Briggs. --
12 Jobst Biirgi. --
13 Applied mathematics and decimal fractions. --
14 Algebraic notations. --
15 Galileo Galilei. --
16 Values of pi. --
17 Reconstruction of Apollonius' On Tangencies. --
18 Infinitesimal analysis. --
19 Johannes Kepler. --
20 Galileo’s Two New Sciences. --
21 Galileo and the infinite. --
22 Bonaventura Cavalieri. --
23 The spiral and the parabola. --
Chapter XVII. The Time of Fermat and Descartes [367] --
1 Leading mathematicians of the time. --
2 The Discours de la methode. --
3 Invention of analytic geometry. --
4 Arithmetization of geometry. --
5 Geometrical algebra. --
6 Classification of curves. --
7 Rectification of curves. --
8 Identification of conics. --
9 Normals and tangents. --
10 Descartes’ geometrical concepts. --
11 Fermat’s loci. --
12 Higher-dimensional analytic geometry. --
13 Fermat’s differentiations. --
14 Fermat’s integrations. --
15 Gregory of St. Vincent. --
16 Theory of numbers. --
17 Theorems of Fermat. --
18 Gilles Persone de Roberval. --
19 Evangelista Torricelli. --
20 New curves. --
21 Girard Desargues. --
22 Projective geometry. --
23 Blaise Pascal. --
24 Probability. --
25 The cycloid. --
Chapter XVIII. A Transitional Period [404] --
1 Philippe de Lahire. --
2 Georg Mohr. --
3 Pietro Mengoli. --
4 Frans van Schooten. --
5 Jan de Witt. --
6 Johann Hudde. --
7 Rene Francois de Sluse. --
8 The pendulum clock. --
9 Involutes and evolutes. --
10 John Wallis. --
11 On Conic Sections. --
12 Arithmetica infinitorum. --
13 Christopher Wren. --
14 Wallis’ formulas. --
15 James Gregory. --
16 Gregory’s series. --
17 Nicolaus Mercator and William Brouncker. --
18 Barrow’s method of tangents. --

Chapter XIX. Newton and Leibniz [429] --
1 Newton’s early work. --
2 The binomial theorem. --
3 Infinite series. --
4 The Method of Fluxions. --
5 The Principia. --
6 Leibniz and the harmonic triangle. --
7 The differential triangle and infinite series. --
8 The differential calculus. --
9 Determinants, notations, and imaginary numbers. --
10 The algebra of logic. --
11 The inverse square law. --
12 Theorems on conics. --
13 Optics and curves. --
14 Polar and other coordinates. --
15 Newton’s method and Newton’s parallelogram. --
16 The Arithmetica universalis. --
17 Later years. --
Chapter XX. The Bernoulli Era [455] --
1 The Bernoulli family. --
2 The logarithmic spiral. --
3 Probability and infinite series. --
4 L'Hospital’s rule. --
5 Exponential calculus. --
6 Logarithms of negative numbers. --
7 Petersburg paradox. --
8 Abraham de Moivre. --
9 De Moivre’s theorem. --
10 Roger Cotes. --
11 James Stirling. --
12 Colin Maclaurin. --
13 Taylor’s series. --
14 The Analyst controversy. --
15 Cramer’s rule. --
16 Tschirnhaus transformations. --
17 Solid analytic geometry. --
18 Michel Rolle and Pierre Varignon. --
19 Mathematics in Italy. --
20 The parallel postulate. --
21 Divergent series. --
Chapter XXI. The Age of Euler [481] --
1 Life of Euler. --
2 Logarithms of negative numbers. --
3 Foundation of analysis. --
4 Infinite series. --
5 Convergent and divergent series. --
6 Life of d’Alembert. --
7 The Euler identities. --
8 D’Alembert and limits. --
9 Differential equations. --
10 The Clairauts. --
11 The Riccatis. --
12 Probability. --
13 Theory of numbers. --
14 Textbooks. --
15 Synthetic geometry. --
16 Solid analytic geometry. --
17 Lambert and the parallel postulate. --
18 Bezout and elimination. --
Chapter XXII. Mathematicians of the French Revolution [510] --
1 The age of revolutions. --
2 Leading mathematicians. --
3 Publications before [1789.] --
4 Lagrange and determinants. --
5 Committee on Weights and Measures. --
6 Condorcet on education. --
7 Monge as administrator and teacher. --
8 Descriptive geometry and analytic geometry. --
9 Textbooks. --
10 Lacroix on analytic geometry. --
11 The Organizer of Victory. --
12 Metaphysics of the calculus and geometry. --
13 Géometrie de position. --
14 Transversals. --
15 Legendre’s Geometry. --
16 Elliptic integrals. --
17 Theory of numbers. --
18 Theory of functions. --
19 Calculus of variations. --
20 Lagrange multipliers. --
21 Laplace and probability. --
22 Celestial mechanics and operators. --
23 Political changes. --
Chapter XXIII. The Time of Gauss and Cauchy [544] --
1 Early discoveries by Gauss. --
2 Graphical representation of complex numbers. --
3 The fundamental theorem of algebra. --
4 The algebra of congruences. --
5 Reciprocity and frequency of primes. --
6 Constructible regular polygons. --
7 Astronomy and least squares. --
8 Elliptic functions. --
9 Abel’s life and work. --
10 Theory of determinants. --
11 Jacobians. --
12 Mathematical journals. --
13 Complex variables. --
14 Foundations of the calculus. --
15 Bernhard Bolzano. --
16 Tests for convergence. --
17 Geometry. --
18 Applied mathematics. --
Chapter XXIV. The Heroic Age in Geometry [572] --
1 Theorems of Brianchon and Feuerbach. --
2 Inversive geometry. --
3 Poncelet’s projective geometry. --
4 Plücker’s abridged notation. --
5 Homogeneous coordinates. --
6 Line coordinates and duality. --
7 Revival of British mathematics. --
8 Cayley’s n-dimensional geometry. --
9 Geometry in Germany. --
10 Lobachevsky and Ostrogradsky. --
11 Non-Euclidean geometry. --
12 The Bolyais. --
13 Riemannian geometry. --
14 Spaces of higher dimension. --
15 Klein’s Erlanger Programm. --
16 Klein’s hyperbolic model. --
Chapter XXV. The Arithmetization of Analysis [598] --
1 Fourier series. --
2 Analytic number theory. --
3 Transcendental numbers. --
4 Uneasiness in analysis. --
5 The Bolzano—Weierstrass theorem. --
6 Definition of real number. 7 Weierstrassian analysis. --
8 The Dedekind “cut”. --
9 The limit concept. --
10 Gudermann’s influence. --
11 Cantor’s early life. --
12 The “power” of infinite sets. --
13 Properties of infinite sets. --
14 Transfinite arithmetic. --
15 Kronecker’s criticism of Cantor’s work. --
Chapter XXVI. The Rise of Abstract Algebra [620] --
1 The Golden Age in mathematics. --
2 Mathematics at Cambridge. --
3 Peacock, the “Euclid of algebra.” --
4 Hamilton’s quaternions. --
5 Grassmann and Gibbs. --
6 Cayley’s matrices. --
7 Sylvester’s algebra. --
8 Invariants of quadratic forms. --
9 Boole’s analysis of logic. --
10 Boolean algebra. --
11 De Morgan and the Peirces. --
12 The tragic life of Galois. --
13 Galois theory. 14 Field theory. --
15 Frege’s definition of cardinal number. --
16 Peano’s axioms. --
Chapter XXVII. Aspects of the Twentieth Century [649] --
1 The nature of mathematics. --
2 Poincare’s theory of functions. --
3 Applied mathematics and topology. --
4 Hilbert’s problems. --
5 Godel’s theorem. --
6 Transcendental numbers. --
7 Foundations of geometry. --
8 Abstract spaces. --
9 The foundations of mathematics. --
10 Intuitionism, formalism, and logicism. --
11 Measure and integration. --
12 Point set topology. --
13 Increasing abstraction in algebra. --
14 Probability. --
15 High-speed computers. --
16 Mathematical structure. --
17 Bourbaki and the “New Mathematics.” --
General Bibliography [679] --
Appendix: Chronological Table [683] --
Index [697] --

MR, 38 #3105