Research Catalog

Title

A source book in mathematics / by David Eugene Smith ...

Author

Smith, David Eugene, 1860-1944.

Publication

New York : McGraw-Hill Book Co., 1929.

Items in the Library & Off-site

Details

Description

xvii, 701 pages : frontispiece (portrait), illustrations, portraits, diagrams; 24 cm.

Series Statement

Source books in the history of the sciences

Uniform Title

Source books in the history of the sciences.

Subjects

• Mathematics
• Mathematics > History

Genre/Form

History.

Note

• Rare Book copy: The author's copy, with his manuscript annotations and laid-in related materials

Bibliography (note)

• Includes bibliographical references and index.

Contents

• Treviso / First printed arithmetic -- Robert Recorde / Declaration of the profit of arithmeticke -- Stevin / Decimal fractions -- Dedekind / Irrational numbers -- John Wallis / Imaginary numbers -- Wessel / Complex numbers -- Pascal / Arithmetic triangle -- Bombelli, Cataldi / Continued fractions -- Bernoulli / Bernoulli numbers -- Euler / Every integer as a sum of four squares -- Euler / Use of e to represent 2.718 -- Hermite / Transcendence of e -- Gauss / Congruence of numbers -- Gauss / Third proof of the law of quadratic reciprocity -- Kummer / Ideal numbers -- Chebyshev / Totality of primes -- Napier / Table of logarithms -- Delamain / Slide rule -- Oughtred / Slide rule -- Pascal / His calculating machine -- Leibniz / His calculating machine -- Napier / Napier rods -- Galileo Galilei / Proportional or sector compasses -- D'Ocagne / Nomography.
• Cardan / Imaginary roots -- Cardan / Cubic equation -- Ferrari-Cardan / Biquadratic equation -- Fermat / Equation x^n + y^n = z^n -- Fermat / So-called pell equation -- John Wallis / General exponents -- Wallis and Newton / Binomial theorem for fractional and negative exponents -- Newton / Binomial theorem for fractional and negative exponents -- Leibniz and the Bernoullis / Polynomial theorem -- Horner / Numerical higher equations -- Rolle / Location of roots -- Abel / Quintic equation -- Leibniz / Determinants -- Bernoulli / Verses on infinite series -- Bernoulli / Theory of combinations -- Galois / Groups and equations -- Abel / Theorem on the continuity of functions defined by power series -- Gauss / Fundamental theorem of algebra.
• Desargues / Perspective triangles -- Desargues / 4-rayed pencil -- Poncelet / Projective geometry -- Peaucellier / Peaucellier's cell -- Pascal / Essay pour les coniques -- Brianchon / Theorem -- Brianchon and Poncelet / Nine-point circle theorem -- Feuerbach / Feuerbach's thesis -- First use of Pi for the circle ratio -- Gauss / Division of a circle into n equal parts -- Saccheri / Non-euclidean geometry -- Bolyai / Non-euclidean geometry -- Fermat / Analytic geometry -- Descartes / Analytic geometry -- Pohlke / Theorem -- Riemann / Surfaces and analysis situs -- Riemann / Hypotheses which lie at the foundations of geometry -- Monge / Purpose of descriptive geometry -- Regiomontanus / Law of sines for spherical triangles -- Regiomontanus / Relation of the parts of a triangle -- Pitiscus / Laws of sines and cosines -- De Moivre / Formula -- Calvius / Prosthaphaeresis as applied to trigonometry -- Clavius / Prosthaphaeresis.
• Gauss / Conformal representation -- Steiner / Quadratic transformation between two spaces -- Cremona / Geometric transformations of plane figures -- Lie / Memoir on a class of geometric transformations -- Moebius, Cayley, Cauchy, Sylvester, and Clifford / Geometry of four or more dimensions -- Moebius / Higher space -- Cayley / Higher space -- Cauchy / Higher space -- Sylvester / Higher space -- Clifford / Higher space.
• Fermat and Pascal / Probability -- De Moivre / Law of normal probability -- Legendre / Least squares -- Chebyshev / Mean values -- Laplace / Probability of errors in the mean results of a great number of observations, etc.
• Cavalieri / Approach to the calculus -- Fermat / Maxima and minima -- Newton / Fluxions -- Leibniz / Calculus -- Berkeley / Analyst -- Cauchy / Derivatives and differentials -- Euler / Differential equations of the second order -- Bernoulli / Brachistochrone problem -- Abel / Integral equations -- Bessel / His functions -- Moebius / Barycentric Calculus -- Hamilton / Quaternions -- Grassmann / Ausdehnungslehre.

LCCN

29028703

OCLC

• ocm01161945
• 1161945
• SCSB-2998706

Owning Institutions

Columbia University Libraries