Lectures on Elementary Mathematics by Lagrange, Joseph Louis -- Read -- Imperial Library of Trantor

Index

Cover Title Page Copyright Page Contents Preface Biographical Sketch of Joseph Louis Lagrange Lecture I. On Arithmetic, and in Particular Fractions and Logarithms

Systems of Numeration. Fractions. Greatest Common Divisor. Continued Fractions. Theory of Powers, Proportions, and Progressions. Involution and Evolution. Rule of Three. Interest. Annuities. Logarithms.

Lecture II. On the Operations of Arithmetic

Arithmetic and Geometry. New Method of Subtraction. Abridged and Approximate Multiplication. Decimals. Property of the Number 9. Tests of Divisibility. Theory of Remainders. Checks on Multiplication and Division. Evolution. Rule of Three. Theory and Practice. Probability of Life. Alligation or the Rule of Mixtures.

Origin of Greek Algebra. Diophantus. Indeterminate Analysis. Equations of the Second Degree. Translations of Diophantus. Algebra Among the Arabs. History of Algebra in Italy, France, and Germany. History of Equations of the Third and Fourth Degree and of the Irreducible Case. Theory of Equations. Discussion of Cubic Equations. Discussion of the Irreducible Case. The Theory of Roots. Extraction of the Square and Cube Roots of Two Imaginary Binomials. Theory of Imaginary Expressions. Trisection of an Angle. Method of Indeterminates. Discussion of Biquadratic Equations.

Lecture IV. On the Resolution of Numerical Equations

Algebraical Resolution of Equations. Numerical Resolution of Equations. Position of the Roots. Representation of Equations by Curves. Graphic Resolution of Equations. Character of the Roots of Equations. Limits of the Roots of Numerical Equations. Separation of the Roots. Method of Substitutions. The Equation of Differences. Method of Elimination. Constructions and Instruments for Solving Equations.

Lecture V. On the Employment of Curves in the Solution of Problems

Application of Geometry to Algebra. Resolution of Problems by Curves. The Problem of Two Lights. Variable Quantities. Minimal Values. Analysis of Biquadratic Equations Conformably to the Problem of the Two Lights. Advantages of the Method of Curves. The Curve of Errors. Regula falsi. Solution of Problems by the Curve of Errors. Problem of the Circle and Inscribed Polygon. Problem of the Observer and Three Objects. Parabolic Curves. Newton’s Problem. Interpolation of Intermediate Terms in Series of Observations, Experiments, etc.

Appendix

Note on the Origin of Algebra.

Index