Book:Peter Barlow/Elementary Investigation of the Theory of Numbers

Accessible online at the Internet Archive.

Subject Matter

 * Number Theory

Contents

 * PART I.


 * CHAP. I. On the Sums, Differences, and Products of Numbers in General
 * CHAP. II. On Divisors, and the Theory of Perfect, Amicable, and Polygonal Numbers
 * CHAP. III. On the Lineal Forms of Prime Numbers, and their most simple Properties
 * CHAP. IV. On the possible and impossible Forms of Square Numbers, and their Application to Numberical Propositions
 * CHAP. V. On the possible and impossible Forms of Cubes, and Higher Powers
 * CHAP. VI. On the Properties of Powers in General
 * CHAP. VII. On the Products and Transformations of certain Algebraical Formulae
 * CHAP. VIII. On the Quadratic Divisors of certain Algebraical Formulae
 * CHAP. IX. On the Quadratic Forms of Prime Numbres, with Rules for determining them in certain Cases
 * CHAP. X. On the different Scales of Notation, and their Application to the Solution of Arithmetical Problems
 * Notation of the Greeks
 * Miscellaneous Propositions


 * PART II.


 * CHAP. I. Continued Fractions, and their Application to various Problems
 * CHAP. II. On the Solution of Indeterminate Equations of the First Degree
 * CHAP. III. On the Solution of Indeterminate Equations of the Second Degree
 * CHAP. IV. On the Solution of Indeterminate Equations of the Third Degree, and those of Higher Dimensions
 * CHAP. V. On the Solution of Indeterminate Equations of the Form $x^n - 1 = M \left({a}\right)$
 * Table of Indeterminate Formulae
 * CHAP. VI. On the Solution of Diophantine Problems
 * Miscellaneous Problems
 * CHAP. VII. On the Analytical and Geometrical Division of the Circle
 * Table of Prime Numbers to $4000$
 * Table containing the least Values of $p$ and $q$ in the Equation $p^2 - Nq^2 = 1$, for every Value of $N$, from $2$ to $102$