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

Peter Barlow: Elementary Investigation of the Theory of Numbers

Published $\text {1811}$

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 $102$