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

## Peter Barlow: *Elementary Investigation of the Theory of Numbers*

Published $1811$.

Accessible online at the Internet Archive.

### Subject Matter

### 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 $102$