# 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.

### 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 $102$