This book, originally published in 1765, is a gentle introduction to algebra by one of history's greatest mathematicians, Leonhard Euler. Starting with basic mathematical concepts such as signs, fractions, powers and roots, logarithms, infinite series, arithmetic and geometric ratios, and the calculation of interest, Euler then discusses how to solve equations of varying degrees, methods of rendering certain formulas rational, and more.

In 1771, Joseph-Louis Lagrange included an addendum to the French edition containing topics such as continued fractions and Diophantine equations.

This edition of Elements of Algebra was completely re-written using Microsoft Word and its Equation Editor over the course of several months and is not just another scanned copy of John Hewlett's original English language translation. This new edition contains Euler's Part I (Containing the Analysis of Determinate Quantities) and Part II (Containing the Analysis of Indeterminate Quantities), Lagrange's Additions as well as all of the footnotes by Johann Bernoulli and others.

While much of the text remains the same as that edition, several changes were made to make it more accessible to the modern reader:

1. The words "shew" and "shewn" were replaced by "show" and "shown", respectively.
2. The original notation for continued fractions has been replaced with the more modern notation.
3. Several French-to-English translation issues were resolved.
4. While the order is the same as John Hewlett's English language translation, in order to give the work more space, each chapter now begins on its own page.
5. Several inline formulas were moved out-of-line to give the work more space.
6. Several errors in the formulas were discovered and corrected.
7. The word "formulae" was replace by "formulas".
8. The footnotes were moved to a Notes section at the end of the book.
9. The overuse of the comma in several places was brought up to modern standards.

It is my hope that by creating this new "modern" edition, a renewed interest will be generated for a work which certainly does not deserve to be forgotten, written by a brilliant mathematician considered "the master of us all".

[UPDATED WITH CORRECTIONS ON JULY 30, 2016.]