Elements of Algebra

by Leonhard Euler, Scott L Hecht

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 German-to-English and 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."

Genres: Mathematics, Science, Classics, Textbooks, Nonfiction, Historical, Education

538 pages, Paperback

First published January 1, 1765

About the author

Noted Swiss mathematician Leonhard Euler worked in analysis and algebra, including complex numbers and logarithms, and he introduced much of the basic notation in mathematics.

This pioneering physicist made important discoveries in fields as diverse as infinitesimal calculus and graph theory. He also introduced much of the modern terminology, particularly for analysis, such as the notion of a function. He is also renowned for his work in mechanics, fluid dynamics, optics, astronomy, and music theory.

People considered Euler the preeminent mathematician of the 18th century and one of the greatest who ever lived. He is also one of the most prolific mathematicians; his collected works fill sixty to eighty quarto volumes. He spent most of his adult life in Saint Petersburg, Russia, and in Berlin, Prussia.

A statement, attributed to Pierre Simon de Laplace, expresses influence of Euler on mathematics: "Read Euler, read Euler, he is the master of us all."

Reviews

[Ronald Lett · Rating 3 out of 5]

Euler presents in some cases quite refreshing viewpoints on basic algebra, especially in the presentation of several methods that can rarely be found explained with such plain elegance. Quite a valuable read, even for the experienced mathematician.

[Mustafa Mohammadi · Rating 5 out of 5]

Detailed

Very detailed, well written!

Couldn’t be any better for someone who aims to master algebra!
Off course no one book makes you the master of algebra, but it’s availing the steps to you by explaining things precisely on point, easy to understand that helps you progress.

[Yogi Saputro · Rating 4 out of 5]

As part of some research, I stumbled upon this book. I thought old books are obsolete. However, this is not the case here and I need to give credits with this review.

I give this book 4 stars not because I really like it, nor I am fan of math (as an engineer, I see it as necessity). I pay homage to Euler for carrying accessible mathematics to modern age.

First, this book influence and construct modern notations for math subject we hate in school. You name it: power, logarithms, roots, sum (Σ, big sigma letter), function f(x), "e" for natural algorithm. Heck, it might even influenced the chapters as well. Euler did not found them all from scratch, but he managed to bring together pieces of math in one book. So... thanks Euler, I guess?

Second, this book brought mathematics down to Earth. Back in 18th century, math was exclusive to academia, and maybe the nobility. It had little practical value and notoriously challenging. Euler had lower the barrier of entry with this book. Instead of bombarding reader with numbers, short description, and tons of exercises (like math books today), this book guided us how to think in math.

Euler knew mathematics was hard. So he presented this book as series of statements. On first statement, he described quantities. On second, he described numbers. Then he described how numbers behave. Then he explain addition, etc. Each statement serves as step, and build foundations for later. The further it goes, the steeper each step. But you can always trace back to previous steps when you have difficulty. It shows real progress in learning. I just wish I had learned math like this. Euler's gentle process to approach math is just outstanding.

[Paul A. · Rating 5 out of 5]

Many geniuses have trouble communicating with ordinary folks. Euler is an exception. this is basically a beginning math book, but one that moves very quickly and with tremendous insight into the connections between different aspects of mathematics. I'm pretty good at math, to put it mildly, but this was a great and interesting read. If you think you are bad at math, I bet you never had as clear and engaging a teacher as Euler. If you are good at math, you will enjoy his clear and clever exposition. This is how math should be taught.

[Anastasia Tuple · Rating 5 out of 5]

Excellent book with a fluent and personable writing style. The book analyzes one algebraic subject in each of its brief (3-4 pages) chapters, in clear-cut and progrssively more advanced paragraphs. It also provides a list of questions for practice and their answers (but only at the end of some chapters).

[Mateo Maldonado · Rating 4 out of 5]

Splendid read on the essence of algebra, the book was a lot bigger than I expected but there’s a ton of cool exercises and detailed explanations in the book. Great for those wanting to learn or brush up on Algebra. Albeit it doesn’t go super far into more advanced topics.

[Cameron · Rating 3 out of 5]

this book is Cronus eating his babbies