Elements of Algebra

Originally published in 1765, this book 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.

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.]
[UPDATED WITH CORRECTIONS ON JULY 7, 2022.]


RESPONSES TO THE FEW NEGATIVE REVIEWS

RECENTLY, "ERIC MOORE", "BUCK" AND "ROBERT O'LEARY" HAVE INDICATED THAT, WHEN VIEWED USING THE KINDLE APP, THERE APPEAR TO BE MISSING LETTERS/NUMBERS AND/OR ADDITIONAL SPACES WITHIN THE TEXT. THIS DOESN'T OCCUR WHEN THE BOOK IS PURCHASED FROM AMAZON AND LOADED AUTOMATICALLY VIA THE APP. I HAVE NOTICED THAT IF YOU EMAIL A PDF TO YOUR KINDLE APP, THESE PROBLEMS DO APPEAR (AND NOT JUST FOR ELEMENTS OF ALGEBRA). IF YOU'VE DOWNLOADED THE PDF VERSION OF THE BOOK, PLEASE READ IT USING A PDF READER LIKE ADOBE ACROBAT READER OR SIMILAR TOOL. NOTE THAT ARTICLES #6 AND #7 WERE MISSING AND HAVE BEEN RESTORED.

"MIKE BYRNE" INDICATED THAT THE BOOK TAKES SEVERAL ADJUSTMENTS TO READ ON AN I-PAD (OR, I'M ASSUMING, ANY OTHER DEVICE). THIS IS BECAUSE THE KINDLE VERSION OF THE BOOK WAS CREATED TO MIMIC THE PAPERBACK COPY OF THE BOOK. THERE HAVE BEEN WAAAAY TOO MANY KINDLE-RELATED COMPLAINTS ABOUT MATHEMATICAL WORKS WHERE THE FORMULAS APPEAR TOO TINY TO READ AND TEXT FLOWS WEIRDLY. BECAUSE OF THAT, I DECIDED TO CREATE A FAITHFUL REPRESENTATION IN PDF FORMAT. IT'S THIS FORMAT THAT'S BEING DISPLAYED IN THE KINDLE APP AND THAT'S THE REASON FOR THE ADJUSTMENTS.

"AMAZON CUSTOMER" COMPLAINED THAT I USED MICROSOFT WORD AND THE CONVERTED THE BOOK TO PDF FORMAT. SIMILAR TO THE RESPONSE ABOVE, IN ORDER TO PRODUCE A FAITHFUL REPRESENTATION OF THE PAPERBACK BOOK FOR KINDLE, I HAD TO GO THIS ROUTE. HE/SHE ALSO COMPLAINED THAT THE MARGINS ARE "RIDICULOUS"...YEAH, MAYBE I SHOULD HAVE INCREASED THE MARGINS A BIT...MY BAD...I'LL TAKE THE HIT ON THAT ONE.

"PLACEVALUE" INDICATED THAT HE/SHE CANNOT TRUST THE EDITOR (THAT WOULD BE ME) OF THE BOOK. IN FACT, I WORKED EXTREMELY HARD TO ENSURE THAT THE TEXT AND THE FORMULAS ARE CORRECT AND REMAIN FAITHFUL TO THE ORIGINAL. THIS PROCESS TOOK MONTHS OF WORK AND I HAVE UPDATED THE BOOK WHEN ERRORS WERE FOUND.

THANKS TO RANDALL GIBBONS, PETER JOHN GENTLES, ALI TUTORSAVANT, VINCENT POIRIER, NICK OH AND OTHERS FOR FINDING THE FEW SCANT ERRORS IN THE TEXT. THANKS VERY MUCH!!

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".[UPDATED WITH CORRECTIONS ON JULY 30, 2016.]