Elements of Algebra by Leonhard Euler (PDF)

Description

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.]COMMENTS ON THE FEW NEGATIVE REVIEWSRECENTLY, “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 REPLACED.”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!!

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Interesting but some awakard word translations made it more difficult to read than necessary.

⭐I really enjoy short focused chapters, unlike in a lot of modern textbooks, they never drag on, but keep you interested. The tone of the book is conversational, not formal at all. You can really tell that Euler enjoyed teaching as much as he enjoyed doing mathematics.The reprint is very high quality. Though normally, I wouldn’t trust anything that comes out of Microsoft Word, the book’s typesetting is of high quality. It’s not TeX, you will not find a single ligature here, or sub-millimeter precision spacing, but it still looks good. Some of the decorum, the squiggly lines announcing each new chapter, seem to have been lost in translation to new format, so pages look a little austere in comparison to original. Title image is noticeably pixelated, a little more care could be taken to pick out a higher resolution image for the title page. But other than that there’s nothing I can nitpick on.EDIT: Found a blooper: reference numbers don’t match up!

⭐I liked the beginning where Euler defines the mathematical symbols to be used. For instance, we learn that equal to (=) is beginning to be used at the time. Further on, when defining numbers (natural, rational,…) It is clear that at the time there was not an axiomatic number definition. Rather, Euler defines number properties with clear applied examples (investment, principal, debts an so on ). The last chapters are devoted to solving equations up to third degree. These turned out being rather cryptic for a non professional practitioner.Altogether, the book is a sort of showcase of the practice and teaching of mathematics at the time, and I bought it for that. I have no complaints about.The translator/editor did a good job updating the symbols and keeping the tangy archaic writing.

⭐Leonhard Euler is both founder of modern algebra and widely believed to be the best pure mathematician ever. According to the story I’ve heard, Euler went blind late in life but to have something to do he obtained the services of a normal person not educated in mathematics and used him as an intellectual mirror to write this book. He only put explanations in this book that helper could master. Amazingly, the helper mastered the material. How clever.

⭐This is more about the review of the book’s physical attributes than the review of Euler’s masterpiece. It is one of the best mathematical book written for general population by one of the greatest mathematician. It is more or less on par with Euclid’s Elements (still I would rate Euclid’s masterpiece above). The other editions I bought earlier, reprinted the older formats with illegible formulas and letters. This version resolves those problems. I wish they would have maintained the notes in the same pages instead of combining in the last pages. Great clarity. Larger print. Have enough space to take notes.

⭐I purchased this book excepting it to be a tad bit shorter but that was my fault as a consumer making spontaneous purchases rather than investigating a bit further. This is a textbook sized book and it packs a lot of information all taught by Euler (possibly the greatest mathematician known to man). Some of the language used in the book can be a bit confusing but considering this is a reprint and probably was translated by people without math degrees it is passable.Definitely worth its value.

⭐Maravilloso enfoque: a pesar de todos los años transcurridos desde su concepción y de lo distinto que somos a su público original, el texto atrae y enseña antiguas/nuevas formas de enfrentar los temas tratados. Ha sido un placer leerlo.Take a look at the pages, the first two in the text proper. Highlighted in yellow are all the formatting issues noticed at a quick scan.What may not be immediately noticed is the lack of paragraphs 6 and 7. This being my first exposure to the book, I can’t be certain that the possibly greatest mathematical mind in history forgot a couple of single-digit numbers existed and neglected to write paragraphs for them. (Spoiler alert: he didn’t.)Don’t waste your money on this.

⭐Beautiful

⭐Para matemáticos: um obra que tem que ser lida, e relida. Várias vezes do grande Mestre Leonhard Euler. Excelente! Notei na obra um paralelo dele com a estupenda obra de Euclides (Elementos)To all mathematicians: a must read, as much as possible. From the great master Leonhard Euler! Excellent. I’ve noticed some sort of inspiration on the superb book of Euclides cornestone of Geometry.Leonhard Euler was one of the greatest and most prolific mathematicians of all time. His work was of vital importance to a bewildering variety of fields, many of which he himself created. Yet, as with most modern mathematicians, his work was and remains inaccessible to most of us. Amitabh Chandra Aruni Vill.+ Po. – Mejorganj, Sitamarhi, Bihar

⭐The contents of the book are good and well written. However, the format is beyond disgrace. It looks as if it was written down using a typewriter. Really, there is no need nowadays to translate such a fantastic book using Word. Latex editors are the best option and relying on something lesser greatly diminishes the value of this book.El algebra de Euler sigue siendo de gran actualidad. La minuciosidad con que plantea los temas es extraordinaria. En muchos detalles se muestra la genialidad del autor. El libro se lee bien aunque aparecen espacios o divide palabras que no debía ocurrir. He podido leerlo en mi PC, pero no en el kindle.

⭐

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