Elements of Algebra

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Elements of Algebra is an elementary mathematics textbook written by mathematician Leonhard Euler and originally published in 1765 in German. Elements of Algebra is one of the earliest books to set out algebra in the modern form we would recognize today (another early book being Elements of Algebra by Nicholas Saunderson, published in 1740), and is one of Euler's few writings, along with Letters to a German Princess, that are accessible to the general public. Written in numbered paragraphs as was common practice till the 19th century, Elements begins with the definition of mathematics and builds on the fundamental operations of arithmetic and number systems, and gradually moves towards more abstract topics.

In 1771, Joseph-Louis Lagrange published an addendum titled Additions to Euler's Elements of Algebra, which featured a number of important mathematical results.

The original German title of the book was Vollständige Anleitung zur Algebra, which literally translates to Complete Instruction to Algebra. Two English translations are now extant, one by John Hewlett (1822), and the other, which is translated to English from a French translation of the book, by Charles Tayler (1824). On the 300th birth anniversary of Euler in 2007, mathematician Christopher Sangwin working with Tarquin Publications published a digitized copy of the first four sections (or Part I) of the book in customizable font.[1] This digitized copy, which is based on Hewlett's translation, is the most reader-friendly version of Elements of Algebra.

In 2015, Scott Hecht published both print and Kindle versions of Elements of Algebra (ISBN-13: 978-1508901181). This version 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.


  1. ^ Sangwin, Christopher. "Elements of Algebra". 

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