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{{Short description|Landmark mathematics textbook by Leonhard Euler}}
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[[File:Elements of algebra (IA elementsofalgebr00eule).pdf|page=7|alt=Elements of Algebra title page|thumb|The title page of ''Elements of Algebra'']]
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'''''Elements of Algebra''''' is an [[elementary mathematics]] textbook written by mathematician [[Leonhard Euler]] around 1765 in German. It was first published in Russian as "''Universal Arithmetic''" (''Универсальная арифметика''), two volumes appearing in 1768-9<ref>Эйлер, Л. ''Универсальная арифметика г. Леонгарда Эйлера''. Переведенная с немецкого подлинника студентами Петром Иноходцовым и Иваном Юдиным. Том 1, содержащий в себе все образы алгебраического вычисления. – СПб. : Имп. АН, 1768. – 8, 376 c.</ref> and in 1770 was printed from the original text. ''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
The original German title of the book was ''Vollständige Anleitung zur Algebra'', which literally translates to ''Complete Instruction to Algebra''.<ref>{{Cite web |last1=Euler |first1=Leonhard |author-link=Leonhard Euler |last2=Joseph-Louis |first2=Lagrange |author-link2=Joseph-Louis Lagrange |last3=Johann |first3=Bernoulli |author-link3=Johann Bernoulli |date=1771 |title=Vollständige Anleitung zur Algebra |url=https://www.digitale-sammlungen.de/de/view/bsb10081749?page=,1 |website=Bayerische Staatsbibliothek |publisher=Kayserliche Academie der Wissenschaften |pages=first part: VII pages, 256 pages, second part: I page, 384 pages; 8 pages appendix |publication-place=St. Petersburg |no-pp=y}}</ref> Two English translations are now extant, one by [[John Hewlett]] (1822),<ref>{{Cite web |last1=Euler |first1=Leonhard; [translated by John Hewlett] |author-link=Leonhard Euler |last2=Lagrange |first2=Joseph-Louis |author-link2=Joseph-Louis Lagrange |year=1828 |title=Elements of Algebra |url=https://archive.org/details/elementsofalgebr00eule/page/n5/mode/2up?q=ber&view=theater |publisher=Ongman, Rees, Orme, and Co. |publication-place=London}}</ref> 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 based on Hewlett's translation of the first four sections (or Part I) of the book.<ref>{{cite web|last1=Sangwin|first1=Christopher|title=Elements of Algebra|url=http://web.mat.bham.ac.uk/C.J.Sangwin/Publications/index.html#euler|access-date=1 August 2014|archive-url=https://web.archive.org/web/20160916180514/http://web.mat.bham.ac.uk/C.J.Sangwin/Publications/index.html#euler|archive-date=16 September 2016|url-status=dead}}</ref>
In 2015, Scott Hecht published both print and Kindle versions of ''Elements of Algebra'' ({{isbn|978-1508901181}}) with Euler's Part I (Containing the Analysis of Determinate Quantities), Part II (Containing the Analysis of Indeterminate Quantities), Lagrange's Additions, and footnotes by Johann Bernoulli and others.<ref>{{Cite web |last1=Euler |first1=Leonhard |author-link=Leonhard Euler |last2=Lagrange |first2=Joseph-Louis |author-link2=Joseph-Louis Lagrange |last3=Bernoulli |first3=Johann |author-link3=Johann Bernoulli |date=2015 |editor-last=Hecht |editor-first=Scott L. |title=Elements of Algebra |url=https://archive.org/details/ElementsOfAlgebraLeonhardEuler2015/page/2/mode/thumb |publisher=CreateSpace, Inc. & Kindle Direct Publishing, Divisions of Amazon.com |isbn=}}</ref>
==See also==
* [[Introductio in analysin infinitorum]] (1748)
* [[Institutiones calculi differentialis]] (1755)
==References==
{{Reflist}}
== External links ==
* [
* [https://web.archive.org/web/20110611025755/http://web.mat.bham.ac.uk/C.J.Sangwin/euler/ElementsAlgebra.html ''Elements of Algebra'', Part I], HTML
* [http://logica.ugent.be/albrecht/thesis/EulerProblems.ps The origin of the problems in Euler's ''Algebra'']
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[[Category:Mathematics books]]▼
[[Category:1760s books]]
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