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{{Short description|Landmark mathematics textbook by Leonhard Euler}}
{{Use dmy dates|date=April 2012}}▼
{{italic title}}
'''''Elements of Algebra''''' is an [[elementary mathematics]] textbook writte 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.▼
[[File:Elements of algebra (IA elementsofalgebr00eule).pdf|page=7|alt=Elements of Algebra title page|thumb|The title page of ''Elements of Algebra'']]
▲{{Use dmy dates|date=April 20122022}}
▲'''''Elements of Algebra''''' is an [[elementary mathematics]] textbook writtewritten by mathematician [[Leonhard Euler]] andaround originally1765 in German. It was first published in 1765Russian as "''Universal Arithmetic''" (''Универсальная арифметика''), two volumes appearing in German1768-9<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 aan follow-upaddendum volume entitledtitled ''[[Additions to Euler's Elements of algebra]]Algebra'', which featured a number of important mathematical results.▼
The original German title of the book is ''Vollständige Anleitung zur Algebra'', which literally translates to ''Complete Instruction to Algebra''. Two English translations are now extant, one by John Hewlett, and the other, which is translated to English from a French translation of the book, by Charles Tayler. On the 300th birth anniversary of Euler, mathematician Christopher Sangwin working with Tarquin Publications published a digitized copy of the first four parts of the book in customizable font. This digitized copy, which is based on Hewlett's translation, is the most reader-friendly version of ''Elements of Algebra''.
 
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 1771, [[Joseph-Louis Lagrange]] published a follow-up volume entitled ''[[Additions to Euler's Elements of algebra]]'', which featured a number of important mathematical results.
 
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 ==
* [httphttps://books.google.com/books?id=X8yv0sj4_1YC&dq=euler+elements+of+algebra&printsec=frontcover&source=bn&hl=en&ei=KiwwS8bdEcutlAe2waCoBw&sa=X&oi=book_result&ct=result&resnum=5&ved=0CCQQ6AEwBA#v=onepage&q=&f=false ''Elements of Algebra''], 1822, Full text
* [https://web.archive.org/web/20110611025755/http://web.mat.bham.ac.uk/C.J.Sangwin/euler/indexElementsAlgebra.html About the ''Elements of Algebra'', Part I], HTML
* [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'']
 
* [http://eulerarchive.org Among other writings of Euler]
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[[Category:Mathematics textbooks]]
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