Article ID: CBB001320800

The Genesis of the Algebra Textbook: From Pacioli to Euler (2012)


Heeffer, Albrecht (Author)

Volume: 3, no. 1
Issue: 1
Pages: 26-61

Euler's Vollständige Anleitung zur Algebra (1770) is the prototype of a successful textbook on elementary algebra. The selection of problems by Euler displays a great familiarity with the typical recreational and practical problems of Renaissance and 16th-century algebra books. A detailed study into the sources of Euler revealed that he copied most of his problems from Christoff Rudolff's Coss, which was first published in 1525 and reissued in 1553 by Michael Stifel. Why would Euler found his popular textbook on algebra on a book published 250 years earlier? Part of the motivation could be sentimental. Euler was taught mathematics by his father using Stifel's edition of the Coss, and the young Euler spent several years studying the problems from the book. However, we propose an explanation based on the evolving rhetorical function of problems in algebra textbooks since the first printed book on algebra by Pacioli (1494). We discern six stages in the evolution from abbacus problem solving to algebraic theory. The first theory emerged through the extraction of general principles from the practice of problem solving. The algebra textbooks of the 18th century close a circle of continuous rhetorical development by using problems for practicing general principles and applying the algebraic language. Euler's Algebra is a prime example of the new rhetoric of problems still prominent in today's textbooks.

Citation URI

Similar Citations

Article Kastanis, Iason; Kastanis, Nikos; (2006)
The Transmission of Mathematics into Greek Education, 1800--1840: From Individual Initiatives to Institutionalization (/isis/citation/CBB001023840/)

Article Sabine Rommevaux–Tani; (2016)
Michael Stifel, lecteur de la "Practica arithmetice" de Gerolamo Cardano (/isis/citation/CBB465327452/)

Article Barrow-Green, June; (2010)
Euler as an Educator (/isis/citation/CBB000933565/)

Article Frejda, Peter; (2013)
Old Algebra Textbooks: A Resource for Modern Teaching (/isis/citation/CBB001212297/)

Chapter Andrea Bréard; Annick Horiuchi; (2014)
History of Mathematics Education in East Asia in Premodern Times (/isis/citation/CBB183789002/)

Chapter João Pedro da Ponte; Henrique Manuel Guimarães; (2014)
Notes for a History of the Teaching of Algebra (/isis/citation/CBB829555358/)

Article Shahidi, Mahmoud; (2013)
Conics in Mathematical Textbooks of Contemporary Educational System of Iran (/isis/citation/CBB001510302/)

Article Brueckler, Franka Miriam; Stilinovi, Vladimir; (2013)
Teaching Arithmetic in the Habsburg Empire at the End of the 18th Century---A Textbook Example (/isis/citation/CBB001320311/)

Book Ellerton, Nerida F.; Clements, M. A.; Kilpatrick, Jeremy; (2012)
Rewriting the History of School Mathematics in North America, 1607--1861: The Central Role of Cyphering Books (/isis/citation/CBB001550656/)

Article Spalt, Detlef D.; (2011)
Welche Funktionsbegriffe gab Leonhard Euler? (/isis/citation/CBB001036227/)

Article Esteve, M<sup>a</sup> Rosa Massa; Delshams, Amadeu; (2009)
Euler's Beta Integral in Pietro Mengoli's Works (/isis/citation/CBB000932080/)

Book Koetsier, Teun; Bergmans, Luc; (2005)
Mathematics and the Divine: A Historical Study (/isis/citation/CBB000500288/)

Article Jeffrey A. Oaks; (2017)
Irrational “Coefficients” in Renaissance Algebra (/isis/citation/CBB825969502/)

Article Fàtima Romero-Vallhonesta; M. Rosa Massa-Esteve; (2018)
The Main Sources for the Arte Mayor in Sixteenth Century Spain (/isis/citation/CBB497329553/)

Article Rommevaux-Tani, Sabine; (2014)
Irrationalité des nombres, irrationalité des lignes selon Michael Stifel et Simon Stevin (/isis/citation/CBB001550678/)

Article Bullynck, Maarten; (2010)
Factor Tables 1657--1817, with Notes on the Birth of Number Theory (/isis/citation/CBB001033636/)

Book Brummelen, Glen Van; Kinyon, Michael; (2005)
Mathematics and the Historian's Craft: The Kenneth O. May Lectures (/isis/citation/CBB001023435/)

Authors & Contributors
Bergmans, Luc
Koetsier, Teunis
Thiele, Rüdiger
Rommevaux-Tani, Sabine
Brouwer, Luitzen E. J.
Harmsen, Ger
British Society for the History of Mathematics Bulletin
Revue d'Histoire des Mathématiques
Historia Mathematica
Llull: Revista de la Sociedad Española de Historia de las Ciencias y de las Técnicas
Kritiki: Critical Science & Education
Archive for History of Exact Sciences
Mathematics education
Science education and teaching
Euler, Leonhard
Stifel, Michael
Cardano, Girolamo
Rudolff, Christoff
Cusanus, Nicolaus
Faulhaber, Johann
Time Periods
18th century
19th century
17th century
16th century
Prussia (Germany)
Jesuits (Society of Jesus)
Panepistēmio Athēnōn

Be the first to comment!

{{ comment.created_by.username }} on {{ comment.created_on | date:'medium' }}

Log in or register to comment