The Genesis of the Algebra Textbook: From Pacioli to Euler (2012)
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.
...MoreSimilar Citations
Article
Noël Golvers;
(2017)
Antoine Thomas, SJ, and his Synopsis Mathematica: Biography of a Jesuit Mathematical Textbook for the China Mission
(/isis/citation/CBB720799742/)
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
Blanco, Mónica;
(2007)
Análisis comparativo de la comunicación del cálculo diferencial en el siglo XVIII: la educación militar en Francia y Prusia
(/isis/citation/CBB000930377/)
Article
Terdimou, Maria;
(2007)
Geometry Versus Algebra. Ancient Greek and Western Mathematics:Parallel or Intersecting Options by the Greek Scholars of the 18th Century?
(/isis/citation/CBB000931865/)
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/)
Be the first to comment!