The Genesis of the Algebra Textbook: From Pacioli to Euler

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.