The Origin of the Problems in Euler's Algebra

Christoff Rudolff's Coss as a source Leonard Euler's Vollstandige Anleitung zur Algebra was published in two volumes by the Academy of Sciences in St- Peterburg in 1770 (2). With the exception of Euclid's Elements it is the most printed book on mathematics ((11), xxxiii). It was translated into Russian (1768-9), Dutch (1773), French (1774), Latin (1790), English (1797, 1822) and Greek (1800). One popular German edition from Reclam Verlag sold no less than 108,000 copies between 1883 and 1943 (5). Euler wrote his Algebra originally in German. Based on internal evidence, Fellmann dates the manuscript at 1765/1766 ((3), 108), when he returned from Berlin to St-Petersburg, some years before he went completely blind. In his selection of problems in the Algebra, Euler shows himself familiar with the typical recreational and practical problems of Renaissance and sixteenth-century algebra books. An extensive historical database with algebraic problems (4) imme- diately reveals Euler's use of the Stifel's edition of Rudolff's Coss for his repository of problems. This work, published 1525 in Strassburg (6), was the first German book entirely devoted to algebra. Stifel used many problems from Rudolff in his Arithmetica Integra of 1544 and found the work too important not to publish his own annotated edition (9). The first volume of Euler's Algebra on determinate equations contains 59 num- bered problems. Two thirds of these can be directly matched with the problems from Rudolff. Some are literal reproductions (see table), others were given new values or were slightly reformulated. The second part on indeterminate equations also has 59 problems and although the correlation here is manifestly lower, many problems still originate from Rudolff.