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Mathematical Treasure: The Arithmetic of Grammateus

Frank J. Swetz (The Pennsylvania State University)

Heinrich Schreiber or Schreyber (1495–1525/26), better known as Henricus Grammateus, was a German mathematician. Grammateus taught for a period at the University of Vienna, where he had Christoff Rudolff as a pupil. His most noteworthy book was Ayn new kunstlich Buech welches gar gewiss und behind lernet nach der gemainen Regel Detre, welschen practic . . . (1518). This German-language arithmetic book contained computations with counters and figures, work in the theory of numbers, a chapter on bookkeeping, use of simple rules in algebra such as the “Rule of False Position,” and a brief treatment of the gauging of casks. Much of the mathematics was directed to the needs of merchants. The following woodcut prints are from the 1518 edition.

Title page for the arithmetic of Grammateus.

Here merchants are busy computing under the heading “Welsch practica,” literally “foreign practices,” referring to mathematical methods used by the Italians in financial matters. The phrase goes on to say “in commercial matters,” i.e. for business.

Folio from the arithmetic of Grammateus.

This print depicts the solution of an addition problem employing counters.

Folio from the arithmetic of Grammateus.

This scene shows financial transactions taking place in a cloth merchant's shop.

The images above are presented courtesy of the University of Pennsylvania Libraries.

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: The Arithmetic of Grammateus," Convergence (July 2016)