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Mathematical Treasure: Johann Kandlern's Arithmetic

Frank J. Swetz (The Pennsylvania State University)

Johann Kandlern was a 16th century German rechenmeister (reckoning master) and burger (free citizen) of Regensburg. His Arithmetica (1578) was a typical German arithmetic text of the time intended mainly for use in business transactions. It included tables of monetary exchange and tariffs.

Title page from Arithmetica by Johann Kandlern, 1578

Although most computational instruction was shown using algorism, the book included some work with a table abacus as well.

Page showing table abacus calculations from Arithmetica by Johann Kandlern, 1578

The images above were obtained through the courtesy of the Erwin Tomash Library on the History of Computing, Charles Babbage Institute, University of Minnesota.

Erwin Tomash (1921-2012) was a pioneering computer scientist, helping launch the U.S. computer industry from the 1940s onward. During the 1970s he became interested in the history of computer science, and founded the Charles Babbage Society, and its research arm, the Charles Babbage Institute. The Institute, an archive and research center, is housed at the University of Minnesota. Its Erwin Tomash Library on the History of Computing began with Tomash's 2009 donation to the Institute of much of his own collection of rare books from the history of mathematics and computing. (Source: Jeffrey R. Yost, Computer Industry Pioneer: Erwin Tomash (1921-2012), IEEE Annals of the History of Computing, April-June 2013, 4-7.)

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Johann Kandlern's Arithmetic," Convergence (August 2018)