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Mathematical Treasures - Johann Neudörffer‘s Rechenbüchlein

Frank J. Swetz (The Pennsylvania State University)

Johann Neudörffer (1497–1563) was a Nuremberg reckoning and writing master who was well respected in his time. Indeed, his skills in calligraphy inspired a number of type families. The Rechenbüchlein (Plimpton MS 209) attributed to him dates from about 1530. Here is the title page for this arithmetic book, with the name of the owner—Hans Dimpfel (1510–1578) of Bavaria—at the top and the name of the author at the bottom:

Title page of arithmetic book by Johann Neudörffer, circa 1530

In the two-page selection shown below, the left page appears to contain calculations concerning monetary conversion; the right page states the “Rule of Three” (“Regula dedre”) and provides an example.

Two more pages from arithmetic book by Johann Neudörffer, circa 1530

An additional page from this text:

Page from a 16th-century German reckoning book.

A page from another copy of Neudörffer’s Rechenbuchlein (Plimpton MS 210), dated 1531, provides a table of multiplication facts and identifies the writer as a rechenmeister (as does the first image above).

Multiplication table from arithmetic book by Johann Neudörffer, 1531

The images above have been obtained through the kind cooperation of the Rare Book and Manuscript Library of the Columbia University Libraries. These and more images may be accessed via Digital Scriptorium, a digital collection of medieval and early Renaissance manuscripts made available by a consortium of cooperating university libraries headed by the University of California, Berkeley. 

A contemporary portrait of Neudörffer teaching mathematics to a young student is available via Wikimedia Commons.

Portrait of Johann Neudorffer showing a geometric figure to a child.

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasures - Johann Neudörffer‘s Rechenbüchlein," Convergence (June 2018)

Mathematical Treasures from the Smith and Plimpton Collections at Columbia University