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Mathematical Treasure: 15th Century Italian Arithmetic

Frank J. Swetz (The Pennsylvania State University)

An anonymous Italian arithmetic manuscript from 1473 contains an interesting composite mathematics diagram. Multiplication facts are presented in a “staircase” diagram, indicating that the author was well aware of the commutative property of the operation. Interfaced with this table is another “staircase” demonstrating place values for numbers increasing by a power of ten. For example, a number representing millions will be succeeded by six decimal places (Plimpton MS 194).

Folio 6 from a 1473 anonymous Italian arithmetic manuscript

The image above has 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. 

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: 15th Century Italian Arithmetic," Convergence (June 2018)