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Mathematical Treasures - Pacioli's Summa

Frank J. Swetz and Victor J. Katz


This is the title page of the Summa de arithmetica, geometria, proportioni et proportionalita, published by Luca Pacioli (1445-1509) in 1494. This was the most comprehensive mathematical text of the time and one of the earliest printed mathematical works. It contained not only practical arithmetic, but also algebra, practical geometry and the first published treatment of double-entry bookkeeping.

Reverse of title page

This page is the reverse of the title page. A translation of this page would be valuable.


Above: On this page (f. 36v) Pacioli illustrates one of the methods of finger counting prevalent at his time in Italy.

Editor's note: The images above, from Columbia University Library's David Eugene Smith and George Arthur Plimpton collections, were posted on 5/14/2008. The images below, obtained through the courtesy of the Dibner Library of Science and Technology, Smithsonian Libraries, were added on 5/14/2017.

The opening page of text in the Summa discusses the properties of numbers:

Pacioli considered constructions involving the geometrical inscription of various figures within a given circle:

For additional images from Pacioli’s Summa, see the Convergence article, Mathematical Treasure: Luca Pacioli's Summa, by Cynthia J. Huffman. The Summa can be viewed in its entirety on Google Books.

Index to the Collection of Mathematical Treasures from the David Eugene Smith and George Arthur Plimpton collections, Columbia University Library

Index to the Convergence Collection of Mathematical Treasures

Frank J. Swetz and Victor J. Katz, "Mathematical Treasures - Pacioli's Summa," Convergence (January 2011)

Mathematical Treasures from the Smith and Plimpton Collections at Columbia University