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Mathematical Treasure: The Arithmetic of Piero Borghi

Frank J. Swetz (The Pennsylvania State University)

Piero Borghi (1424-ca.1496) was an Italian reckoning master who wrote the first influential printed commercial arithmetic book of the 15th century. While the first actual Italian printed commercial arithmetic was the Treviso Arithmetic of 1478, it did not have a large impact, whereas Borghi’s Qui comenza la nobel opera de arithmetica (1484) was well received and set a standard for later commercial arithmetics. As with many early printed books, this work contained neither a formal title nor a title page. The title as given above consists of the first words of the text: Here begins a noble work on arithmetic…. The introductory page for the 1491 edition, on which Borghi stated his purpose of writing a book for merchants, is shown below. The letters at the top of the page, SHSU, are an anagram for the name Jesus and convey the religious devotion of the author.

In his “Table of Contents,” Borghi listed several systems of measure for money, wine, oil, bread, etc.  At the bottom of the page, he designated several rules involving conversions based on proportion, beginning with “The Rule of Three” and “The Rule of Four.”

An “Index” at the end of the arithmetic supplies a further listing of topics discussed by Borghi.


These images are presented through the courtesy of the Lilly Library, Indiana University, Bloomington, Indiana.


Index to Mathematical Treasures


Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: The Arithmetic of Piero Borghi," Convergence (August 2019)