Review of Capitalism and Arithmetic

Frank J. Swetz's Capitalism and Arithmetic is a translation of the Trevisio Arithmetic by an unknown Italian teacher of arithmetic. (The translation is by David Eugene Smith, and there is a thoughtful tribute to him in the book.)

The Trevisio was a rather ordinary book teaching students, mostly merchants how to compute using addition, subtraction, division, multiplication, basic fractions, and the like.

It is historically interesting because we find a lot of mathematical techniques whose import we may not have otherwise been aware. Granted, it makes dull reading if you already know arithmetic through long division, but it does give us a few interesting clues about the life and times of the book.

Mathematically, I never realized how important some of these computing rules, like "casting out nines", or "the rule of three" were. Culturally, we can see the influence on banking and trade on the style of arithmetic and other areas of life. By merely looking at the examples, we can tell what was important to the culture, and money was certainly important.

There is also a good chunk of analysis and historical background thrown in.

The book is probably of interest to people who study the history of mathematics education, and the history of old reckoning books.