Capitalism and Arithmetic: The New Math of the 15th Century by Frank J. Swetz

Abstract

670 Book Reviews TECHNOLOGY AND CULTURE Capitalism, and Arithmetic: The New Math of the 15th Century. By Frank J. Swetz. Peru, Ill.: Open Court, 1987. Pp. xviii + 345; illustrations, notes, bibliography, index. $33.95 (cloth); $16.95 (paper). Despite its sweepingly broad title, Capitalism and Arithmetic is really a detailed analysis of an early arithmetic text printed in 1478 in Treviso, Italy, a town about 16 miles north of Venice. Frank J. Swetz, a historian of mathematics, stumbled across a manuscript translation of the obscure Italian book in the Columbia Library papers of David Eugene Smith, the renowned and prolific scholar of mathematics education, and decided to complete the task that Smith left unfinished eighty years earlier. The Treviso Arithmetic claims our attention be­ cause it is the earliest known printed arithmetic text in existence, and it heralded the widespread usage of arabic numerals and new, written methods of computation competing with older abacus methods in the 15th century. Further, the text was written in Venetian dialect and was aimed primarily at a commercial audience, so it provides a direct window into the mental world of Italian merchants and the ways they thought about profits and losses, partnerships and moneylending, risks and ventures. Swetz begins with a rather schematic, scene-setting chapter describ­ ing the predominance of Venice in the early rise of capitalism. He then presents the translation of the text, 135 pages long, and follows that with three solid but brief chapters explicating the fundamental operations covered by the text—numeration, addition, subtraction, multiplication, and division. The author is very familiar with other European texts of the 16th and 17th centuries and so is able to pinpoint the distinctive elements of this text. The chapter on division is particularly illuminating in its careful explanation of the galley method of long division, the main algorithm used for that operation from the 15th to the 18th centuries. Swetz makes it easy to see why long division remained a daunting and difficult subject even for those who were thoroughly comfortable with multiplication. The most potentially interesting chapters in the book are the last two. Swetz pulls apart the commercial applications presented in the text, offering the clearest explanations I have seen of the actual calculations required to figure the Rule of Three, tare and tret, partnership, and calendar reckoning, and along the way he suggests the utility of these calculations to mercantile life. In the last chapter he finally moves away from his narrow focus on arithmetic technique to consider what the Treviso Arithmetic reveals about society and culture in 15th-century Italy. Some of his observations seem mundane: for example, it is not very remarkable to conclude that word problems commonly mentioned spices, textiles, and wax because Venetian trade dealt extensively in such commodities. Other of Swetz’s observations yield more fruit—for example, his discussion of the importance of TECHNOLOGY AND CULTURE Book Reviews 671 currency exchange in international trade, and of the arithmetic and linguistic subterfuges adopted by Christian merchants to avoid the Church’s usury prohibitions. But Swetz rarely moves beyond a surface reading of the text as a mirror of its time. He sees the Italian merchants as the heroes of the story, pioneering in a “new math” just as they pioneered in opening up new trade routes. In his view, capitalism stimulated the spread of arithmetic; he does not consider the possibility that it may have been more of a two-way street. For the argument that the countinghouse was not the sole impetus to a diffusion of numeracy, readers should turn instead to the intellectually meaty chapters on “The Emergence of an Arithmetical Mentality” by Alexander Murray, in his 1978 book Reason and Society in the Middle Ages. Swetz’s Capitalism and Arithmetic is a valuable and readable analysis of Italian arithmetic techniques; it falls short, however, of fully explaining the cultural milieu that fostered the spread of numeracy. Patricia Cline Cohen Dr. Cohen, of the University of California, Santa Barbara, is the author of A Calculating People: The Spread of Numeracy in Early America (Chicago, 1982). Currently she is at work on two books concerning the history of women in 19th-century America...