Loyola University Chicago Loyola eCommons Classical Studies: Faculty Publications and Other Works Faculty Publications 10-2001 Literary Evidence for Roman Arithmetic with Fractions David W. Maher John F. Makowski Loyola University Chicago,
[email protected] Follow this and additional works at: https://ecommons.luc.edu/classicalstudies_facpubs Part of the Ancient History, Greek and Roman through Late Antiquity Commons Recommended Citation Maher, DW, and Makowski, JF. "Literary evidence for Roman arithmetic with fractions" in Classical Philology 96(4), 2001. 376-399. This Article is brought to you for free and open access by the Faculty Publications at Loyola eCommons. It has been accepted for inclusion in Classical Studies: Faculty Publications and Other Works by an authorized administrator of Loyola eCommons. For more information, please contact
[email protected]. This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License. © University of Chicago Press, 2001. LITERARY EVIDENCE FOR ROMAN ARITHMETIC WITH FRACTIONS DAVID W. MAHER AND JOHN F. MAKOWSKI R OMAN ARITHMETIC IS A PERENNIALLY TROUBLING subject for both classicists and mathematicians.Scholars universally comment on the difficulty posed by Roman alphabetical notation both in expres- sing simple figures and in doing written calculations. For example, Lloyd Motz and Jefferson Weaver with exasperation ask, "How ... can anyone do any arithmetic with DCCCLXXXVIII, the Roman equivalent of 888?," and Florian Cajori concludes that the Romans must have resorted to the abacus in order to multiply a number like 723 (DCCXXIII) by 364 (CCCLXIV).' Yet our sources, literary and inscriptional, indicate that the Romans were capable of highly sophisticated calculations, and, of course, it is well rec- ognized that they had great facility with the abacus and with finger reck- oning.