>I have recently been asked how the Romans computed with Roman numerals. I >don't know the answer. Is there a good reference? My guess is that they >didn't.
"It is widely believed that calculation with Roman numerals is a primitive process, so clumsy that operations beyond simple addition and subtraction become almost impossible. [...] On the contrary, the Roman system incorporates features permitting algorithms that make multiplication and division even easier than in our place value decimal system, as will be demonstrated here." [Kennedy, James G.: "Arithmetic with Roman numerals, AMM, vol. 88, pp. 29-32, January 1981.]
>Instead they just used an abacus (the Britannica has a photo of >one from Roman times.) In any case there ought to be extant evidence, >since Arabic numerals weren't introduced before 1200.
"The intimite connection between Roman numerals and the abacus has often been noted. It may be described by saying that the Roman numeral for a number describes the state of an abacus when it represents that number, the number of ocurrences of each simple numeral corresponding to the number of counters at play in the appropiate columns of an abacus when it represents that number." [Detlefsen M., Erlandson D. K., Heston J. C., Young. C. M.: "Computation with Roman Numerals", AHES, vol. 15, (2), pp. 141-148, 1976.]
See those in Georges Ifrah's bibliography (pp. 499-502): "From one to zero. A universal history of numbers", NY: Viking Penguin Inc., XVI, 503 pp., 1985.
Friedlein Gottfried: "Die Zahlzeichen und das elementare Rechnen der Griechen und Romer und des christlichen Abendlandes vom 7. bis 13. Jahrhundert", Erlangen, 1869.
Taisbak Christian Marinus: "Roman Numerals and the Abacus", Classica et Mediaevalia, Vol. 26, 1965. Journal of philology and history on Graeco-Roman Antiquity and the Middle Ages. ISSN 0106-5815.
Giacardi Livia & Roero Clara S.: "L'origine della numerazione romana : un'ipotesi di Giuseppe Nicasi sul modo di contare dei contadini di Morra; con una nota di M. Raffaella Trabalza, Foligno: Edizioni dell'Arquata, 109 pp., 1987. Series: Centro studi "Cristiano Mancini" per la storia del pensiero matematico; 1.