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34 parentheses. Through Priscian it is established that this notation is at least as old as 500 A.D.; probably it was much older, but it was not widely used before the Middle Ages.

54. While the Hindu-Arabic numerals became generally known in Europe about 1275, the Roman numerals continued to hold a commanding place. For example, the fourteenth-century banking-house of Peruzzi in Florence—Compagnia Peruzzi—did not use Arabic numerals in their account-books. Roman numerals were used, but the larger amounts, the thousands of lira, were written out in words; one finds, for instance, “lb. quindicimilia CXV V  VI in fiorini” for 15,115 lira 5 soldi 6 denari; the specification being made that the lira are lira a fiorino d’oro at 20 soldi and 12 denari. There appears also a symbol much like, for thousand.

Nagl states also: “Specially characteristic is. . . . during all the Middle Ages, the regular prolongation of the last I in the units, as, which had no other purpose than to prevent the subsequent addition of a further unit.”

55. In a book by H. Giraua Tarragones at Milan the Roman numerals appear in the running text and are usually underlined; in the title-page, the date has the horizontal line above the numerals. The Roman four is IIII. In the tables, columns of degrees and minutes are headed “G.M.”; of hour and minutes, “H.M.” In the tables, the Hindu-Arabic numerals appear; the five is printed, without the usual upper stroke. The vitality of the Roman notation is illustrated further by a German writer, Sebastian Frank, of the sixteenth century, who uses Roman numerals in numbering the folios of his book and in his statistics: “Zimmet kumpt von Zailon .CC.VÑ LX. teütscher meil von Calicut weyter gelegen. . . . . Die Nägelin kummen von Meluza / für Calicut hinaussgelegen vij·c. vnd XL. deutscher meyl.” The two numbers given are 260 and 740 German miles. Peculiar is the insertion of vnd (“and”). Observe also the use of the principle of multiplication in vij·c. (=700). In Jakob Köbel’s Rechenbiechlin (Augsburg, 1514), fractions appear in Roman numerals; thus, $\overline{M.D.LVI}$ stands for $IIC⁄IIIIC.LX$.