Page:A History Of Mathematical Notations Vol I (1928).djvu/54

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A HISTORY OF MATHEMATICAL NOTATIONS

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 (Symbol missingsymbol characters) V (Symbol missingsymbol characters) 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 (Symbol missingsymbol characters), for thousand.[1]

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

55. In a book by H. Giraua Tarragones[2] 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 (Symbol missingsymbol characters), 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.”[3] 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, IIC/IIIIC.LX stands for 200/460.

  1. Alfred Nagl, Zeitschrift für Mathematik und Physik, Vol. XXXIV (1889), Historisch-literarische Abtheilung, p. 164.
  2. Dos Libros de Cosmographie, compuestos nueuamente por Hieronymo Giraua Tarragones (Milan, M.D.LVI).
  3. Weltbůch / spiegel vnd bildtnis des gantzen Erdtbodens . . . . von Sebastiano Franco Wördernsi . . . . (M.D. XXXIIII), fol. ccxx.