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30

A HISTORY OF MATHEMATICAL NOTATIONS

numerals, with the zero, began to spread among the Arabs in the ninth and tenth centuries, and they slowly displaced the Arabic and Greek numerals.[1]


ROMANS

40. We possess little definite information on the origin of the Roman notation of numbers. The Romans never used the successive letters of their alphabet for numeral purposes in the manner practiced by the Syrians, Hebrews, and Greeks, although (as we shall see) an alphabet system was at one time proposed by a late Roman writer. Before the ascendancy of Rome the Etruscans, who inhabited the country nearly corresponding to modern Tuscany and who ruled in Rome until about 500 B.C., used numeral signs which resembled letters of their alphabet and also resembled the numeral signs used by the Romans. Moritz Cantor[2] gives the Etrurian and the old Roman signs, as follows: For 5, the Etrurian 𐌡 or (Symbol missingsymbol characters), the old Roman V; for 10 the Etrurian 𐌢 or (Symbol missingsymbol characters), the old Roman X; for 50 the Etrurian 𐌣 or ↆ, the old Roman (Symbol missingsymbol characters) or ↆ or (Symbol missingsymbol characters) or Ʇ or L; for 100 the Etrurian (Symbol missingsymbol characters), the old Roman (Symbol missingsymbol characters); for 1,000 the Etrurian 𐌚, the old Roman ↀ. The resemblance of the Etrurian numerals to Etrurian letters of the alphabet is seen from the following letters: 𐌖, 𐌗, 𐌣, 𐌏, 𐌚. These resemblances cannot be pronounced accidental. “Accidental, on the other hand,” says Cantor, “appears the relationship with the later Roman signs, I V, X, L, C, M, which from their resemblance to letters transformed themselves by popular etymology into these very letters.” The origins of the Roman symbols for 100 and 1,000 are uncertain; those for 50 and 500 are generally admitted to be the result of a bisection of the two former. “There was close at hand,” says G. Friedlein,[3] “the abbreviation of the word centum and mille which at an early age brought about for 100 the sign C, and for 1,000 the sign ʍ and after Augustus[4] M.” A view held by some Latinists[5] is that “the signs for 50, 100, 1,000 were originally the three Greek aspirate letters which the Romans did not require, viz., Ψ, (Symbol missingsymbol characters), i.e., χ, θ, . The Ψ was written Ʇ and abbreviated into L; (Symbol missingsymbol characters) from a false notion of its origin made like

  1. Ibid., 47.
  2. Vorlesungen über Geschichte der Mathematik, Vol. I (3d ed.), p. 523, and the table at the end of the volume.
  3. Die Zahlzeichen und das elementare Rechnen der Griechen und Römer (Erlangen, 1869), p. 28.
  4. Theodor Mommsen, Die unteritalischen Dialekte (Leipzig, 1840), p. 30.
  5. Ritschl, Rhein. Mus., Vol. XXIV (1869), p. 12.