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A HISTORY OF MATHEMATICAL NOTATIONS

sloping line indicative of 100 and the lozenge-shaped figure used for 1,000 were replaced by the forms O for 100, and X for 1,000.


XX  OO     OO        ||  ||  ||   stood for 2,496.


33. The oldest strictly Greek numeral symbols were the so-called Herodianic signs, named after Herodianus, a Byzantine grammarian of about 200 A.D., who describes them. These signs occur frequently in Athenian inscriptions and are, on that account, now generally called Attic. They were the initial letters of numeral adjectives.[1] They were used as early as the time of Solon, about 600 B.C., and continued in use for several centuries, traces of them being found as late as the time of Cicero. From about 470 to 350 B.C. this system existed in competition with a newer one to be described presently. The Herodianic signs were

𐅂 Iota for 1
Π or 𐅃 or 𐅃 Pi for 5
Δ Delta for 10
Η Eta for 100
Χ Chi for 1,000
Μ My for 10,000

34. Combinations of the symbols for 5 with the symbols for 10, 100, 1,000 yielded symbols for 50, 500, 5,000. These signs appear on an abacus found in 1847, represented upon a Greek marble monument on the island of Salamis.[2] This computing table is represented in Figure 12.

The four right-hand signs Ι Ϲ Τ Χ, appearing on the horizontal line below, stand for the fractions 1/4, 1/12, 1/24, 1/48, respectively. Proceeding next from right to left, we have the symbols for 1, 5, 10, 50, 100, 500, 1,000, 5,000, and finally the sign Τ for 6,000. The group of symbols drawn on the left margin, and that drawn above, do not contain the two symbols for 5,000 and 6,000. The pebbles in the columns represent the number 9,823. The four columns represented by the five vertical lines on the right were used for the representation of the fractional values 1/4, 1/12, 1/24, 1/48, respectively.

35. Figure 13 shows the old Herodianic numerals in an Athenian state record of the fifth century B.C. The last two lines are: Κεφάλαιον

  1. See, for instance, G. Friedlein, Die Zahlzeichen und das elementare Rechnen der Griechen und Römer (Erlangen, 1869), p. 8; M. Cantor, Vorlesungen über Geschichte der Mathematik, Vol. I (3d ed.), p. 120; H. Hankel, Zur Geschichte der Mathematik im Alterthum und Mittelalter (Leipzig, 1874), p. 37.
  2. Kubitschek, “Die Salaminische Rechentafel,” Numismatische Zeitschrift (Vienna, 1900), Vol. XXXI, p. 393–98; A. Nagl, ibid., Vol. XXXV (1903), p. 131–43; M. Cantor, Kulturleben der Völker (Halle, 1863), p. 132, 136; M. Cantor, Vorlesungen über Geschichte der Mathematik, Vol. I (3d ed), p. 133.