Page:A History Of Mathematical Notations Vol I (1928).djvu/41

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OLD NUMERAL SYMBOLS

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the forms occurred when the letter was a terminal letter of a word. These end forms were used as follows:

ץ ף ן ם ך
900 800 700 600 500.

To represent thousands the Hebrews went back to the beginning of their alphabet and placed two dots over each letter. Thereby its value was magnified a thousand fold. Accordingly, א߳‎ represented 1,000. Thus any number less than a million could be represented by their system.

31. As indicated above, the Hebrews wrote from right to left. Hence, in writing numbers, the numeral of highest value appeared on the right; ה߳א‎ meant 5,001, א߳ה‎ meant 1,005. But 1,005 could be written also אה‎, where the two dots were omitted, for when א‎ meant unity, it was always placed to the left of another numeral. Hence when appearing on the right it was interpreted as meaning 1,000. With a similar understanding for other signs, one observes here the beginning of an imperfect application in Hebrew notation of the principle of local value. By about the eighth century A.D., one finds that the signs הףמה‎ signify 5,845, the number of verses in the laws as given in the Masora. Here the sign on the extreme right means 5,000; the next to the left is an 8 and must stand for a value less than 5,000, yet greater than the third sign representing 40. Hence the sign for 8 is taken here as 800.[1]


GREEKS

32. On the island of Crete, near Greece, there developed, under Egyptian influence, a remarkable civilization. Hieroglyphic writing on clay, of perhaps about 1500 B.C., discloses number symbols as follows: 𐅀 or 𐄇 for 1, 𐅀𐅀𐅀𐅀𐅀 or 𐄇𐄇𐄇𐄇𐄇 or 𐄋 for 5, (Symbol missingsymbol characters) for 10, (Symbol missingsymbol characters) or (Symbol missingsymbol characters) for 100, (Symbol missingsymbol characters) for 1,000, (Symbol missingsymbol characters) for ¼ (probably), (Symbol missingsymbol characters) for 483.[2] In this combination of symbols only the additive principle is employed. Somewhat later,[3] 10 is represented also by a horizontal dash; the

  1. G. H. F. Nesselmann, Die Algebra der Griechen (Berlin, 1842), p. 72, 494; M. Cantor, Vorlesungen über Geschichte der Mathematik, Vol. I (3d ed.), p. 126, 127.
  2. Arthur J. Evans, Scripta Minoa, Vol. I (1909), p. 258, 256.
  3. Arthur J. Evans, The Palace of Minos (London, 1921), Vol. I, p. 646; see also p. 279.