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A HISTORY OF MATHEMATICAL NOTATIONS

the oldest Egyptian writing; the demotic appeared later. The Coptic writing is derived from the Greek and deinotic writing, and was used by Christians in Egypt after the third century. The Coptic numeral symbols were adopted by the Mohammedans in Egypt after their conquest of that country.

26. At the present time two examples of the old Egyptian solution of problems involving what we now term “quadratic equations”[1] are known. For square root the symbol 𓊋 has been used in the modern hieroglyphic transcription, as the interpretation of writing in the two papyri; for quotient was used the symbol (Symbol missingsymbol characters).


PHOENICIANS AND SYRIANS

27. The Phoenicians[2] represented the numbers 1–9 by the respective number of vertical strokes. Ten was usually designated by a horizontal bar. The numbers 11–19 were expressed by the juxtaposition of a horizontal stroke and the required number of vertical ones.

Fig. 9.—Palmyra (Syria) numerals. (From M. Cantor, Kulturleben, etc., Fig. 48)

As Phoenician writing proceeded from right to left, the horizontal stroke signifying 10 was placed farthest to the right. Twenty was represented by two parallel strokes, either horizontal or inclined and sometimes connected by a cross-line as in (Symbol missingsymbol characters), or sometimes by two strokes, thus (Symbol missingsymbol characters). One hundred was written thus (Symbol missingsymbol characters) or thus (Symbol missingsymbol characters). Phoenician inscriptions from which these symbols are taken reach back several centuries before Christ. Symbols found in Palmyra (modern Tadmor in Syria) in the first 250 years of our era resemble somewhat the numerals below 100 just described. New in the Palmyra numer-

  1. See H. Schack-Schackenburg, “Der Berliner Papyrus 6619.” Zeitschrift für ägyptische Sprache und Altertumskunde, Vol. XXXVIII (1900), p. 136, 138, and Vol. XL (1902), p. 65–66.
  2. Our account is taken from Moritz Cantor, Vorlesungen über Geschichte der Mathematik, Vol. I (3d ed.; Leipzig, 1907), p. 123, 124; Mathematische Beiträge zum Kulturleben der Völker (Halle, 1863), p. 255, 256, and Figs. 48 and 49.