A History of Mathematical Notations/Volume 1/Phoenicians and Syrians

by Florian Cajori

PHOENICIANS AND SYRIANS

27. The Phoenicians^[1] 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 characters), or sometimes by two strokes, thus (symbol characters). One hundred was written thus (symbol characters) or thus (symbol 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 numerals is γ for 5. Beginning with 100 the Palmyra numerals contain new forms, Placing a | to the right of the sign for 10 (see Fig. 9) signifies multiplication of 10 by 10, giving 100. Two vertical strokes || mean 10×20, or 200; three of them, 10×30, or 300.

28. Related to the Phoenician are numerals of Syria, found in manuscripts of the sixth and seventh centuries A.D. Their shapes and their mode of combination are shown in Figure 10. The Syrians employed also the twenty-two letters of their alphabet to represent the numbers 1–9, the tens 10–90, the hundreds 100–400. The following hundreds were indicated by juxtaposition: 500=400+100, 600=400+200, . . . . , 900=400+400+100, or else by writing respectively 50–90 and placing a dot over the letter to express that its value is to be taken tenfold. Thousands were indicated by the letters for 1–9, with a stroke annexed as a subscript. Ten thousands were expressed by drawing a small dash below the letters for one’s and ten’s. Millions were marked by the letters 1–9 with two strokes annexed as subscripts (i.e., 1,000×1,000=1,000,000).

Fig. 10.—Syrian numerals. (From M. Cantor, Kulturleben, etc., Fig. 49)

 

1. 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.