18
A HISTORY OF MATHEMATICAL NOTATIONS
the oldest Egyptian writing; the demotic appeared later. The Cop¬ tic writing is derived from the Greek and demotic 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 solu¬ tion of problems involving what we now term “quadratic equations” 1 are known. For square root the symbol IF 3 has been used in the modern hieroglyphic transcription, as the interpretation of writing in the two
papyri; for quotient was used the symbol oo .
oo
PHOENICIANS AND SYRIANS
27. The Phoenicians 2 represented the numbers 1-9 by the re¬ spective number of vertical strokes. Ten was usually designated by a horizontal bar. The numbers 11-19 were expressed by the juxtaposi¬ tion of a horizontal stroke and the required number of vertical ones.
Palxrtyrenischf Zadtlzeicken I X X) ; 3 ; /, /^3D" , 0'D n
Yirlanten >ei (iruter / V 0- t .V ; VV, Vfr*
Be dent nag 1. d Ifi. 2p 100. 110. 1000 2W.
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 H, or sometimes by two strokes, thus A- One hundred was written thus |<| or thus | £0|. Phoe¬ nician 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 fur dgyptische 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 iiber Geschichte der
Maihematik, Vol. I (3d ed.; Leipzig, 1907), p. 123, 124; Mathematische Beitrage zum Kulturleben der Volker (Halle, 1863), p. 255, 256, and Figs. 48 and 49.
