P. HISTORY OF ' AATHEMATICAL - School of Mathematics

OLD NUMERAL SYMBOLS 29
probably the older form. Sexagesimal fractions were used during the
whole of the Middle Ages in India, and in Arabic and Christian countries.
One encounters them again in the sixteenth and seventeenth
centuries. Not only sexagesimal fractions, but also the sexagesimal
notation of integers, are explained by John Wallis in his Matkesis
universalis (Oxford, 1657), page 68, and by V. Wing in his Astronomia
Britannica (London, 1652,1669)) Book I.
EARLY ARABS
45. At the time of Mohammed the Arabs had a script which did
not differ materially from that of later centuries. The letters of the
early Arabic alphabet came to be used as numerals among the Arabs
FIG. 14.-Arabic alphabetic numerals used before the introduction of the
Hindu-Arabic numerals.
as early as the sixth century of our era.' After the time of Mohammed,
the conquering Moslem armies coming in contact with Greek culture
acquired the Greek numerals. Administrators and military leaders
used them. A tax record of the eighth century contains numbers
expressed by Arabic letters and also by Greek letters.2 Figure 14 is
a table given by Ruska, exhibiting the Arabic letters and the numerical
values.which they represent. Taking the symbol for 1,000 twice, on
the multiplicative principle, yielded 1,000,000. The Hindu-Arabic
Julius Ruska, "Zur altesten arabischen Algebra und Rechenkunst," Sitzungsberichte
d. Heidelberger Alcademie der Wissensch. (Philcs.-histor. Klasse, 1917; 2.
Abhandlung), p. 37.
Ibid., p. 40.