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 Mathesis universalis (Oxford, 1657), page 68, and by V. Wing in his Astronomia Britannica (London, 1652, 1669), Book I.
EARLY ARABS
| 1 | ا | 10 | ی | 100 | ق | 100 | غ | 10 000 | یغ | 100 000 | قغ |
| 2 | ب | 20 | ك | 200 | ر | 200 | بغ | 20 000 | كغ | 200 000 | رغ |
| 3 | ج | 30 | ل | 300 | ش | 300 | جغ | 30 000 | لغ | 300 000 | شغ |
| 4 | د | 40 | م | 400 | ت | 400 | دغ | 40 000 | مغ | 400 000 | تغ |
| 5 | ه | 50 | ن | 500 | ث | 500 | هغ | 50 000 | نغ | 500 000 | ثغ |
| 6 | و | 60 | س | 600 | خ | 600 | وغ | 60 000 | سغ | 600 000 | خغ |
| 7 | ز | 70 | ع | 700 | ذ | 700 | زغ | 70 000 | عغ | 700 000 | ذغ |
| 8 | ح | 80 | ف | 800 | ض | 800 | حغ | 80 000 | فغ | 800 000 | ضغ |
| 9 | ط | 90 | ص | 900 | ظ | 900 | طغ | 90 000 | صغ | 900 000 | ظغ |
Fig. 14.—Arabic alphabetic numerals used before the introduction of the Hindu-Arabic numerals.
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 as early as the sixth century of our era.[1] 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
