reade. And that may appeare in all Hebrewe, Chaldaye and Arabike bookes ... where as the Greekes, Latines, and all nations of Europe, do wryte and reade from the lefte hand towarde the ryghte."^[3] Others, and

among them such influential writers as Tartaglia^[4] in Italy and Köbel^[5] in Germany, asserted the Arabic origin of the numerals, while still others left the matter undecided^[6] or simply dismissed them as "barbaric."^[7] Of course the Arabs themselves never laid claim to the invention, always recognizing their indebtedness to the Hindus both for the numeral forms and for the distinguishing feature of place value. Foremost among these writers was the great master of the golden age of Bagdad, one of the first of the Arab writers to collect the mathematical classics of both the East and the West, preserving them and finally passing them on to awakening Europe. This man was Moḥammed the Son of Moses, from Khowārezm, or, more after the manner of the Arab, Moḥammed ibn Mūsā al-Khowārazmī,^[8] a man of great

learning and one to whom the world is much indebted for its present knowledge of algebra^[9] and of arithmetic. Of him there will often be occasion to speak; and in the arithmetic which he wrote, and of which Adelhard of Bath^[10] (c. 1130) may have made the translation or paraphrase,^[11] he stated distinctly that the numerals were due to the Hindus.^[12] This is as plainly asserted by later Arab

writers, even to the present day.^[13] Indeed the phrase ‛ilm hindī, "Indian science," is used by them for arithmetic, as also the adjective hindī alone.^[14]

Probably the most striking testimony from Arabic sources is that given by the Arabic traveler and scholar Mohammed ibn Aḥmed, Abū 'l-Rīḥān al-Bīrūnī (973-1048), who spent many years in Hindustan. He wrote a large work on India,^[15] one on ancient chronology,^[16] the "Book of the Ciphers," unfortunately lost, which treated doubtless of the Hindu art of calculating, and was the author of numerous other works. Al-Bīrūnī was a man of unusual attainments, being versed in Arabic, Persian, Sanskrit, Hebrew, and Syriac, as well as in astronomy, chronology, and mathematics. In his work on India he gives detailed information concerning the language and

customs of the people of that country, and states explicitly^[17] that the Hindus of his time did not use the letters of their alphabet for numerical notation, as the Arabs did. He also states that the numeral signs called aṅka^[18] had different shapes in various parts of India, as was the case with the letters. In his Chronology of Ancient Nations he gives the sum of a geometric progression and shows how, in order to avoid any possibility of error, the number may be expressed in three different systems: with Indian symbols, in sexagesimal notation, and by an alphabet system which will be touched upon later. He also speaks^[19] of "179, 876, 755, expressed in Indian ciphers," thus again attributing these forms to Hindu sources.

Preceding Al-Bīrūnī there was another Arabic writer of the tenth century, Moṭahhar ibn Ṭāhir,^[20] author of the Book of the Creation and of History, who gave as a curiosity, in Indian (Nāgarī) symbols, a large number asserted by the people of India to represent the duration of the world. Huart feels positive that in Moṭahhar's time the present Arabic symbols had not yet come into use, and that the Indian symbols, although known to scholars, were not current. Unless this were the case, neither the author nor his readers would have found anything extraordinary in the appearance of the number which he cites.

Mention should also be made of a widely-traveled student, Al-Mas‛ūdī (885?-956), whose journeys carried him from Bagdad to Persia, India, Ceylon, and even

across the China sea, and at other times to Madagascar, Syria, and Palestine.^[21] He seems to have neglected no accessible sources of information, examining also the history of the Persians, the Hindus, and the Romans. Touching the period of the Caliphs his work entitled Meadows of Gold furnishes a most entertaining fund of information. He states