ब्राह्मस्फुटसिद्धान्त (ब्रह्मगुप्त - शून्य, कुट्टक, बीजगणित एवं सम्पूर्ण २१ अध्याय सान्वय सटीक)

OPERATIONS AND DETERMINATIONS IN PĀṬĪGAṆITA 155 is found in the works of Bhāskara I about the beginning of the sixth century A.D. Thus for 3179, the expressive words are _Navādrirūpāgni_¹ (nava 9, adri 7. rupa 1 and agni 3). Similarly in the Brāhmasphuṭasiddhānta, for a large number like 2296828522, the expressive terms are DVIYAMAŚARĀṢṬAPAKṢAVASŪRA- SANAVADVIYAMĀḤ(Dviyama two twos 22, Śara 5, aṣṭa 8, pakṣa 2, vasū 8, rasa 6. nava 9, dviyamāḥ 22).² Such usages are to be found in all works, which clearly state the place value concept was popular as a routine. From India, this system reached Arabia. During the reign of the Khalif Al-Mansur (753-774 A.D.) there came embassies from Sindh to Baghdad, and among them were scholars, who brought along with them several works on mathe- matics including the Brāhmasphuṭasiddhānta and the Khaṇḍa- khādyaka of Brahmagupta: With the help of these scholars, Al- fazari, perhaps also Yakub ibn Tarik, translated them into Arabic. Both works were largely used and exercised great influence on Arab mathematics. It was on that occasion that the Arabs first became acquainted with a scientific system of astronomy. It is acceptable to all writers on the subject that it was at that time that the Hindu numerals were first definitely introduced amongst the Arabs. Arabs at first adopted the ghobar form of num- erals which they had already obtained (but without zero) from the Alexandrians or from the Syrians. This they continued for about two centuries, but since they were not suited to their right- to-left script, they gave them up and adopted the more convenient ones. For a detailed discussion on how numerals went to the west from India and spread in Europe one is referred to this dis- cussion in the History of Hindu Mathematics. Part I by Datta and Singh (1935, Single volume Edition, 1962, pp. 83-104). It is remarkable that Brahmagupta's works like the Brāhma- sphuṭasiddhānta and the Khaṇḍakhādyaka became instrumental in the spread of the place-value notation in the neighouring coun- tries of the Middle East, and from their this system spread into Europe. Operations and Determinations in Pāṭīgaṇita The word Pātīgaṇita is a compound formed from the words pāṭī, meaning 'board', and gaṇita, meaning 'science of calculation',

1. MBh. 1. 4;
2. BrSpSi 1-16.