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.