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

CHAPTER VIII
Brahmagupta
and Arithmetic
Scope of Gaṇita
The word Gaṇita means the science of calculation. The
term occurs in the Vedāṅga Jyautiṣa (c. 1200 B. C.) :
Just as the crest is to the peacocks, and just as the head-
gem is to the snakes, so the Gaṇita among the Vedāṅga
Śāstras stands at the head.¹ (VJ. 4)
In the ancient Buddhistic literature, we find mention of
three classes of gaṇita : (i) mudrā (finger arithmetic). (ii)
gaṇana (mental arithmetic), and (iii) saṅkhyāna (higher arith-
metic in general). In the Brāhmasphuṭasiddhānta, Brahmagupta
uses the word gaṇita in the sense of entire calculations. His
gaṇitādhyāya (Chapter XII) includes ;
(i) Miśraka (mixtures). (ii) Śreḍhī (series). (iii) Kṣetra
plane figures), (iv) Vṛtta-kṣetra (circles), (v) Khāta (ex-
cavations), (vi) Citi (piles of bricks), (vii) Krākacika
(sawn pieces of timber), (viii) Rāśi (heaps or mounds of
grain, and (ix) Chāya (shadow).
Brahmagupta also uses the term Dhūlīkarma (literally meaning
“ʇsnpwork”) for higher mathematics :
The one learned man who knows the dhūlīkarma or the
science of mathematics as propounded by Brahmagupta
would far excell them in learning who are taught the
calculations according to Āryabhaṭa, Viṣṇucandra and
others.²
In these ten chapters of the Brahmasiddhānta has been
given the dhūlīkarma or the science of entire calculations

1. यथा शिखा मयूराणां नागानां मणयो यथा ।
   तद् वद् वेदांग-शास्त्राणां गणितं मूर्धनि स्थितम् ॥ VJ. 4.
2. नावायों ज्ञातेरपि तन्त्रैरार्यभटविष्णुचन्द्राद्यैः ।
   यो ब्रह्म धूलिकर्मविदाचार्यत्वं भवति तस्य ॥ —BrSpSi. X. 62.