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.