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

198 BRAHMGUPTA AS AN ALGEBRAIST Technical Terms Coefficient— In the ancient Indian algebra, there is no systematic term for the coefficient. Usually, the power of the unknown is men- tioned when the reference is to the coefficient of that power. At one place, for example, we find Pṛthūdaka Svāmī (the commenta- tor of Brahmagupta's Brāhmasphuṭasiddhānta) writing “the num- ber (aṅka) which is the coefficient of the square of the unknown is called the ‘square’ and the number which forms the coefficient of the (simple) unknown is called the ‘unknown quantity’ (avyakta- māna).”¹ However, at many places, we find the use of a technical term also. Brahmagupta once calls the coefficient saṁkhyā² (number) and on several other occasions guṇaka³ or guṇakāra⁴ (multiplier). Pṛtthūdaka Svāmī (860 A.D.) calls it aṅka (number) or prakṛti (multiplier). These terms may also be seen in the works of Śrīpati⁶ (1039) and Bhāskara II⁷ (1150 A.D.). The former also used the word rūpa for the same purpose.⁸ Unknown Quantity The unknown quantity has been termed as yāvat-tāvat (meaning so-much-as or as-many-as) in literature as early as 300 B. C. (vide the Sthānāṅga-sūtra⁹). In the Bakhasālī Manuscript, it has been termed as yadṛcchā, vāñchā or kāmikā (or any desired quantity)¹⁰. Āryabhaṭa I in one of his verses calls the unknown as gulikā¹¹ (literally meaning a shot) From the early seventh century A.D., the word avyakta was used for unknown quantities. Brahmagupta uses this term in his Brāhmasphuṭasiddhānta¹²

1. BrSpSi. XVIII. 44 (Com.)
2. वर्ण्यप्रमाण भावितघातो भवत्तीष्ट वर्णं संख्येवम् ! —BrSpSi. XVIII 63
3. मूलं द्विषेष्ट वर्गाद् गुणक गुणादिष्ट युत विहीनाच्च । —BrSpSi. XVIII 64 वर्गच्छिन्ने गुणके प्रथमं तन्मूल भाजितं भवति । —BrSpSi. XVIII 70
4. प्रथमोऽन्यमूलमन्यो गुणकार पदोद्धृतः प्रथमः । —BrSpSi. XVIII 69
5. BrSpSi XVIII. 44 (Com.)
6. SiSe XIV. 33-5.
7. Bījagaṇita
8. SiSe XIV. 33-5.
9. Sūtra 747.
10. BMs. Folio 22, verso; 23, recto and verso.
11. गुलिकान्तरेण विभजेद् द्वयोः ।
12. अव्यक्तवर्गं धनवर्गं वर्गपञ्चगत षड्गतादीनाम् ।