198 BRAHMGUPTA AS AN ALGEBRAIST 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 Prthadaka Svami (the commenta- tor of Brahmagupta's Brahmasphatasiddhanta) writing "the num- ber (anka) 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- mana)." However, at many places, we find the use of a technical term also. Brahmagupta once calls the coefficient samkhya² (number) and on several other occasions gunaka³ or gunakara (multiplier). Prtthudaka Svāmī (860 A.D.) calls it anka (number) or prakyti (multiplier). These terms may also be seen in the. works of Sripati (1039) and Bhaskara II (1150 A.D.), The former also used the word rupa for the same purpose.³ Unknown Quantity The unknown quantity has been termed as yavat-tavat (meaning so-much-as or as-many-as) in literature as early as 300 B. C. (vide the Sthananga-sutra). In the Bakhaśali Manuscript, it has been termed as yadrccha, vañcha or kamika (or any desired quantity). Aryabhata I in one of his verses calls the unknown as gulika" (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 Brahmasphutasiddhanta 1. BrSpSi. XVIII. 44 (Com.) 2. वर्णप्रमाण भावितघातो भवतीष्ट वर्ण संख्यैवम् । 3. मूलं द्विषेष्ट वर्गाद् गुणक गुणादिष्ट युत विहीनाच्च । वर्गच्छिन्ने गुणके प्रथमं तमूल भाजितं भवति । 4. प्रथमोन्य मूलमन्यो गुणकार पदोबद्धृतः प्रथमः | 5. BrSpSi XVIII. 44 (Com.) 6. Side XIV. 33-5. 7. Bijaganita 8. Side XIV. 33-5. Technical Terms 9. Sutra 747. 10. BMs. Folio 22, verso; 23; recto and verso. 11. गुलिकान्तरेण विभजेद्द्वयोः । 12: अव्यक्तवर्ग मनवर्ग वर्गपंचगत षड्गतादीनाम् । -BrSpSi. XVIII 63 -BrSpSi. XVIII 64 -BrSpSi. XVIII 70 -BrSpSi. XVIII 69
