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

TECHNICAL TERMS 199 Power Since long, the word varga has been used for the second power; the word also stands for square (Uttarādhyayana Sūtra¹, B. C. c. 300). The third power is similarly known as ghana, the fourth power as varga-varga (square-square), the sixth power as ghana-varga (cube-square) and the twelfth power as ghana-varga- varga (cube-square-square). In later days, the fifth power was called vargaghana ghāta (here the word ghāta means product; the term means product of cube and square). The former system was multiplicative, rather than additive; wheras the latter was on the additive system. The seventh power on the additive system was known as varga-varga-ghana-ghāta (product of square-square and cube). Brahmagupta, however, uses a more scientific system for expressing the powers more than four. He calls the fifth power as Pañca gata (literally meaning, raised to the fifth), the sixth power as ṣaḍ-gat (raised to the sixth) and so on, thus adding the suffix gata to the name of the number indicating that power.² Bhāskara II has followed the system of Brahmagupta almost consi- stently for powers one and upwards. Equation Perhaps Brahmagupta has for the first time used the term samakaraṇa or samīkaraṇa (literally meaning making equal) or simply sama (equal or equation)³. Pṛthūdaka Svāmī (860) employs the term sāmya (equality or equation) for equation⁴. The equation is said to possess two Pakṣas⁵ (sides) Itara-Pakṣa and apara-pakṣa. Absolute Term Brahmagupta uses the term rūpa (literally meaning appear- ance) for an absolute term. It represents the visible or known

1. Chapter XXX, 10, 11.
2. अव्यक्तवर्गे घनवर्ग-वर्ग-पंचगत-षड्गतादीनाम् । सदृश द्विवधो वर्गस्त्यादि वधस्तद्गतोऽन्य जातिवधः ॥
3. वर्णं प्रमाण भावित-घातो भवतीष्टवर्ण संख्यैवम् । सिध्यति विनाऽपि भावित-समकरणात् किं कृतं तदतः ॥ अव्यक्तान्तर भक्तं व्यस्तं रूपान्तरं समेऽव्यक्तः ।
4. Siśe. XIV, 19.
5. Bījagaṇita.