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

204 BRAHMAGUPTA AS AN ALGEBRAIST | 0 5 yu mū 0 | sa 0 7 + mū 0 | | 1 1 1 | 1 1 1 | Here yu (यु) stands for yuta (युत), meaning added, subtraction is+sign, derived from Kṣaya or (क्षय) meaning diminished, gu (गु) for guṇa or guṇita, meaning multiplied; bhā (भा) for division from bhājita and mū (मू) for square-root, from mūla meaning root; zero (०) was used to mark a vacant place. Again, the following equation x+2x+3×3x+12×4x=300 is represented as ; | 0 | 2 1 | 3 3 | 12 4 | dṛśya 300 | 1 | 1 1 | 1 1 | 1 1 | There is no sign for unknown in the Bakhshālī Manuscript. Later on this plan of writing equations as adopted in Bakha- śālī Manuscript was abandoned in India; a new one was adopted in which the two sides are written one below the other without any sign of equality. It must be stated that in this new plan the term of similar denominations are usually written one below the other and even the terms of absent denominations on either side are clearly indicated by putting zeros as their coefficients. We find a reference to this new plan in the algebra of Brahmagupta. From which the square of the unknown and the unkno- wn are cleared, the known quantities are cleared (from the side) below that¹. Here in this verse, the words “adhastāt” clearly indicate that one side of the equation is written below the other., As an illustration, Pṛthūdaka Svāmī represented the equation² :— 10x-8=x²+1 as : ya va 0 ya 10 ru 8̇ (x².0+x.10-8) ya va 1 ya 0 rū 1 (x².1+x. 0+1) which means, x² was written as yāvat-varga (yā va) and x was written as yāvat or yā. The minus sign was represented by a dot at the top of the number.(-8 was written as 8̇). We shall take another illustration from Pṛthūdaka Svāmī. He would write the equation 197x-1644 y-z=6302 as

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1. BrSpSi. XVII. 43; compare also Bhāskara II, Bījagaṇita.
2. Br SpSi. XVIII. 49 (com.)