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

200 BRAHMAGUPTA AS AN ALGEBRAIST portion of the equation whilst its other part is practically invisible or unknown¹. Unknowns and Symbolism Āryabhaṭa I (499 A. D.) probably used coloured gulikās or shots for represtnting different unknowns. Brahmagupta men- tions varṇa as the symobls for unknown. He has, however, not indicated how these varṇas or colours were used as symbols for unknowns. Perhaps we might conculude from this that the method of using colours as symbols for unknown quantities was very common and familiar to the algehraists. Datta and Singh say that the Sanskrit word varṇa denotes colour as well as a letter of alphabet, and therefore, letters of alphabet came into use for unknown quantities : kālaka (black), nīlaka (blue), pītaka (yellow), lohita (red), haritaka (green), śvetaka (white), citraka (variegated), kapilaka (tawny), piṅgalaka (reddish-brown), dhūmraka (smoke- coloured), pāṭalaka (pink), śavalaka (spotted), śyāmalaka (blackish) mecaka (dark blue) etc². It should be further noted that the first unknown quantity yāvat-tāvat is not a varṇa or colour. It thus clearly indicates that the use of colours as symbols came at a later stage, whilst the word yāvat-tāvat was in currency from much earlier times. Some authorities think that the term yāvat-tāvat is a corrupted form of yāvakastāvat (where yāvaka means red). Pṛthūdaka Svāmī has sometimes used the term yāvaka for an unknown quantity³. Laws of Signs Brahmagupta has in his Chaper XVIII devoted a special section entitled "Dhanarṇa Śunyānāṁ Saṁkalanam" or calcu- lations dealing with quantities bearing positive and negative signs and zero,

1. अव्यक्तान्तरं भक्तं व्यस्तं रूपान्तरं समेऽव्यक्तः । —BrSpSi XVIII. 43 वर्गे चतुर्गुणितानां रूपाणां मध्यवर्गे सहितानाम् ॥ —BrSpSi XVIII. 44
2. यावत्-तावत् कालको नीलकोऽन्यो वर्णः पीतो लोहितश्चैतदाद्याः । अव्यक्तानां कल्पिता मानसंज्ञास्तत्संख्यानं कर्तुंमाचार्यवर्यैः ॥ यावत्-तावत् कालक नीलक पीताश्च लोहितो हरितः । श्वेतक चित्रक कपिलक पाटलकाः पण्डु धूम्र शवलाश्च ॥ श्यामलक-मेचक-धवलक-पिशङ्ग-शारङ्ग-बभ्रु-गौराद्याः । —Nārāyaṇa, Bījagaṇita
3. BrSpSi XII, 15. (Com.) ; XII 18.