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

VARGA PRAKṚTI 245 Here in this equation the absolute number c should be rūpa (or unity). which means the equation Nx²±1=y² or it may be any absolute number. The most fundamental equation of this class has been regarded as Nx²+1=y² where N is a non-square integer. This branch of mathematics has originated from the number which is the prakṛti of the square of yāvat, etc. (the unknown x etc.), and therefore, it is called varga-prakṛti. The quantity N of the above equation is known as Prakṛti. Brahmagupta uses the term GUṆAKA (multiplier) for the same purpose¹. This term guṇaka together with its variation guṇa appears occasionally also in the writings of later authors. For example, Śrīpati (Siddhānta-śekhara. XIV. 32) employs the term guṇaka where as Bhāskara II and Nārāyaṇa use the term guṇa in their Bījagaṇitas. In this connection, we would now like to quote from Pṛthūdaka Svāmī (863 A.D.) from his commentary on the Brāhmasphuṭasiddhānta : Here are stated for ordinary use the terms which are well known to people.. The number whose square, multiplied by an optional multiplier and then increased or decreased by another optional number, becomes capable of yielding a square-root, is designated by the term the "lesser root" kaniṣṭha pada or the "first root" ādya-mūla). The root which results, after those opera- tions have been performed is called by the name the "greater root" (jyeṣṭha pada) or the "second root" (anya-mūla). If there be a number multiplying both these roots, it is called the "augmenter" (udvartaka); and on the contrary, if there be a number dividing the roots, it is called the "abridger" (apavartaka), Thus in the equation Nx²±c=y²,

1. मूलं द्विधेष्ट वर्गाद् गुणक गुणादिष्टयुत विहीनाच्च । आद्यवधो गुणकगुणः सहान्त्यघातेन कृतमन्त्यम् ॥ —BrSpSi. XVIII. 64
2. BrSpSi. XVIII. 64 (Com.)