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

174 BRAHMAGUPTA AND ARITHMETIC and the form p/q + r/s of p/q + t/u of (p/q + r/s of p/q) + ......... is written as ┌───┐ │ p │ │ q │ ├───┤ │ r │ │ s │ ├───┤ │ t │ │ u │ └───┘ (iv) Bhāgāpavāha, i.e., the form (a - b/c) is written as ┌───┐ │ a │ │ .b│ │ c │ └───┘ and the form p/q - r/s of p/q - t/u of (p/q - r/s of p/q) - ........ is written as ┌───┐ │ p │ │ q │ ├───┤ │ .r│ │ s │ ├───┤ │ .t│ │ u │ └───┘ (v) Bhāga-bhāga : The form (a ÷ b/c) or (p/q ÷ r/s) There does not appear to have been any notation for divi- sion, such compounds being written as ┌───┐ ┌───┐ │ a │ │ p │ │ b │ or │ q │ │ c │ ├───┤ └───┘ │ r │ │ s │ └───┘ just as for bhāgānubandha. That division is to be performed was known from the problem, e.g., 1 ÷ 1/6 was written as ṣaḍ-bhāga- bhāga, i.e., "one-sixth bhāga-bhāga" or "one divided by one- sixth". It is only in the Bakhshālī Manuscript that the term bha is sometimes placed before or after the quantity affected. (vi) Bhāga-mātṛ, i.e., combinations of forms enumerated above. Mahāvīra, the author of the Gaṇitasārasaṃgraha (850