BRAHMAGUPTA AS AN ALGEBRAIST Brahmagupta lays down the rules regarding evolution and involution as follows: 202 The square of a positive or a negative number is positive ......The (sign of the) root is the same, as was that from which the square was derive d². As regards the latter portion of this rule, Prthudaka Svami has the following comment to make: "The square-root should be taken either negative or positive, as will be most suitable for subsequent operations to be carried on." It will be interesting to observe the following observation of Mahavira (850 A. D.) regarding square root of a negative quantity "Since a negative number by its own nature is not a square, it has no square-root." So says Śrīpati: "A negative number by itself is non-square, so its square-root is unreal; so the rule (for the square-root) should be applied in the case of a posi- tive number.¹3 Algebraic Operations Brahmagupta and other algebraists recognise six operations as fundamental in algebra : addition, subtraction, multiplication. division, squaring and the extraction of the square-root. Regarding addition and subtraction Brahmagupta says: Of the unknowns, their squares, cubes, fourth powers, fifth powers, sixth powers, etc., addition and subtraction are (performed) of the like; of the unlike (they mean simply their) statement severally.* In place of "of the like", Bhaskara II uses the term "of those of the same species (jati) amongst unknowns": Addition and subtraction are performed of those of the same species (jati) amongst unknowns; of different species they mean their separate statement. 1. खोद्धृत मृणं धनं वा तच्छेदं खगृणधनविभक्तं वा । ऋणयनयोवर्गः स्वं खं खस्य पदं कृतिर्यंत् तत् || -BrSpSi, XVIII. 35 2. GS.S. I. 52. 3. Side, XIV. 5. 4. अव्यक्तवर्ग धनव वर्ग पंचगत षड्गतादीनाम् । तुल्यानां संकलित व्यवकलिते पृथगतुल्यानाम् || -BrSpSi.XVIII. 41. 5. थोगोऽन्तरं तेषु समान जात्योर्निभिन्न जात्योश्च पृथक् स्थितिश्च । - Bhaskara II, Bajaganita.
