212 BRAHMAGUPTA AS AN ALGEBRAIST The total value (of the unknown quantities) plus or minus the individual values (of the unknowns) multi- plied by an optional number deing severally (given), the sum (of the given quantities) divided by the num- ber of unknowns increased or decreased by the multi- plier will be the total value; thence the rest (can be determined).' 2xtcx₁=a₁2x=cx₂=a₂, Xxcxs=a....... Zxicx =an Therefore Ex-astastast...... tan n=c Hence ==( and so on for xa x etc. _a₁+as+as+......+an n=c Fai F Now we shall give the rule enunciated by Brahmagupta for solving linear equations involving several unknowns: Removing the other unknowns from (the side of) the first unknown and dividing by the coefficient of the first unknown, the value of the first unknown (is obtai- ned). In the case of more (values of the first un- known), two and two (of them) should be considered after reducing them to comon denominators. And (so on) repeatedly. If more unknowns remain (in the final equation), the method of the pulveriser (should be employed). (Then proceeding) reversely (the values of other unknowns can be found).² Prthudaka Svāmi has commented on this rule as follows: In an example in which there are two or more un- known quantities, colours such as yavat-tavat, etc., should be assumed for their values. Upon them should 1. गच्छधनमिष्ट गुणितैर्धनैयुं तोनं पृथक् पृथक् सहितम् । सुधकयुतोन पदहृतं सर्वधनमतोऽवशेषाणि || 2. आधादूवर्षादन्याम् वर्षान् प्रो ह्याधमान माद्यहृतम् । सशच्छेदाक्सद द्वौं व्यस्तौ कुटुको बहुषु ।। -BrSpSi: XIII. 47 -Br SpSi. XVIII. 51
