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

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).¹ Σx±cx₁=a₁, Σx±cx₂=a₂, Σx±cx₃=a₃,...... Σx±cx =an Therefore Σx = (a₁ + a₂ + a₃ + ...... + an) / (n ± c) Hence x₁ = 1/c ( ±a₁ ∓ (a₁ + a₂ + a₃ + ...... + an) / (n ± c) ); and so on for x₂, x₃ etc. 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