Brahmasphutasiddhanta
composition: secureauthorship: secure
The first surviving text to treat zero as a number with its own arithmetic, and to state rules for negative quantities in terms of fortunes and debts.
- zero handled as a number, not as an absence or a placeholder
- negative quantities given arithmetic through the analogy of debts
- a general quadratic solution admitting negative roots
- division by zero attempted and left unresolved
Brahmagupta gives rules for addition, subtraction and multiplication involving zero and negative numbers, defines zero as what results when a number is subtracted from itself, and attempts division by zero, where his answer is not sustainable and he says enough to show he has considered the problem. The work also gives a general solution to quadratic equations admitting negative roots, a formula for the area of a cyclic quadrilateral, methods for the Pell equation, and interpolation for sine tables, all within an astronomical treatise whose main business is planetary computation.
Commentary
Readers' notes on this work. No account needed - be scholarly, or at least civil.
Loading commentary…