Bakhshālī Manuscript

The Bakhshali manuscript is an ancient Indian mathematical text written on birch bark that was found in 1881 in the village of Bakhshali, Mardan (near Peshawar in present-day Pakistan).

Contents
The manuscript is a summary of rules and illustrative examples. In the form of problems examples are provided and the solution is described and it is verified that the problem has been solved. The sample problems are in verse and commentary is in prose related with calculations. The problems contains arithmetic, algebra and geometry including mensuration. The details covered include fractions, square roots, arithmetic and geometric progressions, solutions of simple equations, simultaneous linear equations, quadratic equations and indeterminate equations of the second degree.

Composition
The manuscript is written in an earlier form of Shardada script.

Mathematics
The manuscript is a compilation of mathematical rules and examples in verse, and prose commentaries on these verses. Generally, a rule is given, with one or more examples, where each example is followed by a "statement" (nyāsa / sthāpanā) of the example's numerical information in tabular form, then a computation that works out the example by following the rule step-by-step while quoting it, and finally a verification to confirm that the solution satisfies the problem.

The rules are algorithms and techniques for a variety of problems, such as systems of linear equations, quadratic equations, arithmetic progressions and arithmetico-geometric series, computing square roots approximately, dealing with negative numbers (profit and loss), measurement such as of the fineness of gold, etc.

Numerals and Zero
The Bakhshali manuscript uses numerals with a place-value system, using a dot as a place holder for zero. The dot symbol came to be called the shunya-bindu