History of Hindu Mathematics: A Source Book v2.c17.s5.t1.1

v2.c17.s5.t1.1

The Rule of False Position bespeaks of an early stage of development of the science of algebra when there was no symbol for the unknown. It naturally disappears with the introduction of a system of notations.¹ This will account for the complete disappearance of the Rule of False Position from the later Hindu treatises on algebra beginning with that of Âryabhaṭa I (499). There are found, however, very limited applications of it in the arithmetical treatises of Śrîdhara (*c.* 750), Mahâvîra (850) and Bhâskara II (1150). This can be accounted for easily. The problems which have been solved by those writers with the help of the Rule of False Position are really of algebraic nature, though incorporated into arithmetical treatises. But as the use of algebraic symbols and notations is not permissible in arithmetic, recourse had to be taken to that Rule. For instance, we take the following problem from the *Gaṇita-sâra-saṁgraha* of Mahâvîra :