Aryabhata

?ryabha?a was an Indian mathematician and astronomer, and the author of the MahaSiddhanta The numeral II is given to him to distinguish him from the earlier and more influential ?ryabha?aAryabhata IIs most eminent work was Mahasiddhanta The treatise consists of eighteen chapters and was written in the form of verse in Sanskrit The initial twelve chapters deals with topics related to mathematical astronomy and covers the topics that Indian mathematicians of that period had already worked on The various topics that have been included in these twelve chapters are: the longitudes of the planets, lunar and solar eclipses, the estimation of eclipses, the lunar crescent, the rising and setting of the planets, association of the planets with each other and with the stars
The next six chapters of the book includes topics such as geometry, geography and algebra, which were applied to calculate the longitudes of the planets In about twenty verses in the treatise, he gives elaborate rules to solve the indeterminate equation: by = ax + c These rules have been applied to a number of different cases such as when c has a positive value, when c has a negative value, when the number of the quotients is an even number, when this number of quotients is an odd number, etc