## bhAskara and differential calculus

It is fair to state that bhAskara provides a clear description of the concept of the differential. This can be seen in his treatise siddhAnta shiromaNi (chapter gaNitAdhyAya; section gatisphuTiprakaraNa). He clearly states that this is a formalization of the approximate formulae given by the earlier AchArya brahmagupta.

He defines two quantities: 1) sthulagati (roughly speed) that is defines as ratio of the distance travelled by a object to the time taken for that.

2) sukShmagati or tatkAlikI gati. This the one used to define velocity of an object. It defined as the value obtained by taking the time duration to be an infinitesmal, which is given the technical term pratikshaNaM. This is evident from the formula he gives for the calculation of the sine tables because he is assuming the tatkAlikI gati of sin(x) to be cos(x)