The use of calculus in Hindu religion dates back to the Vedas. Integral calculus is seen to have been used by Vedic priests in determining measurements in the construction of sacrificial altars, as set out in Sulbasutra. Differential calculus was employed in the Vedic age to determine auspicious times for rituals on the basis of astronomical observations.

Calculus, a branch of mathematics, is divided into two classes – differential calculus, which concerns itself with the momentary state of phenomenon and Integral calculus, which is connected with the summation of a series when the number of terms in the series tends to infinity, each term being infinitely small. Both types had been employed in early and medieval Hindu mathematics for identical purposes, although they were neither given a separate name nor treated as distinct subject.

Hoysaleswara Temple At Halebidu, Karnataka |

Among ancient Hindu mathematicians who have used calculus as set out in their works are – Aryabhata (476 CE), Brahmagupta (598 CE), Munjala (932 CE), Bhaskaracharya (1114 CE), Narayana Pandita (1356 CE), Nilakantha Somayaji (1443) and Jyesthadeva (1500 – 1600 CE).

Bhaskara-II utilizes differential calculus to determine the “motion at a moment”, of a planet (tatalikagati) or “instantaneous motion”, as it is termed in modern calculus (Cf. Siddhanta Siromani, Spastadhikara, 36-38). First, he distinguishes between sthula gati (rough velocity) and sukshmagati (true velocity). The he identifies the successive positions of the planet at short intervals of time called truti, equal to 1/33750 part of a second, from which the true velocity at the desired moment is calculated.

Integral calculus is employed by Bhaskara-II and Nilakantha Somayaji and set out elaborately by Jyesthadeva in his Yuktibhasa (chapter VI) to derive the formula for the determination of the circumference of a circle, the outer surface area of a sphere and the volume of the sphere exactly in the same manner as is done in modern mathematics.

Integral calculus has also been employed for finding the value of Pi, being the relation between the circumferences and the radius of a circle, correct to several decimal places, as set out in Tantrasangraha of Nilakantha Somayaji and its commentaries, ad in Yuktibhasa of Jyesthadeva.

**Source – **

- Encyclopedia of Hinduism Volume III page 14 – Rupa – IHRF
- Mathematics of Ancient and Medieval India (1979) A K Bag – Chaukhamba Varanasi.