## The *Siddhanta-Shiromani*

## Lilavati

The first section Lilavati (also known as patiganita or ankaganita ) consists of 277 verses. It covers calculations, progressions, menstruation permutations, and other topics.

**Bijaganita **

The second section *Bījaga**ṇ**ita* has 213 verses. It discusses zero, infinity, positive and negative numbers, and indeterminate equations including (the now called) Pell’s equation, solving it using a *ku**ṭṭ**aka* method. In particular, he also solved the case that was to elude Fermat and his European contemporaries centuries later.

^{ }

**Grahaganita**

In the third section *Grahaga**ṇ**ita*, while treating the motion of planets, he considered their instantaneous speeds. He arrived at the approximation:

for close to , or in modern notation:

.

In his words:

Bimbardhasya kotihya gunastrijyaharah phalam dorjyayorantram

This result had also been observed earlier by Munjalacarya (or Manjulacarya) in 932, in his astronomical work “Laghu –manasam” ,*in the context of a table of sines.*

Bhaskara also stated that at its highest point a planet’s instantaneous speed is zero.

to be continue…….