The Siddhanta-Shiromani by Bhaskar II

Bhaskaracharya Karmaveera Special 11 May 2014 E

The Siddhanta-Shiromani


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


The second section Bījagaita 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 kuṭṭaka method. In particular, he also solved the case that was to elude Fermat and his European contemporaries centuries later.



In the third section Grahagaita, 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…….

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