**Paramesvara** was an Indian astronomer and mathematician who wrote many commentaries on earlier works as well as making observations.

- This village was in Kerala and Paramesvara himself gives its coordinates with respect to Ujjain.
- From Paramesvara's writing we know that Rudra was his teacher, and Nilakantha, who knew Paramesvara personally, tells us that Paramesvara's teachers included Madhava and Narayana.
- We can be fairly confident that the dates we have given for Paramesvara are roughly correct since he made eclipe observations over a period of 55 years.
- The commentaries by Paramesvara on a number of works have been published.
- Paramesvara gave several illustrative examples of the method in his commentary on the Aryabhatiya Ⓣ(The work of Aryabhata).
- Like many mathematicians from Kerala, Madhava clearly had a very strong influence on Paramesvara.
- One can see throughout his work that it is teachings by Madhava which direct much of Paramesvara's mathematical ideas.
- One of Paramesvara's most remarkable mathematical discoveries, no doubt influenced by Madhava, was a version of the mean value theorem.
- There are other examples of versions of the mean value theorem in Paramesvara's work which we now consider.
- The Siddhantadipika by Paramesvara is a commentary on the commentary of Govindasvami on Bhaskara I's Mahabhaskariya Ⓣ(The big book of Bhaskara).
- Paramesvara gives some of his eclipse observations in this work including one made at Navaksetra in 1422 and two made at Gokarna in 1425 and 1430.
- In the Siddhantadipika Paramesvara also gives a more efficient approximation that works using a two-point iterative algorithm which turns out to be essentially the same as the modern secant method.
- However Paramesvara described the rule 350 years earlier.
- Paramesvara made a series of eclipse observations between 1393 and 1432 which we have referred to above.
- The last observation which we know he made was in 1445 but Nilakantha quotes a verse by Paramesvara in which he claims to have made observations spanning 55 years.
- The known observatons by Paramesvara do not quite square with this statement, there being a discrepancy of three years.
- Although we do not know when Paramesvara died we do know, again from Nilakantha, that the two knew each other personally.
- Since we have a definite date for Nilakantha's birth of 1444 it is hard to believe that Paramesvara died before 1460.
- Using his observations, Paramesvara made revisions of the planetary parameters and, like many other Indian astronomers, he constantly attempted to compare the theoretically computed positions of the planets with those which he actually observed.

Born about 1370, Alattur, Kerala, India. Died about 1460, India.

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Ancient Indian, Astronomy, Origin India

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive