Jyesthadeva 

Born: about 1500 in Kerala, India
Died: about 1575 in Kerala, India Jyesthadeva lived on the southwest
coast of India in the district of Kerala. He belonged to the Kerala
school of mathematics built on the work of Madhava, Nilakantha
Somayaji, Paramesvara and others. Jyesthadeva wrote a famous
text Yuktibhasa which he wrote in Malayalam, the regional language of
Kerala. The work is a survey of Kerala mathematics and, very
unusually for an Indian mathematical text, it contains proofs of the
theorems and gives derivations of the rules it contains. It is one of
the main astronomical and mathematical texts produced by the Kerala
school. The work was based mainly on the Tantrasamgraha of
Nilakantha. The Yuktibhasa is a major treatise, half on
astronomy and half on mathematics, written in 1501. The
Tantrasamgraha on which it is based consists of 432 Sanskrit verses
divided into 8 chapters, and it covers various aspects of Indian
astronomy. It is based on the epicyclic and eccentric models of
planetary motion. The first two chapters deal with the motions and
longitudes of the planets. The third chapter Treatise on shadow deals
with various problems related with the sun's position on the
celestial sphere, including the relationships of its expressions in
the three systems of coordinates, namely ecliptic, equatorial and
horizontal coordinates. The fourth and fifth chapters are
Treatise on the lunar eclipse and On the solar eclipse and these two
chapters treat various aspects of the eclipses of the sun and the
moon. The sixth chapter is On vyatipata and deals with the complete
deviation of the longitudes of the sun and the moon. The seventh
chapter On visibility computation discusses the rising and setting of
the moon and planets. The final chapter On elevation of the lunar
cusps examines the size of the part of the moon which is illuminated
by the sun and gives a graphical representation of it. The
Yuktibhasa is very important in terms of the mathematics Jyesthadeva
presents. In particular he presents results discovered by Madhava and
the treatise is an important source of the remarkable mathematical
theorems which Madhava discovered. Written in about 1550,
Jyesthadeva's commentary contained proofs of the earlier results by
Madhava and Nilakantha which these earlier authors did not give. In
[4] Gupta gives a translation of the text and this is also given in
[2] and a number of other sources. Jyesthadeva describes Madhava's
series as follows: The first term is the product of the
given sine and radius of the desired arc divided by the cosine of the
arc. The succeeding terms are obtained by a process of iteration when
the first term is repeatedly multiplied by the square of the sine and
divided by the square of the cosine. All the terms are then divided
by the odd numbers 1, 3, 5, .... The arc is obtained by adding and
subtracting respectively the terms of odd rank and those of even
rank. It is laid down that the sine of the arc or that of its
complement whichever is the smaller should be taken here as the given
sine. Otherwise the terms obtained by this above iteration will not
tend to the vanishing magnitude. This is a remarkable
passage describing Madhava's series, but remember that even this
passage by Jyesthadeva was written more than 100 years before James
Gregory rediscovered this series expansion. To see how this
description of the series fits with Gregory's series for arctan(x)
see the biography of Madhava. Other mathematical results presented by
Jyesthadeva include topics studied by earlier Indian mathematicians
such as integer solutions of systems of first degree equation solved
by the kuttaka method, and rules of finding the sines and the cosines
of the sum and difference of two angles. Not only does the
mathematics anticipate work by European mathematicians a century
later, but the planetary theory presented by Jyesthadeva is similar
to that adopted by Tycho Brahe. Article by: J J O'Connor and
E F Robertson
Source:www.history.mcs.standrews.ac.uk/Mathematicians



