Bhakar II Arithmatics cover into Leelavati

 

Bhaskaracharya Karmaveera Special 11 May 2014 E

Arithmetic

Bhaskara’s arithmetic text Leelavati covers the topics of definitions, arithmetical terms, interest computation, arithmetical and geometrical progressions, plane geometry , solid geometry, the shadow of the the gnomon, methods to solve indeterminate equations, and combinations.
Lilavati is divided into 13 chapters and covers many branches of mathematics, arithmetic, algebra, geometry, and a little trigonometry and mensuration. More specifically the contents include:
• Definitions.
• Properties of Zero (including division, and rules of operations with zero).
• Further extensive numerical work, including use of negative numbers and surds.
• Estimation of Pi ∏.
• Arithmetical terms, methods of multiplication, and squaring.
• Nverse rule of three , and rules of 3, 5, 7, 9, and 11.
• Problems involving interest and interest computation.
• Indeterminate equations (Kuttaka), integer solutions (first and second order). His contributions to this topic are particularly important since the rules he gives are (in effect) the same as those given by the renaissance European mathematicians of the 17th century, yet his work was of the 12th century. Bhaskara’s method of solving was an improvement of the methods found in the work of Aryabhata and subsequent mathematicians.
His work is outstanding for its systemization, improved methods and the new topics that he has introduced. Furthermore the Lilavati contained excellent recreative problems and it is thought that Bhaskara’s intention may have be.

 

to be continue……………….

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