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Shri Mahavir Jain Aradhana Kendra
www.kobatirth.org
( 612 )
elongated O. This was a most important achievement which in later ages has been in use among all the nationalities. This system of notation was carried by the Arabs from Sind after its conquest by them, and from them it passed to the whole of Europe. Dr. B. B. Dutt in his Science of Sulva has shown how Geometry was developed in India from about 600 B.C. He has also shown that the beginnings of many topics in later Hindu mathematics had been made in this period. In the solution of Indeterminate Equations of the first and second degrees, the achievements of the Hindu mathematicians are also very remarkable. The method employed in solving Indeterminate Equations of the first degree is called Kuttaka or pulverizer. This method in the complete form is found in the Aryabhatiya (499 A.D.) while in Bhaskara II (1150 A.D.) we have a full treatment of all classes of Indeterminate Equations of the first degree. The lemma of Brahmagupta (628 A.D.), called by him Vajrabadha, was rediscovered by Euler (1707-1783). The use of this lemma is made by Brahmagupta in solving Indeterminate Equations of the second degree of a comparatively easy type.
The Indian method of cakravāla or the 'cyclic' rule for the general solution of all Indeterminate Equations of the second degree follows as a corollary to the lemma of Brahmagupta. Who invented this beautiful method has yet remained a riddle. The rules are found in Bhaskara II's work, the Bijaganita.
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Acharya Shri Kailassagarsuri Gyanmandir
In Trigonometry, the Hindu mathematicians and astronomers used generally the functions of 'sine', 'cosine' and 'versed sine' in analysis. The tubular differences of 24'sines' in a quadrant are first found in the Aryabhatiya calculated by the most elementary methods. The most accurate Hindu value of л is also found in the same work 104×8+62000 20000
as given
3-1416. Further, in Hindu
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