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HISTORY OF MATHEMATICS IN INDIA FROM JAINA SOURCES
By
Dr. Sri A. N. Singh, M. Sc. D. Sc., Etc Lucknow University (Conld. From Page 46 Vol XV No. II).
E
GEOMETRY AND MENSURATION
A
The Hindus were acquainted with the formulae for finding out the areas of the parallelogram, the trapezium the cyclic quadrilateral, the triangle, the circle and its sector. Formulae for the volumes of the parallelopiped, the pyramid on a plane base, the cylinder and the cone were also known The Hindu works, how ever, do not give us any inkling as to how these results obtained. In the Dhavala we find a full description of a method for finding out the volume of a trustum of a cone. This des cription shows that the method used in India for the study of
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geometry was quite unlike that of the Greeks. The principle of deformation of a given area or
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Fig. 1.
volume into a simpler area or volume without change of area or volume has been employed in the demonstration referred to above. It is possible now to reconstruct the proofs for the mensuration formulae found in the works of Hindu and Jaina mathematicians. We shall attempt such a reconstruction. But before doing that, we give below the original text of the Dhavala along with its translation.
The problem is to find the volume of the Universe which is supposed to be of the form of three conical frustums placed one on top of the other as shown in fig. 1. The dimensions are shown in the figure. The volume of the Universe is calculated in the Dhavala.
