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No.11 )
History of Mathematics in India from Jaina Sources
63
Third principle of deformation: If a sector of a circle is deformed into a triangle whose base is equal in length to the arc of the sector and whose height is equal to the radius, the area remains unaltered.
The deformation is brought about by keeping the bisector of the angle at the centre fixed and then making the circular arc straight.
6. CIRCLE The area of a circle is equal to half the length of its circumíerence multiplied by its radius.
Consiruction: Cut the circle along a radius and spread it out into a triangle. The area of the circle is equal to the area of this triangle wioso base is equal to the circumference and whose height is equal to the radius of the circle. Hance the result.
Corollary: The area of the figure bounded by two concentric circles of radii a and k. and two radi is equal to the area of the trapezium 'whose pallel sides are equal to the length of the two arcs ant whouse height is equal to the sifference between the radi of the circles.
Fig. 12
7. The volume i cylinder of uniform cross-sections) is connaitissin : he multiplief hy its height.
1: non tetrahedron s equal to one-third the area Bili bazalticdi: its height.
prisan 41. triangular base can be divided into three equal tetrahedrons, hence this result.
