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The Jaina Antiquary
[ Vol. XVII
The main items of interest in the above, from the point of view of History of Mathematics, are as follows:
60
(i) It has been assumed that a body with curved boundaries can be deformed into another with plane boundaries in such a way that its volume remains unchanged. In particular, if the hollowed out cone of figure (2) is deformed into the figure (3) which has plane boundaries, then the volume remains unchanged,
(ii) The principle of construction for the purpose of demons tration or proof has been assumed to hold true. In particular, this principle has been used to find the volume of the tetrahedrons बस द and मा वा सा दा.
8
-I
series Sa+ar+ar3 + has been assumed.
(iii) The formula S=
r<l, for the sum of the geometric
+ar" +.....
(iv) The value of has been taken to be
"
.= 113.
RECONSTRUCTION OF PROOFS OF MENSURATION FORMULAE
The principles of deformation and construction employed in the above demonstartion can be used to obtain the mensuration formulae known and used in India as follows:
AREA
1. RECTANGLE: The area of a rectangle is equal to its length multiplied by its breadth.
Fig. 5.
