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one of the most popular topics in Indian mathematics since the times of the Sulbasūtras (ca. 6th century BC and later). For Mahāvīra's treatment of frustum-like solids including a truncated cone, see Gupta 1986.
Formulas Not Used
Why Virasena did not use the formula for the volume of a truncated cone,
_di + d1d2+2h,
=
V=T
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which can be obtained through his own computation, is an interesting question. The only plausible answer is that he did not know it. This may suggest that the date of the composition of the Dhavala (C.E. 781) is an upper limit of the date of Śrīdhara, who gave the correct formula for a truncated cone ( Trisatikā 54):
10 { d2 + d2 + (d2 + db)2 } 2
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x h
It is, however, observed that Vīrasena did not use even the formula for the volumes of a cone and of a triangular pyramid,
Ah V = 3'
(π = √10).
which would have made his computation of the volume of a truncated cone much easier. This last formula had already been known to Brahmagupta (Brāhmasphuṭasiddhānta 12.44, C.E. 628). The upper limit of Śrīdahara's date stated above is, therefore, not at all definitive, and why Vīrasena did not use these formulas is yet an open question. []
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