________________
6. Formula for the sum of an infinite geometric progression:
ap
S=Q+-
+-
+
-
+
oc,
where I <p.
7. Transformation of an annulus into a trapezoid without changing its area.
8. Transformation of a truncated cone without the central cylinder into a pentahedron called 'winnowingbasket' (suppu-khetta = Skt. sūrpa-kşetra) without changing its volume.
See $4 above for Items I and 2. In an infinite geometric progression (Item 6), successively decrease the volumes of the rectangular solids which have been cut out of the pentahedron, into which the truncated cone without the central cylinder has been tranformed. Vīrasena says:
A method for adding up the volumes of all the figures produced in this way is told. It is as follows. When one has supposed that all the volumes are arranged in the order of quadruples (i.e., in reverse order), multiplied the last volume (a) by four, and divided (the result) by the divisor multiplied by three decreased by one (? rūvūnutigunidachedenu ovaddhide; one of the manuscripts used for the edition reads: rūvūņam kāūņa tigunida-) this much is produced: 65 1320/1356 rujjuz (Dhavalā on CK 1.3.2; vol. 4, pp. 15 16)
The verbal expression of the last step has been perhaps corrupted, but the computation meant by Vīrasena is clear:
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