________________
No. II]
MATHEMATICS OF NEMICANDRA.
=1/10
4
(iv) A:
(v) A' = (c+h)h, neatly.
c2 +(2h) 2
(vi) d
4h
(vii) h=
(viii) h =
-ch grossly,
(ix) d =
a
2
-c2
6
(d — √√ã3 — c2),
-
-n).
a2
√( a
"
2h
√d2 + a- -d,
(x) h = (xi) a2 = 4h (d+1h), (xii) c2=a2-6h2,
37
1
Most of these formulæ were known before Nemicandra. (i), (ii)=(xii), (iii)=(vi), (vii), (viii) are as old as the early Jaina canonical works (500-300 B.C.). So far as known the formula (iv) was first given by Jinabhadra Gani (529-589 A.C.) and (v) by Sridhara (=750 A.C.) Though the formula (ix)-(xi) are not found stated elsewhere, they can be easily deduced from the others.
Prism, Cone and Sphere. According to Nemicandra, Volume of a prism* = (base) X (height),
Volume of a cone or pyramid5 = (base) X (hight), Volume of a sphere = (radius)3.
For measuring the volume of a heap of certain seeds such as mastard, etc., which resembles a cone in shape, he gives an approximate formula, 7
(circumference )* × (height).
Volume =
1 See the article of the writer on "Geometry in the Jaina Cosmography" in the Quellen and Studien zur geschichte der mathematik.-Abteilving B, Bd. 1, 1930, pp. 24L-254; "The Jaina School of Mathematics " in the Bulletin of the Calcutta Mathematical Society, vol. 21, 1929, pp. 115-145.
2 Brhat Keetra-samāsa, i.122. 3 Trisatikā, Rule 47, 4 Trilokasara, Gatha 17. Ibid, Gatha 19, 6 Ilid, Gathā 19. 7 Ibid, Gathas 22-23
