Comparing this equation with ux 2 +vy 2 +w2 2 +22G'y2+2v'zx+2W'xy=0, we obtain as the condition for the general equation of the second degree to represent a circle :- (v+w-2u')Ia 2 = (w +u -2v')/b2 = (u+v-2w')lc2 In tangential q, r) co-ordinates the inscribed circle has for its equation(s - a)qr+ (s - b)rp+ (s - c) pq = o, s being equal to 1(a +b +c); an alternative form is qr cot zA+rp cot ZB +pq cot2C =o; Tangential the centre is ap+bq+cr = o, or sinA +q sin B+rsinC =o.
Rate at which the plane HOJ revolves about OH, we have sina Ccosa ii~~A cosI3iU~, (8)
X sina ce.
The Sina river, another tributary of the Bhima, flows through the Nagar and Karjat talukas.
We might note besides that it is quoted in the Book of Adam and Eve, the Apocalypse of Moses, the Apocalypse of Paul, the anonymous work De montibus Sina et Sion, the Sibylline Oracles ii.