vs. 17]
AN ASTRONOMICAL PROBLEM
99
The Moon, situated at her ascending node, occults (the
junction-stars of) Pusya and Revati (i.e., £ Piscium). 1
The above occultations (bheda) of the stars by the planet
(Moon) are based on the minutes of latitude determined from
actual observation by means of the instrument (called) Yasti. 8
An astronomical problem on indeterminate equations :
17. The sum, the difference, and the product increased by
one, of the residues of the revolution of Saturn and Mars— each
is a perfect square. 3 Taking the equations furnished by the
above and applying the method of such quadratics obtain the
(simplest) solution by the substitution of 2, 3, etc. successively
(in the general solution). Then calculate the ahargana and the
revolutions performed by Saturn and Mars in that time together
with the number of solar years elapsed.
Let * and y denote the residues of the revolution of Mars and Saturn
respectively. Then we have to find out two numbers x and y such that each
of the expressions * ±y t x-y, and xy±l may be a perfect square.
Let *+jr=4< 2 , and *-j>=40 2 , so that
JC =2< 5! -f2j3 2
and y=2°(*-2$
Therefore xy+l = (2a< 2 - l) 2 +4(c( 2 - 0*).
Hence the condition that xy+l be a perfect square is that
Consequently, we have
- =2(p ,4 4-P 2 )
and ^=2(j3 4 -jS 2 ), 1 Cf. MBh, iii. 73(H). 2 Cf. MBH, iii. 75(i). 3 According to Parames'vara's interpretation, the first half of this stanza means: "The sum, the difference, and the product of the residues of the revolution of Saturn and Mars, each increased by cJne, is a perfect
