पृष्ठम्:लघुभास्करीयम्.djvu/१७२

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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