पृष्ठम्:लघुभास्करीयम्.djvu/१७५

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102 CONJUNCTION OF A PLANET AND A STAR [CH. VIII would run as follows : “The residue of the minute of Mars multiplied by the cube of 2 yields a square root (without remainder); that souare root being increased by one, then multiplied by 7 and then increased by one is again a perfect 59uare. Having ascertained the residue from this (hypothesis), one who can find out the longitude of Mars and the alhargarm2 together with the number of years elapsed is (indeed) the foremost amongst the intelligent mathematicians on this earth girdled by the oceans.” so that where P and s are integers. 7 (.78R +1) + 1=s, say, Putting ऽ=0, 1, 2, ..., we see that only ऽ=6 and s=8 give integral values to R, the corresponding values being 2 and 8 respectively. Thus the residue of the minute of Mars is either 2 or 8. Let us take R८=2. Then to find out the required alhargao we have to solve the equation 1653713289-2 । 5259725 where x denotes the alhargapa and y the total number of minutes traversed by The general solution of this equation is

  • =5259725t +4386086,

y=1653713281-+137903192, where t=0, 1, 2, If we take R=8, we shall get 4alhargan4 = 52597255-+3726384 , Sarikaranārāyapa gives the alhangap0 as equal to 3726384 or 4386086 . The former corresponds to s=0, and the latter to t=0. told by Bhaskara. Object, scope, and authorship of the book : 19. For acquiring a knowledge of the true motion of the planets by those who are afraid ofreading voluminous works,