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OF THE HINDUS. 25 1 



and he; to find the hypotenuses®, by means of 

 which the angles © m may be determined; for its 

 sine is 1 m, and, in the similar triangles he® and 

 / m © , as c © is to ;// ©, so is // c to lm, the sine of 

 the angle of equation. From the third to the ninth 

 sine of anomaly, the co-sine c b must be subtracted 

 from the radius 343 8' for the side h ©. 



It is, however, only in computing the retrograda- 

 tions and other particulars respecting the planets M§t- 

 cury, Vctvts, Mars, Jupiter, and Saturn, where circles 

 greatly excentric are to be considered, that the Hindus 

 find the length of the carta, or hypotenuse c © ; in 

 other cases, as for the anomalistic equations of the sun 

 and moon, they are satisfied to take he as equal to the 

 sine lm, their difference, as the commentator on the 

 Biddhanta observes, being inconsideiable. 



Upon this hypothesis are the Hindu tables of ano- 

 maly computed with the aid of an adjustment, which, 

 as far as 1 know, may be peculiar to themselves. Find- 

 ing that, in the first degree of anomaly, both from 

 the higher and lower apsis, the difference between the 

 mean and observed places of the planets was greater 

 than became thus accounted for, they enlarged the 

 epicycle in the apogee and perigee, proportionably to 

 that observed difference for each planet respectively, 

 conceiving it to diminish in inverse proportion to the < 

 sine of the mean anomaly, until at the distance of three 

 sines, or half-way between those points, the radius of 

 the epicycle should be equal to the excentricity or sine 

 of the greatest equation. This assumed difference in 

 the magnitude of th^epicycle, they called the dif- 

 ference of the paridhi ansa, between vishama and sama ; 

 the literal meaning of which is odd and even. From 

 the first to the third sign of anomaly, or rather in the 

 third, a planet is in vishama ; from the third to. the 



