338 ; HINDU- .ASTRONOMERS 



epicycle, which reprefents the excentrick, to fee augmented in "the- 

 proportion which Carria (or thediftance of the planet's place from the 

 the earth's centre) bear* to the Radius of the concentric-It; andit- is on this- 

 account, and not as a mere approximation, that the Endings of the CarUa^. 

 with the fubiequent optration to which it is- applicable, is- difpcnfed : 



With.* 



ban hls\ \ d& i - | " .-.: ■£ 



1 *tnk icholiaftof B*aiwegupta obje£ls to- his. authors do&rine tm 



fthis point, that, upon the fame principle, the procefs- of; finding the 

 'Carria', with the fub fequent employment ©f it to find the Sine of the 

 tooWalffiick 'E'qiiatid'n, fhoiild m like manner be omitted in the proper 

 €picycleVbl' i the o fiVe- ?l mir!0r planets "j and he concludes therefore, that 

 Ifie ^yifiibn of that prticels has no ©ther ground, but the very incon* 

 liderable : difference of the refill! in the inftance 06 a- frnaU- epicycle,, 

 For as remarked by another ai2thof,f treating ©n the fame fuhjeft, the 

 Equation -'itfelf and its Sine are ¥ery fmall near the line of the apfidesg 

 and at a di fiance from that liue* fcte Cards aad Radius approach Z® 



Bha'scarAj in the S'iromani, quotes fuccinclly BIiahmegupta's doc«- 



trine s and the Scholialt's objection to it j and replies to the latter : and 



® F@r Rsd : Periphery of the rpieycle ; J C*rns,° augmented epicycie,. 



And Ciffcle; Siae of Anomaly ;• augmented epicycle; Sine of Anomaly in augmented epicycle^ 



Laftly Cema ; Sine of Anomaly in augmented epicycle :: Rad s. Sine of Anosnaliftiek Equation* 



Carna Rad, Sine of Anomaly 

 ^Whence Periphery » —- - X - — - * ———«—=— —•. S»se ©f AnoraaliRkk Equation. 

 Radius Cams Circle 



Sine ©f Anomaly 

 And,, abridging, Periphery x < zz Sine of AnoiBaMick Eqssatios, 



Circle 



Wherefore Circle : Periphery cfepicjsle ;; Sio® of- Anomaly s Sins of ABosualiJliek E$«nti©Sa - 



