﻿494 APPENDIX. 



<s will be 29,75 N, 53,94 N, and 63,77 N", which are 

 ci nearly equal to thirty N ; fifty -four N, and sixty- 

 «' four N respectively; and hence the foundation of the 

 " Rramin rule is evident, which directs to multiply 

 «« the equatorial shadow by thirty, fifty-four, and 

 u sixty-four respectively ; and to divide the products 

 " by three for the Chorardo in puis : and these parts 

 " answer to one, two, and three signs of longitude 

 " hum. the true equinox; and therefore th&Ayanongsh, 

 " or Bramin precession of the equinox, mud be add- 

 " ed to find the intermediate Chorardo by propor- 

 " tion." 



Though the agreement of this investigation with 

 the Bramin results, is no proof that the Hindus had 

 either the differential method, or Algebra, it gave me 

 at the time a strong suspicion cf both; and yet, for 

 want of knowing the name that Algebra went by in 

 Sanscrit ; , I was near two years before 1 found a treatise 

 on it, and 'even then I should not have known what to 

 enquire for, if it had not come into my mind to ask 

 how they investigated their rules. Of the differential 

 method, I have yet met with no regular treatise, but 

 have no doubt whatever that there were such, for the 

 reasons I before hinted at; and I hope others will be 

 more fortunate in their enquiries after it than myself. 



With respect to the Binomial Theorem, the applica- 

 tion of it to fractional indices will perhaps remain for 

 ever the exclusive property of Newton ; but the fol- 

 lowing question and its solution evidently shew that 

 the Hindoos understood it in whole numbers, to the 

 full as well as Briggs, and much better than 

 Pascal. Dr. Hut ton, in a valuable edition of Sher- 

 ivirfs tables, has lately done juftice to Briggs ; but 

 Mr. Whitchell, who some years before pointed out 

 Briggs as the undoubted inventor of the differential 



