for compuling Eclipses, Tables of Sines, ^c. 21 



It is evident that, excepting a few sines, in which we 

 differ some tenths, the agreement is perfect throughout the 

 table; l>«t with the divisor 225 we obtain only the three 

 first sines with any accuracy, after which the error increases 

 very rapidly. I snppose this false divisor is only a repeti- 

 tion of the divisor 225, which served to fuid the lirsl of the 

 first differences. 



The Indian author does not- show how he found his di- 

 visor; we can therefore only exaniine it by the work : now 

 the work shows that a divisor differing very little from mine 

 must be used. 



This process is extremely curious ; nothing like it is to 

 be found in Ptolemy's Tria;onometry, and all the authors 

 on that subject were turned over to no purpose before ue 

 could find any vestige of it, till we came to Briggs, who waj 

 acquainted with this divisor, which he appeared to have 

 discovered by the work, after coniparins; the second differ- 

 ences found out by other methods. Briggs himself did not 

 know that it was the square of the chord of the differential 

 arc A A . 



But it may be asked why the Indians have made A A = 

 3° 45' instead of 1°. The following, I think, is the rea- 

 son; it appears to carry great probability: — It cannot be 

 doubted that the Indians were acquainted with the following 

 theorems: s",A + t^jA = rad.*; ver. sin, A = rad.— cos, A 



= 2i*.-i-A ; whence s,-lrA — [^ rad. — -i- r,A)^. Now 

 these three theorems arc suflicient to find all the sinesv^f their 

 table, and will not give any other : they have therefore done 

 all that they were able to do, and their table shows us tlie bounds 

 of their knowledge : we see, indeed, p. 2(;0, that they have 

 actually used these tliree formuire to compute their table, and 

 that they knew, besides, that s,30'> = -^- rad., which appears 

 to leave not a doubt respecting what I have said. Their table 

 being constructed, they then examined the lirst and second 

 differences, and remarked that the first eonslamly decreased, 

 but they could not immediately perceive according to what 

 law; the second differences, on the contrary, continually 

 increased, and it wai nut ditficult to perceive thai they \ere 

 B 3 proptjition.tl 



