for compuiing Eclipses, Tables of Sines, &c. 23 



all its purity the table which was to serve for computing all 

 the others : but lliey have given thtir t;ibles of the equation 

 of the centre lor every degree. 



Their theory for computing these tables of equations was 

 incomplete and inaccurate; although they used epicycles, 

 like the Greeks, to compute the inequalities of the ilanets, 

 this calculation wa* with the.n less geometric than those of 

 Ptolemy. Thev had introduced an empiric correction, which 

 was very badly conceived ; and they supposed that from 90° 

 to 180° the same equations returned in an inverted order. 

 The Greeks, in this respect, were further advanced than the 

 Hindoos; their trigonometry was .much more compktf, al- 

 though that of the Hindoos had a greater resemblance to 

 ours; and the Hindoos appear to have had some theorems 

 unknown to the Greeks. These tables of equations, although 

 defective, are, nevertheless, very curious: in the explanation 

 of them given by the Hindoos we observe that the diller- 

 ences of the equation are proportional to the sine of the 

 anomaly; or, which is nearlv the same, that the variation 

 of the sine is proportional to the cosine. 



It is evident also from this memoir, that the Hindoos 

 found the latitude of a place by computing the lengtli of 

 the shadow of a gnomon, especially when the sun was in 

 the equator; they miaht have found it also by the solstitial 

 shadow, using the sun's greatest declination, which accord- 

 ing to them was 24". 



To determine their longitudes they observed eclipses, and 

 compared them with the computations made from their lunar 

 tables adapted to their first meridian. 



In page 3 1 5 is shown their method of calculating the sun's 

 right %scension by means of their sines, without knowing 

 the tangents. 



In the same place is also shown how they con>putod the 

 ascensional differences and the point of the equator which 

 rises with each sign. The table whicii they made has been 

 published by M. Le Gentil, who acknowledged lie was un- 

 acquainted with the principle on uhjeh it was consli'ucted : 

 this principle is givea in the memoir, and I have explained 

 it at full length in a note. 



li 4 We 



