130 Journal of the Asiatic Society of Bengal. [March, 1908. 
and that 
HD=CD (OG—CD)/(#FD-CD+CG-CD) 
CH=CD.FC/(FC+GD) and ED=CD.GD/(FC+GD). 
For from 17(b) we get 
FE.ED=GE.EC or ED/CE=(CD+ ED) FC + C£), 
whence 
ED/CE=GD/FC and ED/CD=GD/(FC+GD). 
rahmagupta, M. ibn bg and Bhaskara use terminology 
similar to that of Aryabhata. Brahmagupta gives the same mat 

s bo If you want to compute the area of 
the "bows" tinltiply, etc.” > (Rosen, p- 75). 
vious oS the source of information is the same in all three 
eo and obviously M. ibn Musa did not get his rules through the 
in who nowhere, before his time, dealt with the area of seg- 
ments i circles. 
19. (a) That sought diminished by one and halved added to the 
foregoing and multiplied by the common difference added to the 
first term gives the mean: this result multiplied by that sought ds 
the answer. (b) Or you multiply the first and last by half the 
number of terms. 
We are here introduced to a set of propositions on progres- 
sions, etc., which, se some respects, correspond eked Se to 
S=(p+n){at+ (atn—1)d/2} —pla+ (p—1)d/2} 
=nJa+(* ja 
If we put p=n, we get S—S,=n*d, which was given by 
eee in ihe second century B.C. 


l After Theon of Alexandria. 
