a a EEO sr rrerererer~ ee 

Vol. tw No. 3. | Notes on Indian Mathematics. 129 
S.] 
16. Multiply by the shadow the distance between the ends of the 
shadows and divide by the difference: this will give the side. 
height multiplied by the style and divided w the shadow gives the 
other side 
17(a). And so the square he the height with the square of the 
base gives the square of the hypoten 
Here the fei hos ST (Pig. 5) is peer to be moved to S’T’. 
Now OL: ST:: OH: SH and OL: S'T’ :: OH’: S’H' but ST=S'T" 
therefore OH : SH Pin: sig whence OH = SH. HH’ /(S'H’- 
SH) as expressed oy the 
“ According to Pliny oe Diogenes Laertius, Thales ascer- 
tained the height of 

self. Plutarch, how- 
ever, puts into the ~ s xs! x 
mouth of Niloxenus a Fig. 5. 
different account of the 
process. * Placing your staff at the extremity of the shadow 
of the pyramid,’ says he to Thales, ‘you made, by impact of the 
sun’s rays, two triangles, and so showed that the pyramid was 
to the staff as the shadow to the staff's shadow.’ This is obviously 
only another calculation of the seqt” ane — and is identical 
with the rules 15 and 17a given by Aryabha 

17(b). In te ae the product of the arrows is the square of the 
semi-chord of the 
18. Two circles diminished by the ‘bite’ — rp ogrnt 
by this ‘bite’ and divided by the sum of the circles les. ‘ bite 
give respectively the arrows starting from the intersection 
The ‘arrows’ are the segments of the diameter bisecting 
the are Thus in the circle 
FAB the arrows are an 
ED. Yhe word ‘bite’ is 
here applied to CD, and is 


Rahu, who is supposed to F - 
cause — by peat 
moon. 3 
Simtaied rule is a par sisal 
case of Ruclid iii,, 35. The ‘Fig. 6. 
latter (18) is easily deduced 
therefrom and means 
CE=CD (FD-QD)/(FD—0D+ 0G — OD) 
