ell 
4 

Vol. ov No, 3.] Notes on Indian Mathematics. 123 
N.S.) 
See Tare generally fall into error (see § 7 above). Albiruni 
writes (I., 167): ‘The elements of the calculations of the Hindus 
on the peal of the circle rests on the assumption that it 
is thrice the diameter.” 
a2. the fourth part of a circle be cut by a triangle and 
Sy the semi-diameter is divided into as many half chords 
of arcs as we choose 
12. (a) Ifthe aie rg second be bisected in succession the sine 
of the half ate is obtain 
) The differences are » diminished by successive quotients by 
the first sine 
~ These ners are obscurely expressed and difficult to translate. 
Rodet confessed he did not understand the former, and left the 
first part of the latter a Er They 
ay be simply a rough attempt at the A 
following is meant: Let OP ane. 3 2) be a 
O 
if the angles OPB and OQB are an eat in 
V aud U, then the angle OVU a. 
— bisected is 33°, which i is the sees Fig. 2. 
angle. 
ww 


Fig. 4. 
Fig. 3. 
The theorem of Ptolemy referred tois: Ina quadrilatera 
inscribed in a circle, the rectangle contained by the diagonals is 
equal to the sum of the two rectangles contained by its opposite 
sides. Thus (Fig. 3) ac+ bd=ay, and in the ped cree aed 
y bisects B we have c+d=ay/a, and it was this parti : oi ne 
eeeuss was known to Euclid) that provides ae rule “( e 0 
Fig. 4) areAD=areDC=y a and arecBA=(n—1)y then 
arc Bp: =ny and are BO=(n+1)y, and we have 
chd (n+1)y+chd (n—l)y = (chd ny. chd 2y) /chdy 
