194 Problems by Bapu Deva Shasiri. 
Art, XXIIIl—Two Problems by Bapu Deva Shastri, Native 
Professor of Mathematics in the Benares College.* mmu- 
_nicated for this Journal by Mr. B. H. Hatt, and transmitted to 
: this country by Prof. Frrz-Epwarp Hatt, of the College of 
_ Benares. ) 
: Prostem I. 
- Given an are and its chord to find the sagitta. 
Let A = the given arc, and B = the given chord. 
Also let a be an are similar to A having a rad = 1. 
~; = (Dif. Cal.) =m — 
$—-93,31 26.9.4.56 7 & 
1 1 i 
“.m= a? a’ ~1-Aa?+ Ba!—Ca* + &e. 
1-53-53 +95-3-4.5 ~ &- 
1 
aed - Aa? + Ba! —Ca*+ &e. 
1 m-l 
*. By trans. Aa* —- Ba'+Ca* —Da*+ &e. =1-—= rae 
$ 1 
“ae B” A-B 
mes Sop OR PRT 
B 
Then = n=Aa?—Ba‘+Ca*—Da*+ &e. 
*. By reversion of the series, 
n Bn? (2B?—AC)n? (5B3?—5ABC+A?2D)n* 
¢ : a? a‘*t a® r 2 
Again, sagitta of a= 5;—5; 3 4+a7-3 4.5.6 & (Dif. Cal. ) 
=3Aa? —5Ba'+7Ca* — &c. (By subtrn.) 
3Bn? 3(2B?—AC)n* 3(5B2—5ABC+A*D)n‘_ 
<n Ae Mt be 
_ 5Bn? 10B2n? (20B* —20ABC)n* 
A? Aé iS 
interest connected with these nan etaieg arises from their 
of the mathematical science of India.— 
