Coiiomelrlc Prollems. 25 



rows, where be wishes to prove that Newton's binomial theo- 

 rem was known to the Indians. In the notes I have an- 

 swered the proofs which he brings forward to support his 

 opinion, as they appear to me to have no foundation. 



The first voknrie, which is very interesting to orientahsts, 

 contains nothing for astronomers ; but every reader will see 

 there, with great pleasure, a menujir on the gous of Italy, 

 Greece, and India, by sir William Jones, with notes by 

 M. Lancles. 



I i I. Problems on the Pwduclio/: of Angles. Bi/ T. S. EvanS, 

 F.L.S., of the Royal Mllltanj ykademy, IFouhcich*. 



J. HE following problems are concerning the reduction of 

 angle', from one point or plane to another. They are nol 

 all of t'..cm new. One or two, v.iih their solutions, will 

 be foii-^.i »mone: the writings of each of the following cele- 

 brated uiaLhenraiicians ; Boscovich, Cagnoli, Carnot, De- 

 Jambre, and jrobajly some others : but few, if any of them, 

 have ever Icen published by our Jlnglish authors. It was 

 therefore thoudit, if their solutions were given in one uni- 

 form maimer, in our own language, they might be of ser- 

 vice ; and this is what I have here attempted, with a few 

 additions of my own. 



As they bear a very near relation to both plane and spheric 

 trigonometry, but cannot, v.'ith propriety, bi- considered 

 as actually belonging to either of lliem separately, i have 

 taken the liberty of classing them under the title «)f Cofiio- 

 metry. 



Their ntihly will be evident to every person who has any 

 concern in tieodcsie operations, ft seldom happens in prac- 

 tice that all the three objects at the angular points of a tri- 

 angle are situated precisely in the horizontal plane passing 

 through the observer's eye ; therefore when one or two of 

 them are above or below ihat plane the angles are diflerent, 

 and will require to be reduced to what they would be if the 



* Coramunicated by the Author. 



three 



