New Demonstration of a Problem in Trigonometri/. 391 



Nov. 1. — The following paper was read : An account of an 

 easy and successfiil method of destroying wasps, by Mr. Charles 

 Harrison, F.H.S. 



SOCIETY OF PHYSICIANS OF THE UNITED KINGDOM. 



At a meeting of the Society of Physicians of the United 

 Kingdom, held November the 2d, the following officers were 

 elected for the ensuing j'ear: — President, Dr. Birkbeck; 

 Treasurer, Dr. Clutterbuck ; Secretary, Dr. Shearman. 



Communications, whether from members or others, ad- 

 dressed to the Secretary, No. 30, Northampton-square, will 

 be submitted to the consideration of the Society, and the most 

 interesting and important of them selected for publication, as 

 soon as sufficient materials shall be collected to form a volume. 



LXII. Intelligence and Miscellaneous Articles, 



NEW DEMONSTRATION OF A PROBLEM IN TRIGONOMETRY. 



To the Editor of the Philosophical Magazine and Journal. 

 Sir, 

 CHOULD the following new and concise demonstration of a 

 ^ well-known proposition be deemed worthy a place in the 

 Philosophical Magazine, its insertion will oblige 



Your humble servant, 



Wisbech. ISAAC NewTON. 



" The angles at the base of an isosceles triangle are equal 

 to each other." 



Let ABC be the isosceles triangle, a. 



whose equal sides are AB, AC; then 

 will < B = < C. For in AB, AC, 

 take the points F and G equidistant 

 from A, and draw the right lines CF, 

 BG; then (Euc. iv. 1.) it is plain that 

 < F = < G ; and for the same reason 

 the < F will always = the < G as 

 long as F and G, the extremities of CF and BG, are equi- 

 distant from A. Thei-efore if F and G be made to fall on 

 B and C, CF and BG will each coincide with BC; and the 

 angles F and G coincide with B and C respectively : but F 

 and G are always equal angles, therefore their coincident 

 angles B and C are also e(jual. Q. e. d. 



P.S. The above, as may be perceived, requires not the aid 

 of any subsequent proposition in Euclid. 



ON 



