Direct Solution of a Geometrical Problem, 



355 



Oakland, Feb. 15, 1874. 



Sir, — In a Number of the London, Edinburgh, and Dublin 

 Philosophical Magazine for the year 1852 or 1862, is a discussion 

 of a simple geometrical problem by J. J. Sylvester, in which 

 this gentleman attempts to illustrate a conjectured principle in 

 the Theory of Geometrical Method. The problem appears to 

 have been given out at Cambridge many years before, and to 

 have excited the attention of some of the first mathematicians of 

 Europe for a number of years. A direct solution of the problem 

 was demanded ; and after a protracted discussion it was concluded 

 that none was possible. Upon that some mathematicians lent 

 their attention, by a study of the nature of the problem under 

 question, to discovering some rule by which on inspection they 

 might be able to tell whether a given problem admitted of only 

 an indirect solution, a question of some importance in astronomy. 



I have not been able to discover that any direct solution has 

 been brought forth as yet ; so I send you this, given to me by a 

 friend of mine, Mr. Hesse, who solved it in 1842. I send it, 

 thinking that every mistake cleared up in science is a step 

 toward truth. 



If it would not be too much trespassing on your good nature, 

 I should be pleased to hear of the fate of my solution. 



Christine Chart. 



In the triangle ABC, two angles, CAB and CBA, are 

 2 A 2 



