SIMSON. 515 



opinion expressed by one of his most eminent pupils, 

 Professor Robison, that he might have better suc- 

 ceeded in his favourite object of recovering the purely 

 geometrical methods of investigation, had he relaxed 

 a little more from their rigour in applying them to the 

 present state of science, and shown the ancient analy- 

 tical investigation dismembered of its prolixity, relieved 

 from its extreme scrupulousness, and subservient to the 

 investigations of the problems now become the main sub- 

 jects of mathematical inquiry. This has in a great 

 measure been performed by the most celebrated of his 

 school, Matthew Stewart, who actually has solved 

 Kepler's problem, and treated almost the whole doc- 

 trine of central forces by means of the ancient method.* 

 At the same time we have only to cast our eye upon 

 his diagrams to be convinced that though he has solved 

 the problems and demonstrated the theorems with a 

 most wonderful skill, by means purely geometrical, yet 

 he never could have obtained either the solutions or 

 the demonstrations had not Newton preceded him, 

 " his own analysis carrying the torch before."f The 

 most celebrated proposition in all the ' Principia,' the 

 general solution of the inverse problem of central 

 forces J, (lib. i. prop, xli.) is closely followed by Stewart, 

 and the diagrams are nearly the same. 



* His paper on the sun's distance, in which he also employs the 

 ancient analysis, has been long since proved erroneous by my friend 

 Mr. Dawson of Sedbergh, who wrote anonymously a demonstration 

 of the error in 1772. 



f " Sua mathesi facem praeferente." H ALLEY. 



J I am aware of Professor Robison's statement, already cited, of 

 Dr. Simson's opinion that the thirty-ninth proposition is the greatest 

 of all, but I cannot help suspecting the forty-first to be intended. 



