APPENDIX. 61 



IN the fummer of 1746, the Mathematical Chair in the Uni- 

 verfity of Edinburgh became vacant by the death of Mr MAC- 

 LA UR IN. The General Theorems had not yet appeared ; Mr 

 STEWART was known only to his friends ; and the eyes of the 

 public were naturally turned on Mr STIRLING, who then re- 

 fided at Leadhills, and who was well known in the mathemati- 

 cal world. He, however, declined appearing as a candidate for 

 the vacant chair j and feveral others were named, among whom 

 was Mr STEWART. In the end of this year, the General Theo- 

 rems were publifhed, and gave to their Author a decided fupe- 

 riority above all the other candidates. He was accordingly 

 elected ProfeiTor of Mathematics in the Univerfity of Edin- 

 burgh, in the beginning of September 1747. 



THE duties of this office gave a turn fomewhat different to 

 his mathematical purfuits, and led him to think of the moft 

 fimple and elegant means of explaining thofe difficult propofi- 

 tions, which were hitherto only acceffible to men deeply verfed 

 in the modern analyfis. In doing this, he was purfuing the ob- 

 ject which, of all others, he moft ardently wifhed to attain, viz. 

 the application of Geometry to fuch problems as the alge- 

 braic calculus alone had been thought able to refolve. His fo- 

 lution of KEPLER'S problem was the firft fpecimen of this 

 kind which he gave to the world ; and it was impoffible to have 

 produced one more to the credit of the method he followed, or 

 of the abilities with which he applied it. When the Aftrono- 

 mer, from whom that problem takes its name, difcovered the 

 elliptical motion of the planets, and their equable defcription 

 of areas round the fun, he reduced the problem, of computing 

 the place of a planet for a given time, to that of drawing a 

 line through the focus of an ellipfe, that mould divide the area 

 of the femi-ellipfe in a given ratio. It was foon found, that 

 this problem did not admit of an accurate folution ; and that 

 no more was to be expected, than an eafy and exact approxima- 

 tion. In this, ever fince the days of KEPLER, the Mathema- 

 ticians 



