58 HISTORY of the SOCIETT. 



coveries which had been made by it. The learning and genius 



Dr Stewart. J 



of VIVIANI, FERMAT,HALLEY,and of other excellent Mathema- 

 ticians, had already been employed in removing this difficulty ; 

 but their efforts had not been attended with complete fuccefs. 

 Dr SIMSON was now engaged in perfecting what they had begun, 

 and in rending the encroachments, which he conceived the mo- 

 dern analyfis to be making upon the ancient. With this view, 

 he had already publimed a treatife of Conic Sections, and 

 was now preparing a reftoration of the Loci Plant of APOLLO- 

 NIUS, in which that work was to refume its original elegance 

 and fimplicity. To thefe, and other ftudies of the fame kind, 

 he conftantly directed the attention of his young friend, while 

 he was delighted, and aftonifhed at the rapidity of his pro- 

 grefs. 



Mr STEWART'S views made it neceffary for him to attend 

 the lectures in the Univerfity of Edinburgh in 1741 j and that 

 his mathematical ftudies might fuffer no interruption, he was 

 introduced by Dr SIMSON to Mr MACLAURIN, who was then 

 teaching, with fo much fuccefs, both the Geometry and the 

 Philofophy of NEWTON. Mr STEWART attended his lectures, 

 and made that proficiency which was to be expected from the 

 abilities of fuch a pupil, directed by thofe of fo great a matter. 

 But the modern analyfis, even when thus powerfully recom- 

 mended, was not able to withdraw his attention from the an- 

 cient Geometry. He kept up a regular correfpondence with 

 Dr SIMSON, giving him an account of his progrefs, and of His 

 difcoveries in Geometry, which were now both numerous and 

 important, and receiving in return many curious communica- 

 tions with refpect to the Loci Plant, and the Porifms of EUCLID. 

 Thefe laft formed the moft intricate and paradoxical fubject in 

 the hiftory of the ancient Mathematics. Every thing concern- 

 ing them, but the name, had periftaed. PAPPUS ALEXANDRINUS 

 has made mention of three books of Porifms written by EU- 

 CLID, and has given an account of what they contained ; but 



this 



