60 HISTORY of the SOCIETY. 



tenfive view, guided Mr STEWART in the difcovery of them 

 all. It feems probable, that, while he aimed at extending Geo- 

 metry beyond the limits it had reached with the ancients, he 

 had begun to confider the Locus ad quatuor rettas, beyond which 

 their analyfis had not reached. With this view, he, no doubt, 

 thought of extending the hypothefes of that problem to their 

 utmoft generality ; that is, to any number of perpendiculars 

 drawn to an equal number of lines, and to any power what- 

 ever of thefe perpendiculars. In doing this, he could not fail 

 to meet with many curious porifms ; for a porifm is nothing 

 elfe than that particular cafe, when the data of a problem are fo 

 related to one another, as to render it indefinite, or capable 

 of innumerable folutions. Thefe cafes, which rarely occur, 

 except in the conftruclion of very general and complicated 

 problems, mud always intereft a Geometer, becaufe they trace 

 out the divifions of his fubjecT:, and are ufually diftinguifhed 

 by an elegance and fimplicity peculiar to themfelves. Such, ac- 

 cordingly, were the propofitions which Mr STEWART now com- 

 municated to the world. He fupprefled his inveftigations, how- 

 ever, which were geometrical, and which, if given with all the 

 precifion required by the forms of the ancient Geometry, 

 would probably have occupied feveral volumes. 



THE hiftory of thefe geometrical difcoveries has led us to 

 neglect the order of time. For Mr STEWART, while engaged 

 in them, had entered into the Church, and, through the patro- 

 nage of the Earl of BUTE and the Duke of ARGYLE, had ob- 

 tained the living of Rofeneath. It was in that retired and ro- 

 mantic fituation, that he difcovered the greater part of the pro- 

 pofitions that have juft been mentioned. There, alfo, he ufed 

 to receive the vifits of his friend Mr MELVIL, whofe ingenious 

 obfervations in the Phyfical and Literary EJJays, give us caufe to 

 regret that he was fo early taken from the world of fcience *. 



IN 



* Obfervations on Light and Colours, Phyf. and Lit. Eflays, vol. ii. art. 4. 



