A P P E N'D I X. 75 



{hip. It was pleafmg to obferve, in thefe two profound Mathe- 

 maticians, the moft perfect efteem and affe&ion for each other, 

 and the moft entire abfence of jealoufy, though no two men 

 ever trode more nearly in the fame path. The fimilitude of 

 their purfuits, as it will ever do with men fuperior to envy, 

 ferved only to endear them to one another. Their fentiments 

 and views of the fcience they cultivated were nearly the fame ; 

 they were both profound Geometers ; they equally admired 

 the ancient Mathematicians, and were equally verfed in their 

 methods of inveftigation j and they were both apprehenfive, 

 that the beauty of their favourite fcience would be forgotten 

 for the lefs elegant methods of algebraic computation*. This 

 innovation they endeavoured to oppofe ; the one, by reviving 

 thofe books of the ancient Geometry which were loft ; the 

 other, by extending that Geometry to the moft difficult enqui- 

 ries of the moderns. Dr STEWART, in particular, had remark- 

 ed the intricacies, in which many of the greateft of the modern 

 Mathematicians had involved themfelves in the application of 

 the calculus, which a little attention to the ancient Geometry 

 would certainly have enabled them to avoid. He had ob ferved, 

 too, the elegant fynthetical demonftrations that, on many oc- 

 cafions, may be given of the moft difficult propofitions, invefti- 

 gated by the inverfe method of fluxions. Thefe circumftances 

 had, perhaps, made a ftronger impreffion than they ought, on 

 a mind already filled with admiration of the ancient Geometry, 

 and produced too unfavourable an opinion of the modern ana- 

 lyfis. But, if it be confefled, that Dr STEWART rated, in any 

 refpeft too high, the merit of the former of thefe fciences, 



(K. 2) this 



* ON the reverfe of a miniature picture of Dr SIMSON, now in the pofleflion of Mr 

 Prof. STEWART, is an infcription, written by Dr MOOR, late Profeflbr of Greek at Glaf- 

 gow, an intimate friend of Dr SIMSON, and a great admirer of the ancient Geometry: 

 GEOMETRIAM, SUB TYRANNO BARBARO SAEVA SERVITUTE DIU siyjALENTEM, IN 



LIBERTATEM ET DBCCS ANTKipUM VINDICAVIT VNH*. 



