APPENDIX. 71 



ferve as a proof that it is not equal to fuch difficult refearches ; 

 and that in thofe cafes, efpecially, where approximation is to be 

 ufed, it is neceflary to facrifice the rigour of the ancient de- 

 monftration for the accuracy of the modern analyfis. 



THE Suns Dijlance was the lad work which Dr STEWART 

 publifhed ; and though he lived to fee the animadverfions made 

 on it, that have been taken notice of above, he declined enter- 

 ing into any controverfy. His difpofition was far from pole- 

 mical ; and he knew the value of that quiet, which a literary 

 man mould rarely fuffer his antagonifts to interrupt. He 

 ufed to fay, that the decifion of the point in queftion was now 

 before the public ; that, if his investigation was right, it would 

 never be overturned, and that, if it was wrong, it ought not to 

 be defended. 



A FEW months before he publifhed the Eflay jufl mention- 

 ed, he gave to the world another work, entitled, Propojitiones 

 Geometrica More Veterum Demonftratce. This title, I have been 

 told, was given it by Dr SIMSON, who rejoiced in the publica- 

 tion of a work fo well calculated to promote the ftudy of the 

 ancient Geometry. It confifts of a feries of geometrical 

 theorems, for the moft part, new ; invefligated, firft, by an 

 analyfis, and afterwards fynthetically demonftrated by the in- 

 verfion of the fame analyfis. In the former, the propofition to 

 be inveftigated is fuppofed true ; from thence confequences are 

 deduced, and the reafoning is carried on till fome confequence 

 is drawn that is already known to be true. A neceflary con- 

 nection is thus traced between the propofition that was fuppofed 

 true, and another that is certainly known to be fo ; and, thus, 

 an ingenious method is laid down for making the knowledge 

 of any truth fubfervient to the difcovery of its demonflration. 

 This method made an important part in the analyfis of the 

 ancient Geometers ; but few examples of it have been pre- 

 ferred in their writings, and thofe in the Propofitiones Geometric*?, 

 are, on that account, the more valuable. 



Dr 



