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V, Some Geometrical Porisms, with Examples of their 

 Application /o the Solution o/" Problems. By Mr 

 William Wallace, JJJiJlant-Teacber of the Mathematics in 

 the Academy of Perth. Communicated by Mr Playfaib. 



[Read March y. 1796.] 



THE nature of tkofe mathematical pfopofitions, which were 

 called Porifms by the ancient geometers, is now no longer a 

 matter of uncertainty. The relation which they bear to other 

 mathematical truths, the way in which they may at firft have 

 been obferved, the kind of analyfis to be employed in their in- 

 veftigation, their application to the folution of problems, have 

 all been confidered by fome eminent mathematicians of the pre- 

 fent age. 



These propositions appear to have been held in high eflima- 

 tion by the mathematicians of antiquity, becaufe of their great 

 ufe in the analyfis of difficult problems, as we learn from the 

 writings of Pappus of Alexandria : And fome fpecimens, which 

 late inquirers into this fubjeft have given us, of their applica- 

 tion to the folution of problems, fcem to juftify his very high 

 character of them. 



The following paper contains fome porifms intimately con- 

 nedled with each other, and which feem Capable of being ap- 

 plied to the folution of a nximber of geometrical problems. Ex- 



N 2 amplcs 



