V. Some Geometrical Porisms, with Examples of their 

 Application fo the Solution o/" Problems. By Mr 

 William Wallace, AJJiJiant-'Teacher of the Mathematics in 

 ti?e Academy of Perth, Communicated by Mr PLArFAIR. 



[Rgad March 7. 1 796.] 



THE nature of ckofc 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 problemSj have 

 all been confidered by fome eminent mathematicians of the pre« 

 fent age. 



These propofirions appear to have been held in high eftima- 

 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 fubjedl have given us, of their applica- 

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

 character of them. 



The following paper contains fome porifins intimately con- 

 ne(5led with each other, and which feem Capable of being ap- 

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



N 2 amplcs 



