VII. On the Origin and Investigation of Porisms. By 

 John Plat fair, F. R. S. Edin. and Profejfor of Ma- 

 thematics in the Univerfity of Edinburgh. 



PART I. 



[Read April 2. 1792.] 



1. nr^HE reftoration of the ancient books of geometry would 

 A have been impoflible, without the coincidence of two 

 circumftances, of which, though the one is purely accidental, 

 the other is effentially connected with the nature of the mathe- 

 matical fciences. The firft of thefe circumftances is the pre- 

 fervation of a fhort abftract of thofe books, drawn up by 

 Pappus Alexandrinus, together with a feries of fuch lem- 

 mata, as he judged ufeful to facilitate the ftudy of them. The 

 fecond is, the necejfary connection that takes place among the 

 objects of every mathematical work, which, by excluding what- 

 ever is arbitrary, makes it poflible to determine the whole 

 courfe of an inveftigation, when only a few points in it are 

 known. From the union of thefe circumftances, mathematics 

 has enjoyed an advantage of which no other branch of know- 

 ledge can partake ; and while the critic or the hiftorian has 

 only been able to lament the fate of thofe books of Livy and 

 Tacitus which are loft, the geometer has had the high fatis- 

 faction to behold the works of Euclid and Apollonius re- 

 viving under his hands. 



2. The firft reftorers of the ancient books were not, how- 

 ever, aware of the full extent of the work which they had un- 

 dertaken. 



