SIMSON. 501 



Here the locus has nothing to do with the solution, 

 as if the proposition were a kind of a local theorem : 

 it is only the line dividing the curvilineal areas, and it 

 divides innumerable such areas. Professor Playfair, 

 who had thoroughly investigated the whole subject, 

 never in considering this proposition doubted for a 

 moment its being most strictly a porism. 



Therefore, although Fermat must be allowed to 

 have made a considerable step, he was unacquainted 

 with the true nature of the porism ; and instead of 

 making good his boast that he could restore the lost 

 books, he never even attempted to restore the investi- 

 gation of the first proposition, the only one that re- 

 mains entire. A better proof can hardly be given of 

 the difficulty of the whole subject.* 



Indeed it must be confessed that Pappus's account of 

 it, our only source of knowledge, is exceedingly obscure, 

 all but the panegyrics which, in a somewhat tanta- 

 lizing manner, he pronounces upon it. " Collectio," 

 says he, " curiosissima multarum rerum spectantium ad 

 resolutionem difficiliorum et generaliorurn problema- 

 tum" (lib. vii., Proem). His definition already cited 

 is, as he himself admits, very inaccurate ; because the 



* The respect due to the great name of Fermat, a venerable 

 magistrate and most able geometrician, is not to be questioned. He 

 was, indeed, one of the first mathematicians of the age in which he 

 flourished, along with the Robervals, the Harriots, the Descartes. 

 How near he approached the differential calculus is well known. 

 His correspondence with Roberval, Gassendi, Pascal, and others, 

 occupies ninety folio pages of his posthumous works, and contains 

 many most ingenious, original, and profound observations on va- 

 rious branches of science. 



