172 On the ORIGIN and 
have a given ratio to one another: the propofition becomes a 
Porifm, and is the fame that has been juft inveftigated. 
Herz it is evident, that the local theorem is changed into a 
Porifm, by leaving out what relates to the determination of the 
point D, and of the given ratio. But though all propofitions 
formed in this way, from the converfion of Loci, be Porifms, 
yet all Porifms are not formed from the converfion of Loci, 
The firft and fecond of the preceding, for inftance, cannot by 
converfion be changed into Loci; and therefore the definition 
which defcribes all Porifms as being fo convertible, is not fuf- 
ficiently comprehenfive. FERMAT’s idea of Porifms, as has 
been already obferved, was founded wholly on this definition, 
and therefore could not fail to be imperfect. 
18. Ir appears, therefore, that the definition of Porifms 
given above, (§ 16.) agrees with Pappus’s idea of thefe propo- 
fitions, as far at leaft as can be collected from the imperfect 
fragment which contains his general defcription of them. © It 
agrees alfo with Dr Simson’s definition, which is this *: “ Po- 
“ rifma eft propofitio in qua proponitur demonftrare rem ali- 
“* quam, vel plures datas efle, cui, vel quibus, ut et cuilibet ex 
“‘ rebus innumeris, non quidem datis, fed que ad ea que data 
fant eandem habent relationem, convenire oftendendum eft 
“ affetionem quandam communem in propofitione defcrip- 
“ tam.” 
Ir cannot be denied, that there is a confiderable degree of 
obfcurity in this definition + ; notwithftanding of which, it is 
certain, 
“ce 
* Sumson’s Opera Reliqua, p. 323. 
+ Tue following tranflation will perhaps be found to remedy fome of the ob{curity 
complained of. 
«¢ A Porism is a propofition, in which it is propofed to demo ftrate, that one or more 
things are given, between which and every one of innumerable other things, not given, 
but aflumed according to a given law, a certain relation, defcribed in the propolition, - 
is to be fhewn to take place.” ° 
Iv 
