INFESTIGA^ION of PORISMS. 173 



certain, that every propofition to which it applies mud contain 

 a problematical part, viz. " in qua proponitur demonftrare rem 

 " aliquam, vel plures datas effe;" and alfo a theoretical part, 

 which contains the property, or communis affeclio, affirmed of cer- 

 tain things which have been previoufly defcribed. 



It is alfo evident, that the fubjecl of every fuch propofition 

 is the relation between magnitudes of three different kinds ; de- 

 terminate magnitudes, which are given ; determinate magni- 

 tudes, which are to be found ; and indeterminate magnitudes, 

 which, though unlimited in number, are connected with the 

 others by fome common property. Now, thefe are exactly the 

 conditions contained in the definition that has been given 

 here. 



1 9. To confirm the truth of this theory of the origin of Po- 

 rifms, or at leaft the juflnefs of the notions founded on it, 

 I mufl add a quotation from an EfTay on the fame fubject, 

 by a member of this Society, the extent and correclnefs of 

 whofe views make every coincidence w th his opinions pecu- 

 liarly flattering. In a paper read feveral years ago before the 

 Philofophical Society, ProfefTor Dugald Stewart defined a 

 Porifm to be, " A propofition affirming the poffibility of find- 

 tl ing one or more of the conditions of an indeterminate theo- 

 u rem " where, by an indeterminate theorem, as he had pre- 

 vioufly explained it, is meant one which exprefTes a relation be- 

 tween certain quantities that are determinate, and certain o- 

 thers that are indeterminate, both in magnitude and in num- 

 ber. The near agreement of this with the definition and ex- 

 planations which have been given above, is too obvious to re- 

 quire 



It may be proper to remark, that there is an ambiguity in the word given, as ufed 

 here and on many other occafions, where it denotes indifferently things that are both de- 

 terminate and known, and things that, though determinate, are unknown, provided they can 

 be found. This holds as to the firft application of the term in the above definition 5 

 from which however no inconveniency arifes, when the reader is appriled of it. In the 

 courfe of this paper, I have endeavoured, as much as poflible, to avoid the like ambi- 

 guity. 



