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INVESTIGATION of PORISMS. 173 
certain, that every propofition to which it applies muft contain 
a problematical part, viz. “ in qua proponitur demonftrare rem 
“ aliquam, vel plures datas efle;” and alfo a theoretical part, 
which contains the property, or communis affectio, affirmed of cer- 
tain things which have been previoufly defcribed. 
It is alfo evident, that the fubject 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 conne¢ted with the 
others by fome common property. Now, thefe are exaétly the 
conditions contained in the definition that has been given 
here. 
19. To confirm the truth of this theory of the origin of Po- 
rifms, or at leaft the juftnefs of the notions founded on it, 
I muft add a quotation from an Effay on the fame fubjedt, 
by a member of this Society, the extent and correctnefs of 
whofe views make every coincidence w th his opinions pecu- 
liarly flattering. Ina paper read feveral years ago before the 
Philofophical Society, Profeflor DuGALp Stewart defined a 
Porifm to be, “ A propofition affirming the poffibility of find- 
** ing one or more of the conditions of an indeterminate theo- 
“ rem ;” where, by an indeterminate theorem, as he had pre- 
vioufly explained it, is meant one which expreffes 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 
Ir 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 £nown, 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 ; 
from which however no inconveniency arifes, when the reader is apprifed of it. Inthe 
courfe of this paper, I have endeavoured, as much as poflible, to avoid the like ambi- 
guity. 
