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XVII. General Theorems , chiefly Porisms, in the higher Geo- 
metry. By Henry Brougham, Jun. Esq. Communicated by 
Sir Charles Blagden, Knt. F. R. S. 
» 
Read May 24, 1798. 
The following are a few propositions that have occurred to 
me, in the course of a considerable degree of attention which I 
have happened to bestow upon that interesting, though diffi- 
cult branch of speculative mathematics, the higher geometry. 
They are all in some degree connected; the greater part refer 
to the conic hyperbola, as related to a variety of other curves. 
Almost the whole are of that kind called porisms, whose nature 
and origin is nozv well known ; and, if that mathematician to 
whom we owe the first distinct and popular account of this 
formerly mysterious, but most interesting subject,* should 
chance to peruse these pages, he will find in them additional 
proofs of the accuracy which. characterizes his inquiry into the 
discovery of this singularly beautiful species of proposition. 
Though each of the truths which I have here enunciated is 
of a very general and extensive nature, yet they are all disco- 
vered by the application of certain principles or properties still 
more general; and are thus only cases of propositions still more 
extensive. Into a detail of these, I cannot at present enter : 
they compose a system of general methods* by which the dis- 
covery of propositions is effected with certainty and ease ; and 
* See Mr, Playfair’s Paper, in Vol. III. of the Edinburgh Trans. 
