Abstract
The Porism referred to is as follows, viz. two conics may be so related to each other, that a polygon may be inscribed in the one, and circumscribed about the other conic, in such manner that any point whatever of the circumscribing conic may be taken for a vertex of the polygon. I gave in the year 1853, in the Philosophical Magazine, a general formula for the relation between the two conics, viz. if U = 0 is the equation of the inscribed conic, V = 0 that of the circumscribed conic, and if disc (U + ξ V), where ξ is an arbitrary multiplier, denotes the discriminant of U + ξ V in regard to he coordinates ( x, y, z ) (such discriminant being of course a cubic function in regard to ξ, and also in regard to the coefficients of the two conics U, V, jointly), then if we write.
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