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In the present Treatise the Conic Sections are defined with reference to afocus and directrix, and I have endeavoured to place before the student themost important properties of those curves, deduced, as closely as possible, from the definition.The construction which is given in the first Chapter for the determinationof points in a conic section possesses several advantages; in particular, it leadsat once to the constancy of the ratio of the square on the ordinate to therectangle under its distances from the vertices; and, again, in the case ofthe hyperbola, the directions of the asymptotes follow immediately from theconstruction. In several cases the methods employed are the same as thoseof Wallace, in the Treatise on Conic Sections, published in the EncyclopaediaMetropolitana

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