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THE prominence which the modern geometrical methods have recently acquired in the studies of the University of Cambridge, appears to justify the publication of a treatise devoted exclusively to these branches of Mathematics. This remark applies more especially to the method of Trilinear Co-ordinates, which forms the subject of the greater part of the following work. My object in writing on this subject has mainly been to place it on a basis altogether independent of the ordinary Cartesian system, instead of regarding it as only a special form of Abridged Notation
A desire not unduly to increase the size of the book has prevented me from proceeding beyond Curves of the Second Degree.
I have introduced a short Chapter on Determinants. The great utility of these expressions in investigations connected with curves of the second degree will, I hope, be a sufficient excuse for the employment of a notation which has hitherto been hardly admitted into Cambridge text-books. I have, however, confined myself rigorously to the demonstration of such elementary properties as are required in the course of this work. I should be glad if the very slight sketch contained in Chapter III. should be the means of inducing any of my readers to refer to the original memoirs on this and kindred subjects.