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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,