Alex Ziwet 9-12-1922 First Edition 1861, Second Edition 1866, Third Edition 1876, Fourth Edition 1890. PREFACE. 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. 406787 In this Second Edition several new articles have been added, especially in the latter part of the work, and the chapter on Reciprocal Polars considerably enlarged. GONVILLE AND CAIUS COLLEGE, N. M. F. In the Third Edition, I have rewritten some articles where the demonstrations were imperfect or obscure, and have added some examples, taken from various Cambridge Examination papers. DECEMBER, 1875. 8. 9. Every Equation of the First Degree represents a Straight Line Point of Intersection of Two Straight Lines Equation of a Straight Line passing through Two given Points. ib. 11. Equation of a Straight Line passing through the Point of Inter- Condition that Three Points may lie in the same Straight Line. ib. 13. Condition that Three Straight Lines may intersect in a Point 14 ARTS. PAGE 27-29. Anharmonic Properties of Points and Lines in Involution 2, 3. Equation of the Conic described about the Triangle of Refer- 3333 Equation of the Conic which touches two sides of the Triangle of Reference in the points where they meet the third Equation of a Line joining Two given Points Equation of the Tangent at a given Point. |