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. Every Equation of the First Degree represents a Straight Line Point of Intersection of Two Straight Lines II Equation of a Straight Line passing through Two given Points ib. Equation of a Straight Line passing through the Point of Inter- Condition that Three Points may lie in the same Straight Line ib. Condition that Three Straight Lines may intersect in a Point Condition that Two Straight Lines may be parallel to one Anharmonic Ratio of a given Pencil Fourth Harmonic to Three given Straight Lines Anharmonic Properties of Points and Lines in Involution 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 Pole of a given Straight Line. Condition of Tangency. Condition for a Parabola ib. |