Smart, Edward Howard · London : Macmillian and Co. · leaf 179
rpendicular to that directrix which corresponds to a focus S,SP/PK is a constant ratio (called the Eccentricity). Let P be any point on the curve and let PA, PA meet thedirectrix in E, E (Fig. 77). THE FOCI 151 Then SE, SE are conjugate lines at right angles. It has been proved that if ES meets AP… … Fig. 77. .*. angle PSV = angle ASV = angle PLS if SV meets KP in L. .. SP = PL. Hence SP/PK = LP/PK = SA/AX. Similarly if SE meets PK in L, PL = PS, and either of theabove ratios is equal to SA/AX. The student should draw the figure for the case of thehyperbola. § 6. The Eccentricity in terms of…
Geometry, Projective
Internet Archive · California Digital Library · Public Domain Mark 1.0. Free to use for anything.
