A Second Chapter on Conics

Extract

Let PQ, PQ′ (Fig. 1) be tangents to a conic, S, H the foci, Q′Cq a diameter, then Kq the tangent at q is ⅡPQ′. By a construction and a proof identical with those of an article in the second number of this Gazette we can show that rect^le PQ.QK = SQ.QH, ∠ SKQ = QHP = PHQ′, ∆^s PKS and PHQ′ similar, and ∴ rect^le PS . PH = PK. PQ′. Through C draw a straight line ⅡQQ′, meeting PQ, PQ′ in F, F′, and cutting the tangent qK in E. QQ′ being ⅡFF′ and bisected by CP, CF = CF′; also Q′q being a diameter, CE = CF′. Thus E and F are the same point and coincide with K, and ∴ KC is ⅡQQ′.