ll respects, and IIP=PW, andHZ=WZ. (Euc. 1.26.) .-. SW=SP + PW=SP+HP = 2AC (Prop, i.) Again, in the triangles HQZ, WQZ, we have HZ, WZ equal by the preceding de-monstration, QZ common, and the included angles HZQ, WZQ equal, being rightangles; hence the triangles are equal in all respects, and HQ =… … THE ELLIPSE. 175 Then in the triangles HPZ, WPZ, we have the sides HP,WP equal by construction, PZ common, and the angles HPZ,WPZ equal by the property of the tangent: therefore thetriangles are equal in all respects, and 4 PZH— z. PZW, eachof which is therefore a right angle. Hence HZ is the…
