Smart, Edward Howard · London : Macmillian and Co. · leaf 199
ellipse inmagnitude and position, to construct the axes. Let KPK, the normal at P, cut DCD, the diameter conjugateto CP in F (Fig. 89). Mark off PK = PK = CD on this normal. Then CK^ = CP^ + PK^ + 2FP. PK = CP2 + CD2 + 2FP.CD = ^2 + 62 + 2a6. (Chap. IX., §§ 8 and 9.) Thence CK = <x + 6, and… … Fig. 69. Also, by Cor. 2 above, — = -. .. — = -. *^ CD a PK a PK +PG a + b KG CK . . i i • = J-, I.e. — = —, irom the above. •• PK-PG a-b GK CK .*. CG bisects the angle KCK. Accordingly, when CK and CK are constructed as above, theinternal and external bisectors of the angle between them arethe…
Geometry, Projective
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