Newcomb, Simon, 1835-1909 · New York, H. Holt and company · leaf 111
roaches indefinitely near the centre ofthe circle, the polar recedes indefinitely, and vice versa. 82. Fundamental Theorem. If a line jkiss through apoint, the polar of the point ivillpass through the pole of the line. Proof. Let the line CD passthrough the point P. By definition, we find the… … such that OQ:r = r. OP. (b) We have to prove that P lies on the polar PQ. If wecall Q the point in which OQ meets the polar PQ, the tri-angles POQ and QOP, being both right-angled and havingthe angle at 0 common, are equiangular and therefore similar. Hence OQ: 0P= OP : OQ. (r) Comparing the…
Geometry, Analytic
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