Smart, Edward Howard · London : Macmillian and Co. · leaf 73
t is a circle. Let O and k be as before. Let 0 (Fig. 17) be the centre of the circle to b?^^inverted. Then if P is the inverse of P, OP. OP = k^. If OP meet the circle again in Q, OP. 0Q = 0T2. OP k^ Whence — = —i^, which is constant for all positions of the,. ^„^ OQ 0T2line OPQ. OX Divide OC at X… … Pig. 17. It is a good exercise in the application of the principle ofcontinuity to deduce from this the result of § 5. § 7. Prop. If two curves cutone another, their inverses cut atthe same angle. Consider first a single curve andits inverse. Take two near positions of theradius vector, and let P,…
Geometry, Projective
Internet Archive · California Digital Library · Public Domain Mark 1.0. Free to use for anything.
