The elements of Euclid for the use of schools and colleges; comprising the first six books and portions of the eleventh and twelfth books; (1903)
Euclid, Todhunter, I. (Isaac), 1820-1884, ed. edt, Simson, Robert, 1687-1768, ed. edt · London; New York, Macmillan · leaf 421
meter lies along theperpendicidar drawn from O to the given straight line. Conversely, since if OP —t^, then OQ^^Yp, the locus of P is ob-tained from that of Q by the same process by which the locus of Q isderived from that of P. It follows that the inverse of the circle OQB with respect to O isthe… … (1) Draw the diameter OA and on it take a point B such thatOA . OB^P, the constant of inversion. B is then a fixed point. Join O to any point P on the curve, and on it take Q such thatOP ..OQ, = B. Then Q is the inverse of P.Since OP . OQ = OA . OB, .. P, Q, B, A lie on a circle ; [III. 36. .-.…
Euclid's Elements · Geometry · Mathematics, Greek
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