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 422
. 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. .-. zABQ + zAPQ = two right l\ [III. 22. But zAPQ is a right z, [III.… … Let C be the centre of the circle. Join O to any point P on thecircle, and on it take Q such that OP . OQ = P, the constant ofinversion. Let OP produced meet the circle in P. Draw OD the tangentfrom 0 to the circle, and for simplicity put OD = t. Then OP . OP^OD^:.:^^ . |-ni. 36. .-. OP . OQ : OP .…
Euclid's Elements · Geometry · Mathematics, Greek
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