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 418
)asses through a fixed point is cutharmonically by the pointy any circle, and the polar of the point. Let P be the fixed point and PQSR any straight line drawn through Pto cut the circle in Q and R and the polar KNK of P in S. ThenPQ, PS, PR shall be in harmonical progression. … Let KK meet OP in N. Join OK, OQ, and PK; then PK is thetangent at K and zPKO is a right z. [Art. 42, Cor. 2. We have PN. PO^PK^ [VL 8. -PQ.PR; [IIL 36. .-. Q, R, 0, N lie on a circle ;.-. z ORQ== supplement of zONQ^zPNQ.But zORQ-zOQR, since OQ-^OR.Also zOQR —zONR in the same segment,since 0, N, Q,…
Euclid's Elements · Geometry · Mathematics, Greek
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