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 432
cyclic quad^ then the point 0 lies onthe third diagonal PQ. For zPOD = zBCQ and zQOD = zBAD. .-. zP0D + zQ0D=2 rt. z% since ABCD is cyclic. .*. POQ is a str. line. Ixxxviii EUCLIDS ELEMENTS. 109. In a complete quadrilateral each diagonal is divided harmonic-ally hy the other two diagonals. Let the… … By Art. 105, since R is a point in the a BCQ, /. BU.CD.QA=UC.DQ.AB (1) By Art. 103, since ADP is a transversal of the same a , .-. BP.CD.QA = PC.DQ.AB. (2) From (1), (2), BU : BP :: UC : PC, z.e. BU : UC :: BP : PC. /. B, U, C, P form a harmonic range ; [Art. 95. .*. QB, QU, QC, QP are a harmonic…
Euclid's Elements · Geometry · Mathematics, Greek
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