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 406
ng 00 in L. Then, by YI. 3 and A, OK : KO:: OP : PO,and OL : LO :: OP : PO. .*. the ratios OK : KO and OL : LO are each equal to the givenratio, and thus K, L are both fixed. Since PK, PL bisect the interior and exterior angles at P, .*. KPL is a right angle. .*. the locus of P is a circle… … i [We will take the case in which the points are in the following order,0, A, B, C, D.] Let P be a point such that zAPB = zCPD. APPP]N1)IX. LOCI. BOOK VI. Ixiii Describe a circle round the A APD, and let PO be the tangent to itat P meeting the given line at O. Then z OPA = z ODP ; [III. 32. .-.…
Euclid's Elements · Geometry · Mathematics, Greek
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