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 263
to BO. [I. 31.CE shall be a third proportional to AB, AC. Proof, Because BC is parallel to DE, a side of the A APE; [Construction. .. AB:BD :: AC : CE; [VL 2. but BD = AC ; [Construction. r. AB:AC::AC:CE. Wherefore, to the given straight lines AB, AC, a third propor-tional CE is found, [q.e.f. BOOK… … Construction. Take two straight lines, DE, DF, contain-ing any angle EDF ; and in these make DGr equal to A, GEequal to B, and DH equal to C ; [I. 3. join GH, and through E draw EF parallel to GH to meetDF in F. [I. 31. HF shall be a fourth proportional to A, B, C. Proof. Because GH is parallel to…
Euclid's Elements · Geometry · Mathematics, Greek
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