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 246
thesame ratio which the other sides of the triangle have to one another. Conversely, if the segments of the base have the same ratio whichthe other sides of the triangle have to one another^ the straight linedrawn from- the vertex to the point of section shall bisect the verticalangle. Let ABC be a… … Proof, (i.) Because AC meets the parallels AD, EC, the ^CAD = the ^ACE, and the ^BAD = the ^AEC; [L 29. But the /.CAD = the /.BAD; [Hypothesis. .. the ^ACE-the Z.AEC; [Axiom 1. .-. AE = AC. [L6. Also, because AD is parallel to EC, [Construction. one of the sides of the ABCE ; .-. BD :DC ::BA : AE;…
Euclid's Elements · Geometry · Mathematics, Greek
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