| William Chauvenet - Geometry - 1871 - 380 pages
...AB — A'B', BC— B'C', etc. PROPOSITION II.— THEOREM. 19. Conversely, if a straight line divides **two sides of a, triangle proportionally, it is parallel to the third side.** Let DE divide the sides AB, AC, of the triangle ABC, proportionally; then, DE is parallel to BC. For,... | |
| William Chauvenet - Geometry - 1872 - 382 pages
...have AB = A'B', BC=B'C', etc. PROPOSITION II.— THEOREM. 19. Conversely, if a straight line divides **two sides of a triangle proportionally, it is parallel to the third side.** Let DE divide the sides AB, AC, of the triangle ABC, proportionally; then, DE is parallel to £C. For,... | |
| William Guy Peck - Conic sections - 1876 - 376 pages
...FH. In like manner, we have, EG : GK :: FH : HL, and so on. PROPOSITION XII. THEOREM. If a line cuts **two sides of a triangle proportionally it is parallel to the third side.** Let EF cut the sides AD and CD, of the triangle ACD, so that AE : ED :: CF : FD; . . (1) then is EF... | |
| Richard Wormell - 1876 - 268 pages
...one of the sides of a triangle, cuts the other sides proportionally ; and conversely, if a line cuts **two sides of a triangle proportionally, it is parallel to the third side.** This theorem may also be proved from LXXI., thus : — In Д А B С let DE be parallel to B С, then... | |
| George Albert Wentworth - Geometry - 1877 - 416 pages
...base, as the other side is to the corresponding part. Now EB : AE : : FC : A F. §275 By composition, **PROPOSITION III. THEOREM. 277. If a straight line...side. A In the triangle ABC let EF be drawn so that** — = —. AE AF We are to prove EF II to B C. From E draw EH \\ to B C. A~=A' (one side of a A is... | |
| George Albert Wentworth - Geometry - 1877 - 436 pages
...corresponding part. Now EB : AE :: FC : AF. §275 By composition, EB + AE : AE : : FC+ AF : AF, §263 **PROPOSITION III. THEOREM. 277. If a straight line...third side. A In the triangle ABC let EF be drawn so** AEAF We are to prove EF II to BC. From E draw EH II to B С. Then — = — , § 276 AEAH (one side... | |
| George Albert Wentworth - Geometry - 1877 - 416 pages
...to the corresponding part. Now EB : AE : : FC : AF. §275 By composition, I 142 GEOMETRY. BOOK III. **PROPOSITION III. THEOREM. 277. If a straight line...proportionally, it is parallel to the third side. A** 111 the triangle ABC let EF- be drawn so fiai — ^ ^. AEAF We are to prove EF II to B С. -.•'.i-/... | |
| George Albert Wentworth - Geometry - 1877 - 426 pages
...corresponding part. Now EB : AE : : F С : A F. § 275 By composition, PROPOSITION III. THEOREM. 277. 1f **a straight line divide two sides of a triangle proportionally, it is parallel to the third side. A** la the triangle ABС let EF be drawn so that — = — . AE AF We are to prove EF II to B С. From... | |
| George Albert Wentworth - Geometry - 1877 - 416 pages
...proportionally, it is parallel to the third side. A In the triangle ABC let EF be drawn so _ AЛ AF **We are to prove EF II to B С. From. E draw EH** \\ to B С. rrv ABAC , „_,. .h,,, rï-jff' §2'6 (one sule of а Л is to either part cut off by... | |
| William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...PROVED. OA : Oa = OB : O& = OC : Oc = OD : Od. xvni. Theorem. Converse!y, if a straight line divides **two sides of a triangle proportionally, it is parallel to the third side.** HYPOTH. In the triangle ABC, AD : DB=AE : EC. To BE PROVED. The line DE [| BC. \ BOOK III.] PROPORTIONAL... | |
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