 | Adrien Marie Legendre - Geometry - 1863 - 464 pages
...II., P. IV., C.), AE : EG : : CF : FH. In like manner, EG : GB : : FH HD ; and so on. PROPOSITION XVI. THEOREM. If a line divides two sides of a triangle proportionally^ it will be parallel to the third side. Let ABC be a triangle, and let DE divide AB and AC, so that AD... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...should then 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 BC. For,... | |
 | William Chauvenet - Geometry - 1872 - 382 pages
...should then 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 - 426 pages
...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... | |
 | William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...|| ad. To BE 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... | |
 | George Albert Wentworth - Geometry, Modern - 1881 - 266 pages
...AF : AF, §263 or, AB : AE : : A С : A F. PROPOSITION III. THEOREM. 277. If a straight line divide two sides of a triangle proportionally, it is parallel to the third side. A In the triangle ABC let EF be drawn so that =. We are to prove EF II to B С. From E draw EH II to... | |
 | Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...: : CF : FH. In like manner, EG : GB :: FH : HD; and so on. PROPOSITION XVI. THEOREM. // a straight line divides two sides of a triangle proportionally, it is parallel to the third side. Let ABC be a triangle, and let DE divide AB and AC, so that AD : DB :: AE : EC; then DE is parallel... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...to the base of a triangle .divides the other two sides proportionally. PROPOSITION II. If a straight line divides two sides of a triangle proportionally, it is parallel to the third side. PROPOSITION III. Two triangles are similar when they are mutually equiangular. PROPOSITION IV. Two... | |
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If a line divides two sides of a triangle proportionally, it is parallel to the third side. 
