 | George Albert Wentworth - 1882 - 442 σελίδες
...By composition, EB + AE : AE : : FC+AF : AF, §263 or, AB : AE : : AC : A F. 142 GEOMETRY. BOOK III. PROPOSITION III. THEOREM. 277. If a straight line...sides of a triangle proportionally, it is parallel to the'third tide. A In the triangle ABC let EF be drawn so ¿¿at — = — . AE AF We are to prove EF... | |
 | George Albert Wentworth - 1884 - 422 σελίδες
...base, as the other side is to the corresponding part. Now EB : AE : : F С : A F. §275 By composition, PROPOSITION III. THEOREM. 277. If a straight line...proportionally, it is parallel to the third side. In the triangle ABC let EF be drawn so that •— = aJ?. AEAF We are to prove EF II lo B C. From E... | |
 | George Albert Wentworth - 1885 - 424 σελίδες
...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...drawn so that — = — . We are to prove EF II to B C. From E draw EH II to B C. AEAF Then — = — , § 276 AE AH' * (one side of a A is to either part... | |
 | Charles Davies, Adrien Marie Legendre - 1885 - 538 σελίδες
...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 - 1887 - 331 σελίδες
...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... | |
 | George Albert Wentworth - 1889 - 264 σελίδες
...D AH: AM= AF: AL = FH: LM= HB : MN. That is, AF:CG= FJI: GK= HB : KD. PROPOSITION II. THEOREM. 312. If a straight line divide two sides of a triangle proportionally, it is parallel to the third side. ln the triangle ABC let EF be drawn so that A13 = AC AE AF To prove EF\\ to BC. Proof. From E draw... | |
 | James Wallace MacDonald - 1889 - 80 σελίδες
...segments. See Book II., Proposition VI. Proposition XVII. A Theorem. 142. If a straight line divide the sides of a triangle proportionally, it is parallel to the third side. Proposition XVIII. A Problem. 143. To divide a given line into parts proportional to given lines, or... | |
 | James Wallace MacDonald - 1894 - 76 σελίδες
...segments. See Book II., Proposition VI. Proposition XVII. A Theorem. 142. If a straight line divide the sides of a triangle proportionally, it is parallel to the third side. Proposition XVIII. A Problem. 143. To divide a given line into parts proportional to given lines, or... | |
 | Edward Albert Bowser - 1890 - 414 σελίδες
...angles with AB and AC : prove that Proposition 1 3. Theorem. 301. Conversely, if a straight line divides two sides of a triangle proportionally, it is parallel to the third side. Hyp. Let DE cut AB, AC in the A ABC so that 7^ = -r=. To prove DE || to BC. Proof. If DE is not ||... | |
 | William Chauvenet - 1893 - 340 σελίδες
...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. 
