 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 554 pages
...AE To PROVE DE parallel to BC. From D draw DE' parallel to BC. AB AC Then §270 AD AE' [A straight line parallel to one side of a triangle divides the other two sides proportionally.] AB AC But — =— ' Hyp. Hence Ax. i AC_AC AE~ AE' The numerators of these equal... | |
 | Henry W. Keigwin - Geometry - 1897 - 254 pages
...QB. The lines must be divided either both internally or both externally. PROPOSITION I. THEOREM. 233. A line parallel to one side of a triangle divides the other two sides proportionally. Let ABO be a triangle, and let HKbe parallel to BC. It is to be proved that HA : HB... | |
 | George Washington Hull - Geometry - 1897 - 408 pages
...Therefore Iff + £C 5 + 'DC* + ~J& = Ic * + 5F. QED PROPORTIONAL LINES. PROPOSITION XIII. THEOREM. 242. A. parallel to one side of a triangle divides the other two sides proportionally. To Prove- £4_£L CE DE Dem. — Draw AD and BC. Then, since the triangles ADC and... | |
 | James Howard Gore - Geometry - 1898 - 232 pages
...having the same ratio, it is said to be divided harmonically. PROPOSITION XI. THEOREM. 213. A straight line parallel to one side of a triangle divides the other two sides proportionally. In the triangle ABC let DE be parallel to BC. To prove AD : DB = AE : EC. CASE I. When... | |
 | Webster Wells - Geometry - 1898 - 250 pages
...proportions (1), (2), (3), and (4), of §§ 245 and 246, are all included in the general statement, A parallel to one side of a triangle divides the other two sides proportionally. PROP. XII. THEOREM. 248. (Converse of Prop. XI.) A line which divides two sides of... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry, Modern - 1899 - 272 pages
...difference, by increasing n, .-. to assume any difference leads to an absurdity. BDAC COROLLARIES. 1. A line parallel to one side of a triangle divides the other two sides proportionally. D.\ I/A C\\Q *jt/ /B> C\ \D, For in the figure, if BCO is the triangle, the lines OB,... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1899 - 412 pages
...difference, by increasing n, .'. to assume any difference leads to an absurdity. BDAC . COROLLARIES. 1. A line parallel to one side of a triangle divides the other two sides proportionally. .« \* 3 , ,. r I D8\ \C, i /B, CJi \0; For in the figure, if BCO is the triangle,... | |
 | Webster Wells - Geometry - 1899 - 424 pages
...Thus, lines AB and CD are divided ! II proportionally if CFD AE CF DP CD PROP. XI. THEOREM. 244. A parallel to one side of a triangle divides the other two sides proportionally. Case I. When the segments of each side are commensurable. Given, in A ABC, segments... | |
 | Arthur Schultze - 1901 - 392 pages
...according as C lies in AB or in the prolongation of AB. PROPORTIONAL LINES PROPOSITION XIII. THEOREM 280. A line parallel to one side of a triangle divides the other two sides proportionally. B c Hyp. In A ABC, DE is parallel to BC. To prove AD : DB = AE : EC. PLANE GEOMETRY... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 396 pages
...according as C lies in AB or in the prolongation of AB. PROPORTIONAL LINES PROPOSITION XIII. THEOREM 280. A line parallel to one side of a triangle divides the other two sides proportionally. Hyp. In A ABC, DE is parallel to BC. To prove AD : DB = AE : EC. Proof. CASE I. AD... | |
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A line parallel to one side of a triangle divides the other two sides proportionally. 
