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" A line parallel to one side of a triangle divides the other two sides proportionally. "
New Plane Geometry - Page 172
by Wooster Woodruff Beman, David Eugene Smith - 1899 - 252 pages
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Dictionary of the Mathematical and Physical Sciences, According to the ...

James Mitchell - Mathematics - 1823 - 666 pages
...side into two segments, which are in proportion to the adjacent sides. 11. The line which is drawn parallel to one side of a triangle divides the other two sides proportionally. 1*2. The three lines which bisect the three angles of a triangle intersect in one common point, as...
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1841 - 186 pages
....... 45 Lines divided into equal parts (158), 45 To divide a line into equal parts (159), ..... 45 A line parallel to one side of a triangle divides the other two proportionally (K;0 - 162) ; and the converse (163), . . 46 To divide a line into parts proportional...
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1847 - 204 pages
...LINES, .... 45 Lines divided into equal parts (158), 45 To divide a line into equal parts (159) 45 A line parallel to one side of a triangle divides the other two proportionally (160 - 162) ; and the converse (163), . . 46 To divide a line into parts proportional...
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Nature, Volume 65

Sir Norman Lockyer - Electronic journals - 1902 - 1074 pages
...propositions, Euc. VI., I and 33, already referred to, are proved, and also the proposition "that a straight line parallel to one side of a triangle divides the other two sides in the same ratio,'1 Euc. VI., 2 (first part). Taking the proof furnished of this last theorem as a...
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Nature, Volume 65

Sir Norman Lockyer - Electronic journals - 1902 - 688 pages
...propositions, Eue. VI., i and 33, already referred to, are proved, and also the proposition " that a straight line parallel to one side of a triangle divides the other two sides in the same ratio," Eue. VI., 2 (first part). Taking the proof furnished of this last theorem as a...
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Elements of Geometry

Simon Newcomb - Geometry - 1881 - 418 pages
...:: AB' : B'C?. CZ But BB' is parallel to the side (70" of the triangle. Therefore: 388. A straight line parallel to one side of a triangle divides the other two sides similarly. THEOREM IV. 182 Hypothesis. ABC, a triangle of which, the sides CA and CB are cut (internally...
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Wentworth & Hill's Exercise Manuals: Geometry, Issue 3

George Albert Wentworth - 1884 - 264 pages
...lines, third proportional, mean proportional, extreme and mean ratio, segments of a line. 139. Theorem. A line parallel to one side of a triangle divides the other two sides into proportional parts ; and these two sides have the same ratio as two corresponding segments. 140....
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The Elements of Geometry

George Bruce Halsted - Geometry - 1885 - 389 pages
...—7 499. COROLLARY I. If the points A and A' coincide, the figure ACCr will be a triangle ; therefore a line parallel to one side of a triangle divides the other two sides proportionally. 500. COROLLARY II. If two lines are cut by four parallel lines, the intercepts on the one are to one...
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The Elements of Geometry

Webster Wells - Geometry - 1886 - 392 pages
...and CD are divided proportionally at E and F if i L i = CFD AE CF ' ' PROPOSITION XIV. THEOREM. 261. A line parallel to one side of a triangle divides the other two sides proportionally. Let DE be parallel to the side BC of the triangle ABC. To prove that — = — . AD AE CASE I. When...
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The Elements of Geometry

George Bruce Halsted - Geometry - 1886 - 394 pages
...z 499. COROLLARY I. If the points A and A' coincide, the figure ACC' will be a triangle ; therefore a line parallel to one side of a triangle divides the other two sides proportionally. 500. COROLLARY II. If two lines are cut by four parallel lines, the intercepts on the one are to one...
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