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" A line parallel to one side of a triangle divides the other two sides proportionally. "
Elements of Plane and Solid Geometry - Page 139
by Alan Sanders - 1903 - 384 pages
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Dictionary of the Mathematical and Physical Sciences, According to the ...

James Mitchell - Mathematics - 1823 - 666 pages
...opposite 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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The English Cyclopaedia

Encyclopedias and dictionaries - 1866 - 520 pages
...should have found that the equation (3.) is true, and a necessary consequence of the proposition, that a line drawn parallel to one side of a triangle divides the other sides into proportional segment?. The synthetical form of the preceding process differs from it much...
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Arts and Sciences: Or, Fourth Division of "The English Encyclopedia", Volume 1

Charles Knight - Encyclopedias and dictionaries - 1866 - 532 pages
...should have found that the equation (3.) is true, and a necessary consequence of the proposition, that a line drawn parallel to one side of a triangle divides the other sides into proportional segments. The synthetical form of the preceding process differs from it much...
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Nature, Volume 65

Sir Norman Lockyer - Electronic journals - 1902 - 688 pages
...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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Nature, Volume 65

Sir Norman Lockyer - Electronic journals - 1902 - 1074 pages
...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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An Elementary Geometry

William Frothingham Bradbury - Geometry - 1872 - 124 pages
...altitude and the line joining the middle points of tlio sides which are not parallel. THEOREM VI. 161 A line drawn parallel to one side of a triangle divides the other sides proportionally. In the triangle ABC let DE be drawn parallel to BC ; then AE :EC=AD :DB A< Draw...
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An Elementary Geometry and Trigonometry

William Frothingham Bradbury - Geometry - 1873 - 288 pages
...altitude and the line joining the middle points of the sides which are not parallel. THEOREM VI. 16. A line drawn parallel to one side of a triangle divides the other sides proportionally. In the triangle ABC let DE be drawn parallel to B С ; then AE :EC=AD :DB Draw...
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Elements of Plane Geometry, Part 1

Thomas Hunter - Geometry, Plane - 1878 - 142 pages
...same line and between the same parallels are to each other as their bases. PROPOSITION Id.—THEOREM. A line drawn parallel to one side of a triangle divides the other tico sides into proportional parts. Let ABC be any triangle, and DE a line drawn parallel to AB; then...
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An Elementary Geometry: Plane, Solid and Spherical

William Frothingham Bradbury - Geometry - 1880 - 260 pages
...altitude by the line joining the middle points of the sides which are not parallel. THEOREM XIX. 50. A line drawn parallel to one side of a triangle divides the other sides proportionally. In the triangle ABC let DE be drawn parallel to BC ; then or AC: AE—AB:AD line...
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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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