...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...

...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...

...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...

...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...

...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...

...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...

...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...

...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...

...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...

...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...