 | William Chauvenet - 1871 - 380 페이지
...if a straight line divides two sides of a triangle proportionally, it is parallel to the third side. Let DE divide the sides AB, AC, of the triangle ABC, proportionally; then, DE is parallel to BC. For, if DE is not parallel to BC, let some other line DE', drawn through... | |
 | William Chauvenet - 1872 - 382 페이지
...if a straight line divides two sides of a triangle proportionally, it is parallel to the third side. Let DE divide the sides AB, AC, of the triangle ABC, proportionally; then, DEis parallel to BC. For, if DE is not parallel to BC, let some other line DE', drawn through... | |
 | Association for the improvement of geometrical teaching - 1876 - 66 페이지
...except the ratio of equality : and in each case there is only one such point of division. THEOR. 3. A straight line which divides the sides of a triangle...proportionally is parallel to the base of the triangle. THEOR. 4. Rectangles of equal altitude are to one another in the same ratio as their bases. COR. Parallelograms... | |
 | James Maurice Wilson - 1878 - 450 페이지
...less than i there are two positions for P, one between O and A, and one to the left of A. THEOREM 3. A straight line which divides the sides of a triangle...proportionally is parallel to the base of the triangle. For let AP : PB :: AQ : QC, and suppose PQ not parallel to BC, but if possible let PQ' be parallel... | |
 | Mathematical association - 1883 - 86 페이지
...demonstration will shew that there can be only one point of external division in the given ratio.] THEOR. 3. A straight line which divides the sides of a triangle...proportionally is parallel to the base of the triangle. THEOR. 4. Rectangles of equal altitude are to one another in the same ratio as their bases. [Let AC,... | |
 | William Chauvenet, William Elwood Byerly - 1887 - 331 페이지
...if a straight line divides two sides of a triangle proportionally, it is parallel to the third side. Let DE divide the sides AB, AC, of the triangle ABC, proportionally; then DE is parallel to BC. For, if DE is not parallel to BC, let some other line DE', drawn through... | |
 | Association for the Improvement of Geometrical Teaching - 1888 - 208 페이지
...case there is only one such point of division. For demonstration, See Part I., Theor. 10. THEOR. 17. A straight line which divides the sides of a triangle...proportionally is parallel to the base of the triangle. For demonstration, See Part I., Theor. n. THEOR. 18. Eectangles of equal altitude are to one another... | |
 | William Chauvenet - 1893 - 340 페이지
...if a straight line divides two sides of a triangle proportionally, it is parallel to the third side. Let DE divide the sides AB, AC, of the triangle ABC, proportionally; then DE is parallel to EC. For, if DE is not parallel to BC, let some other line DE', drawn through... | |
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Conversely, if a straight line divides two sides of a triangle proportionally, it is parallel to the third side. Let DE divide the sides AB, AC, of the triangle ABC, proportionally; then DE is parallel to BC. For, if DE is not parallel to BC, let some... 