 | Ferdinand Rudolph Hassler - 1828 - 180 páginas
...different from CE; the same would be the case with any other point like E; therefore, the line cutting two sides of a triangle proportionally, is parallel to the third side of the triangle; as was to be demonstrated. . Carol. Also, the perpendicular from an angular point... | |
 | William Frothingham Bradbury - 1872 - 124 páginas
...AC = AD : AB or (Pn. 16) AC : AE = AB : AD THEOREM VII. CONVERSE OF THEOREM VI. 18. A line dividing two sides of a triangle proportionally is parallel to the third side of the triangle. For if DE is not parallel to BC, through D draw DF parallel to BC ; then (16) AD :DB—AF:FC... | |
 | William Frothingham Bradbury - 1872 - 262 páginas
...is AE:AC=AD:AB or(Pn. 16) AC :AE — AB:AD THEOREM VII. CONVERSE OF THEOBEM VI. 18, A line dividing two sides of a triangle proportionally is parallel to the third side of the triangle. In the triangle ABC it DE divides AB and AC so that AE : EC = AD : DB, then DE is... | |
 | Harvard University - 1873 - 732 páginas
...three parts proportional to the numbers 2, 4, and 3, and prove the principle involved. 6. Prove that a line which divides two sides of a triangle proportionally is parallel to the third side. 7. Prove that a tangent to a circle is perpendicular to the radius drawn to the point of contact. 8.... | |
 | Robert Fowler Leighton - 1877 - 372 páginas
...three parts proportional to the numbers 2, 4, and 3, and prove the principle involved. 6. Prove that a line which divides two sides of a triangle proportionally is parallel to the third side. 7. Prove that a tangent to a circle is perpendicular to the radius drawn to the point of contact. 8.... | |
 | William Frothingham Bradbury - 1880 - 260 páginas
...(17) AE+EC :AE=AD + DB:AD that is AC:AE=AB:AD THEOREM XX. CONVERSE OF THEOREM XIX. 51i A line dividing two sides of a triangle proportionally is parallel to the third side of the triangle. In the triangle ABC if DE divides AB and AC so that AB : AD = AC : AE, then DE is... | |
 | Franklin Ibach - 1882 - 208 páginas
...— DA : DA :: CB — EB : EB, or CD : DA :: CE : EB; CD : CE :: DA : EB. (160) THEOREM XIII. 268. A straight line which divides two sides of a triangle proportionally is parallel to the third side. In the A ABC, let DE divide the sides AB and AC proportionally. A To prove that DE is II to BC. Suppose... | |
 | John Casey - 1885 - 360 páginas
...by \Ax + \By + \C — o on the axes are the same as those made by Ax + By + C = o. 5. Prove that the line which divides two sides of a triangle proportionally is parallel to the third side. 6. Find the locus of a point which is equally distant from the origin and the point (2x', 2y'). If (xy)... | |
 | George Bruce Halsted - 1885 - 389 páginas
...there can be only one point of external division in the given ratio. N%<? \* -* 503. INVERSE OF 499. A line which divides two sides of a triangle proportionally is parallel to the third. For a parallel from one of the points would divide the second side in the same ratio, but there is... | |
 | Webster Wells - 1886 - 392 páginas
...(§ 245), AB:AC=AD:AE, and AB:AC=DB:EC. Therefore, AC AE EC PROPOSITION XV. THEOREM. 264. CONVERSELY, a straight line which divides two sides of a triangle proportionally is parallel to the third side. In the triangle ABC let DE be drawn so that AB = AC AD AE' To prove that DE is parallel to BC. If DE... | |
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A line which divides two sides of a triangle proportionally is parallel to the third side. 
