| John Playfair - 1829 - 210 páginas
...divided into two equal angles by the straight line AD. Therefore, if the angle &c. Qi ED CoR. If any angle of a triangle be bisected by a straight line which meets the opposite side, the sum of the two sides containing that angle is to either of them, as the base is... | |
| Euclides - 1846 - 292 páginas
...so is the sector BGC to the sector EHF. Wherefore, In equal circles %c. QED PROP. B. THEOR. If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle shall be equal to the... | |
| Euclides - 1860 - 288 páginas
...between fhe same parallels (I. 89)} therefore DE is parallel to BC. PEOPOSITION HI. THEOHEM. If the vertical angle of a triangle be bisected by a straight line which also cuts the base, the segments of the base shall have the same ratio which the other sides of the... | |
| Benjamin Greenleaf - 1861 - 638 páginas
...PROPOSITION XXI. — THEOREM. 258. If the exterior angle farmed by producing one of the sides of any triangle be bisected by a straight line which meets the base produced, the distances from the extremities of the base to the point where the bisecting line meets the base... | |
| Benjamin Greenleaf - 1863 - 504 páginas
...PROPOSITION XXI. — THEOREM. 258. If the exterior angle formed by producing one of the sides of any triangle be bisected by a straight line which meets the base produced, the distances from the extremities of the base to the point where the bisecting line meets the base... | |
| Euclid, Isaac Todhunter - 1867 - 426 páginas
...the sector EHF. [V. Definition 5. "Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM. Jf the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle... | |
| Benjamin Greenleaf - 1868 - 340 páginas
...PROPOSITION XXI. — THEOREM. 258. If the exterior angle formed by producing one of the sides of any triangle be bisected by a straight line which meets the base produced, the distances from the extremities of the base to the point where the bisecting line meets the base... | |
| Cambridge univ, exam. papers - 1870 - 272 páginas
...each to each, prove that the third side of the one is equal to the third side of the other. 4. If the vertical angle of a triangle be bisected by a straight line which also cuts the base, the segments of the base shall have the same ratio which the other sides of the... | |
| Henry William Watson - 1871 - 320 páginas
...the points B and D are also harmonic conjugates with respect to the line AC. PROPOSITION 8. If the vertical angle of a triangle be bisected by a straight line which also cuts the base, the segments of the base shall have to one another the same ratio that the adjacent... | |
| Euclides, James Hamblin Smith - 1872 - 376 páginas
...point of bisection of its diagonals, bisects the two parallel sides. PROPOSITION III. THEOREM. If the vertical angle of a triangle be bisected by a straight line, which also cuts the base, the segments of the base must have the same ratio, which the other sides of the... | |
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