 | John Playfair - Geometry - 1829 - 210 pages
...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 pages
...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 pages
...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 - Geometry - 1861 - 638 pages
...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 - Geometry - 1863 - 504 pages
...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 - Euclid's Elements - 1867 - 426 pages
...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 - Geometry - 1868 - 340 pages
...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 pages
...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 - Geometry - 1871 - 320 pages
...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 - Geometry - 1872 - 376 pages
...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... | |
| |
If the vertical angle of a triangle be 'bisected 'by a straight line which also cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight... 
