 | Robert Potts - 1868 - 434 pages
...sector BGCto the sector EHF. (v. def. 5.) Wherefore, in equal circles, &c. QED PROPOSITION B. THEOREM. If an 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... | |
 | General Medical Council (Great Britain) - 1869 - 402 pages
...Inscribe a circle in a given triangle. 4. If the angle of a triangle be divided into two equal angles 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 triangle have to one another ; and conversely, if... | |
 | Cambridge univ, exam. papers - 1870 - 272 pages
...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...also cuts the base, the segments of the base shall have the same ratio which the other sides of the triangle have to one another; and if the segments... | |
 | Henry William Watson - Geometry - 1871 - 320 pages
...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...also cuts the base, the segments of the base shall have to one another the same ratio that the adjacent sides of the triangle have, and if a straight... | |
 | Thomas Steadman Aldis - 1872 - 84 pages
...drawn parallel to AC to meet the opposite side in S and T. Prove that ST is parallel to BD. THEOREM X. If an angle of a triangle be bisected by a straight line that cuts the base of the triangle, then shall the segments of the base be proportional to the sides... | |
 | Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...same ratio as the arcs which subtend them ; and so also have the sectors. PROPOSITION B. THEOREM. // an 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,... | |
 | Braithwaite Arnett - 1874 - 130 pages
...and circumscribing circles. 5. Inscribe an equilateral and equiangular hexagon in a given circle. 6. If an angle of a triangle be bisected by a straight...also cuts the base the segments of the base shall have the same ratio which the other sides of the triangle have to one another. 7. Similar triangles... | |
 | Euclides - 1874 - 342 pages
...BGC to the sector EHF (V. Def. 5). Wherefore, in equal circles, &e. QED PROPOSITION B. — Theorem. If an 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... | |
 | Francis Cuthbertson - Euclid's Elements - 1874 - 400 pages
...CG : GK. (v. 6) Similarly FJ : JP as GK : KQ. Hence BP, CQ are divided proportionally. THEOREM (/). If an 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... | |
 | Robert Potts - Geometry - 1876 - 446 pages
...having each of the angles at the base equal to seven times the third angle. 5. (a) If the vertical angle of a triangle be bisected by a straight line...which also cuts the base, the segments of the base have the same ratio which the other sides of the triangle have to one another ; and, if the segments... | |
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IF an 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 contained by the segments of the base, together with the square of the... 
