 | Euclides - 1855 - 270 pages
...geometers. PROP. B. THEOREM If any 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 straight line which bisects the angle. Let... | |
 | 1855 - 264 pages
...mean ratio. 3. If an angle of a triangle he bisected by a straight line which likewise cuts the hase, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the ha;e, together with the square of the straight line which bisects the angle. SECT.... | |
 | Euclides - 1855 - 230 pages
...triangle is isosceles. The rectangle under the sides of the triangle is equal to the rectangle under the perpendicular and the diameter of the circle described about the triangle. The triangles on each side of it are si mil at to the whole triangle, and to one another. Eaon of the... | |
 | Cambridge univ, exam. papers - 1856 - 252 pages
...equal to another given rectilineal figure. 6. If from any angle of a triangle a straight line be drawn perpendicular to the base, the rectangle contained...diameter of the circle described about the triangle. The rectangle contained by the two sides can never be less than twice the triangle. EUCLID. BOOKS I.... | |
 | 1856 - 376 pages
...compounded of the ratios of their sides. 3. If from any angle of a triangle a straight line be drawn perpendicular to the base, the rectangle contained...the perpendicular, and the diameter of the circle deseribed about the triangle. SECT. II. — I . If the line bisecting the vertical angle of a triangle... | |
 | Elias Loomis - Conic sections - 1857 - 242 pages
...external segments. PROPOSITION XXIX. THEOREM. If an angle of a triangle be bisected by a line which cuts the base, the rectangle contained by the sides of the triangle, is equivalent to the rectangle contained by the segments of the. base, together with the square of the... | |
 | Elias Loomis - Conic sections - 1858 - 256 pages
...external segments. PROPOSITION XXIX. THEOREM. If an angle of a triangle be bisected by a line which cuts the base, the rectangle contained by the sides of the triangle, is equivalent to the rectangle contained by the segments of the. base, together with the square of the... | |
 | Great Britain. Parliament. House of Commons - Bills, Legislative - 1859 - 140 pages
...another given rectilineal figure. 4. If from the vertical angle of a triangle a straight line be drawn perpendicular to the base, the rectangle contained...diameter of the circle described about the triangle. 5. Given the perimeter and the angles of a triangle ; required to construct it geometrically. Required... | |
 | Sandhurst roy. military coll - 1859 - 672 pages
...the radius of the circle. 2. If an 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 of the straight line which bisects the angle. If... | |
 | Thomas Stantial - Examinations - 1859 - 352 pages
...triangles of the same circle. 8. If an 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 of the straight line which bisects the angle. 9.... | |
| |
Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM 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 is equal to the rectangle contained by the... 
