 | Cambridge univ, exam. papers - 1856 - 252 pages
...and 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
...ratio 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
...to 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... | |
 | 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.... | |
 | 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... | |
 | Robert Potts - Geometry, Plane - 1860 - 380 pages
...if an angle, &c. UKI). PROPOSITION C. THEOREM. If from any angle of a triangle, a straight line be drawn perpendicular to the base ; the rectangle contained...AD the perpendicular from the angle A to the base BC. The rectangle .B^, AC shall be equal to the rectangle contained by AD and the diameter of the circle... | |
 | Euclides - 1860 - 286 pages
...together with the square on AD. PROPOSITION C. THEOREM. 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. Given a triangle ABC, and AD the perpendicular from the angle A to the base BC ; to prove that the... | |
 | John Playfair - Geometry - 1860 - 332 pages
...sector PROP. B. THEOR. If an angle of a triangle be bisected by a straight line, which likewse cuts the base; the rectangle contained by the sides of the triangle is equal to th« rectangle contained by the segments of the base, together with the square of the straight line... | |
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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... 
