| Samuel Constable - Geometry - 1882 - 222 pages
...last.] 13. Prove that the rectangle contained by a side of this square and a line equal to the sum of **the sides of the triangle is equal to the rectangle contained by** the sides. 14. Inscribe a square in any triangle; and prove that the rectangle contained by a side... | |
| Thomas Grenfell Vyvyan - 1882 - 150 pages
...point of BC, shew that 62 =cs+ -JCHAPTER XII. CIRCLES RELATED TO THE TRIANGLE. 46. To find the radius **of the circle described about the triangle. Let ABC be a triangle:** describe a circle about it, and draw BD perpendicular to BC to meet the circle in D : join CD. (See... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 pages
...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 segments of the base, together with the square on the straight line which bisects the angle. Let... | |
| Euclides - 1884 - 434 pages
...to that included by them. If from the vertical angle of a triangle a perpendicu1ar be drawn to tJie **base, the rectangle contained by the sides of the...by the perpendicular and the diameter of the circle** circumscribed about the triangle. A Let ABC be a triangle, AD the perpendicular from A on the base... | |
| Woolwich roy. military acad - 1884 - 148 pages
...parallel. 11. 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 segments of the base, together with the square on the straight line which bisects the angle. II.... | |
| 1885 - 522 pages
...three divisions of this paper.) I. — 1. 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.** 2. Prove that the tangent to a parabola at any point is the bisector of the angle which the focal distance... | |
| John James Milne - 1885 - 392 pages
...cos (A - £)}. 5. 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** two lines equally inclined to the bisector, one terminated by the base and the other by the rircum-uircle.... | |
| Euclides - 1885 - 340 pages
...extended to each of the escribed circles of the triangle ACB. 5. The rectangle contained by two sides of a **triangle is equal to the rectangle contained by the perpendicular and the diameter of the** circumscribed circle. For, let CE be the diameter. Join AE. Then the triangles ACE, DCB are equiangular... | |
| Euclid, John Casey - Euclid's Elements - 1885 - 340 pages
...extended to each of the escribed circles of the triangle ACB. 6. The rectangle contained by two sides of a **triangle is equal to the rectangle contained by the perpendicular and the diameter of the** circumscribed circle. For, let CE be the diameter. Join AE. Then the triangles ACE, DCB are equiangular... | |
| 1887 - 644 pages
...circumscribing circle. 15. 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** that contained by the segments of the base together with the square on the straight line which bisects... | |
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