| John Playfair - Geometry - 1855 - 334 pages
...rectangle EA.AD. PROP. D. THEOR. The rectangle contained by the diagonals of a quadrilateral inscribed ma **circle, is equal to both the rectangles, contained by its opposite sides. Let ABCD** bo any quadrilateral inscribed in a circle, and let AC, BD be drawn ; the rectangle AC.BD is equal... | |
| Cambridge univ, exam. papers - 1856 - 252 pages
...similarly described figures upon the sides containing the right angle. 6. The rectangle contained by the **diagonals of a quadrilateral figure inscribed in a...both the rectangles contained by its opposite sides.** If the diagonals cut one another at an angle equal to one third of a right angle, the rectangles contained... | |
| 1857 - 408 pages
...duplicate ratio of their homologous sides. 3. The rectangle contained by the diagonals of a quadrilateral **inscribed in a circle is equal to both the rectangles contained by its opposite sides.** SECT. II, — 1. Describe a rhombus, of which one diagonal shall be double the other. 2. In a given... | |
| Royal University of Ireland - Universities and colleges - 1859 - 490 pages
...to the value of the real root of the equation xs — 6*= 100. 4. Prove that the rectangle under the **diagonals of a quadrilateral figure inscribed in a circle is equal to** the sum of the rectangles under the opposite sides ; and hence calculate the side of a regular quindecagon... | |
| Robert Potts - Geometry, Plane - 1860 - 380 pages
...(Vi. 16.) If therefore from any angle, &c. QED PROPOSITION D. THEOREM. The rectangle contained by the **diagonals of a quadrilateral figure inscribed in a...the rectangles contained by its opposite sides. Let** AB CD be any quadrilateral figure inscribed in a circle, and join AC, BD. The rectangle contained by... | |
| Eucleides - 1860 - 396 pages
...VI. 5. 6) III. 21 ) III. 31. ) VI. 4. e) VI. 16. PROPOSITION D. THEOREM. — The rectangle under the **diagonals of a quadrilateral figure inscribed in a...both the rectangles contained by its opposite sides.** DEMONSTRATION. Let ABCD he any quadrilateral figure inscribed in a circle, and join AC, BD : the rectangle... | |
| Euclides - 1860 - 288 pages
...AD (VI. 16). I'JtorOSITJON D. THEOBEM. The rectangle contained by the diagonals of a quadrilateral **inscribed in a circle, is equal to both the rectangles contained by its opposite sides.** Given any quadrilateral ABCD inscribed in a circle, and join AC and BD ; to prove that the rectangle... | |
| Euclides - 1861 - 464 pages
...other : ie BA . AC : EC . CA = AD : perp. from C. PROP. D. — THEOR. The rectangle contained by the **diagonals of a quadrilateral figure inscribed in a...both the rectangles contained by its opposite sides.** Cow. 23, 1. DEM. 21, Ш. 4, VI. 16, VI. 1, II. If there be two st. lines, one of which is divided into... | |
| War office - 1861 - 714 pages
...touch the circle. VOLUNTARY PORTION. 1. The rectangle contained by the diagonals of a quadrilateral **inscribed in a circle is equal to both the rectangles contained by its opposite sides.** 2. If two straight lines are at right angles to the same plane they shall be parallel to each other.... | |
| Woolwich roy. military acad - 1864 - 588 pages
...equilateral triangle, and compare the area of the hexagon so inscribed with the area of the triangle. **a quadrilateral figure inscribed in a circle is equal...both the rectangles contained by its opposite sides.** If the diagonals of the quadrilateral intersect at right angles, show that the sum of the squares of... | |
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