| Euclides - 1855 - 262 pages
...is equal to the rectangle E AA D (VI. 16). Therefore, if from any angle, &c. QED PROP. D. THEOREM. **The rectangle contained by the diagonals of a quadrilateral...both the rectangles contained by its opposite sides.** Let AB С D be any quadrilateral figure inscribed in a circle, and A С and BD its diagonals. The rectangle... | |
| Robert Potts - 1855 - 1050 pages
...which makes BAE an isosceles triangle: shew that BC or DE is a mean proportional to BE and CD. 11. **The rectangle contained by the diagonals of a quadrilateral...both the rectangles contained by its opposite sides.** 13. If in the same circle there be inscribed two triangles of equal area, then the rectangle contained... | |
| Euclides - 1855 - 230 pages
...PROPOSITION D. (a) VI. 5. (6) III. 21 (c) III. 31. (<Z) VI. 4. (e) VI. 16. THEOREM.—The rectangle under **the diagonals of a quadrilateral figure inscribed...both the rectangles contained by its opposite sides.** DEMONSTRATION. Let ABCD be any quadrilateral figure inscribed in a circle, and join AC, BD : the rectangle... | |
| Mathematics - 1857 - 478 pages
...ас Т«* hence Oa.bc=0b.ac+0c. ab. Or, the rectangle contained by the diagonals of a quadrilateral **inscribed in a circle is equal to both the rectangles contained by its opposite sides;** as we know by Euclid, book vi., prop. D. Again, it is known that if О be any point in the circumference... | |
| John Playfair - Euclid's Elements - 1855 - 340 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 be any quadrilateral inscribed in a circle, and let AC, BD be drawn ; the rectangle AC.BD... | |
| Cambridge univ, exam. papers - 1856 - 200 pages
...a polygon of irregular shape, how would it have to be dealt with in the course of construction ? 6. **The rectangle contained by the diagonals of a quadrilateral...both the rectangles contained by its opposite sides.** EUCLID. BOOKS I. II. III.—(B.) For all Candidates for a SA Degree. 2. If a straight line fall upon... | |
| 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
...Approximate 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
...equal to the rectangle EA, AD. (Vi. 16.) If therefore from any angle, &c. QED PROPOSITION D. THEOREM. **The rectangle contained by the diagonals of a quadrilateral...both 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... | |
| Eucleides - 1860 - 396 pages
...a) 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...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... | |
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