| Euclides - 1848 - 52 pages
...diameter of the circle described about the triangle. PROP. D. THEOREM. The rectangle contained by the **diagonals of a quadrilateral figure inscribed in a...both the rectangles contained by its opposite sides.** BOOK XL DEFINITIONS. I. A SOLID is that which hath length, breadth, and thickness. II. That which bounds... | |
| Education - 1851 - 502 pages
...about the equal angles of equiangular triangles are proportionals. 3. The rectangle contained by the **diagonals of a quadrilateral figure inscribed in a circle is equal to** the sum of the rectangles contained by its opposite sides. 2. If one diagonal of a quadrilateral bisects... | |
| Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...any angle, etc. QED PROPOSITION D. THEOR. The rectangle contained by the diagonals of a quadrilateral **inscribed in a circle, is equal to both the rectangles...its opposite sides. Let ABCD be any quadrilateral** inscribed in a circle, and join AC, BD : the rectangle contained by AC, BD is equal to the two rectangles... | |
| Euclid, John Playfair - Geometry - 1853 - 336 pages
...rectangle EA.AD. PROP. D. THEOR. The rectangle contained by the diagonals of a quadrilateral inscribed tn **a circle, is equal to both the rectangles, contained...its opposite sides. Let ABCD be any quadrilateral** inscribed in a circle, and let AC, BD be drawn ; the rectangle AC.BD is equal to the two rectangles... | |
| Euclides - Geometry - 1853 - 176 pages
...angle, &c. QED PROPOSITION D. — THEOREM. The rectangle contained by the diagonals of a quadrilateral **inscribed in a circle is equal to both the rectangles contained by its** opposiie sides. LET abcd be any quadrilateral inscribed in a circle, and join ac, bd ', the rectangle... | |
| Euclides - 1855 - 270 pages
...D (VI. 16). Therefore, if from any angle, &c. QED PROP. D. THEOREM. The rectangle contained by the **diagonals of a quadrilateral figure inscribed in a...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
...triangle: shew that BC or DE is a mean proportional to BE and CD. 11. The rectangle contained by the **diagonals of a quadrilateral figure inscribed in a...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 in a...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... | |
| 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...its opposite sides. Let ABCD be any quadrilateral** inscribed in a circle, and let AC, BD be drawn ; the rectangle AC.BD is equal to the two rectangles... | |
| 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... | |
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