 | Euclides - 1848 - 52 pages
...the triangle. PROP. D. THEOREM. The rectangle contained by the diagonals of a quadrilateral figure inscribed in a circle, is equal to 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... | |
 | Elias Loomis - Conic sections - 1849 - 252 pages
...But ADxDE=BDxDC (Prop. XXVII.); hence BA x AC=BD x DC+AD'. BAxAC=:ApxAE. PROPOSITION XXX. THEOREM. The rectangle contained by the diagonals of a quadrilateral inscribed in a circle, is equivalent to the sum of the rectangles of the opposite sides. Let ABCD be any quadrilateral inscribed... | |
 | Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...equal (16. vi.) to the rectangle EA, AD. If, therefore, from any angle, etc. QED PROPOSITION D. THEOR. The rectangle contained by the diagonals of a quadrilateral...both the rectangles contained by its opposite sides. Let ABCD be any quadrilateral inscribed in a circle, and join AC, BD : the rectangle contained by AC,... | |
 | Euclides - Geometry - 1853 - 176 pages
...(vi. 16) to the rectangle ea, a d. If therefore from an angle, &c. QED PROPOSITION D. — THEOREM. The rectangle contained by the diagonals of a quadrilateral...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... | |
 | 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 by its opposite sides. Let ABCD be any quadrilateral inscribed in a circle, and let AC, BD be drawn ; the rectangle AC.BD... | |
 | Robert Potts - 1855 - 1050 pages
...mean proportional to BE and CD. 11. The rectangle contained by the diagonals of a quadrilateral figure inscribed in a circle, is equal to 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 - 270 pages
...angle, &c. QED PROP. D. THEOREM. The rectangle contained by the diagonals of a quadrilateral figure inscribed in a circle, is equal to 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... | |
 | Euclides - 1855 - 230 pages
...31. (<Z) VI. 4. (e) VI. 16. THEOREM.—The rectangle under the diagonals of a quadrilateral figure inscribed in a circle, is equal to 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 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 - 252 pages
...sides containing the right angle. 6. The rectangle contained by the diagonals of a quadrilateral figure inscribed in a circle is equal to 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... | |
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THE rectangle contained by the diagonals of a quadrilateral inscribed in a circle, is equal to both the rectangles contained by its opposite sides.* Let ABCD be any quadrilateral inscribed in a circle, and join AC, BD ; the. 
