 Tin; rectangle, contained by the diagonals of a quadrilateral inscribed in a circle, is equal to the sum of the rectangles contained by its opposite sides.  Science Examination Papers - Page 248by Great Britain. Education Department. Department of Science and Art - 1899Full view - About this book
 | Euclides - 1842 - 320 pages
...equivalent (16. 6.) to the rectangle EA, AD. If, therefore, from an angle, &c. QED PROP. D. THEOR. THE rectangle contained by the diagonals of a quadrilateral inscribed in a circle, is equivalent to both the rectangles contained by its opposite sides. Let ABC D be any quadrilateral inscribed... | |
 | Charles Hutton - Logarithms - 1842 - 456 pages
...and of the chord of its supplement to a semicircle. 2. The rectangle under the two diagonals of any quadrilateral inscribed in a circle, is equal to the sum of the two rectangles under the opposite sides. 3. The sum of the squares of the sine and cosine (often called the sine of... | |
 | Euclid - Geometry - 1845 - 218 pages
...to the rectangle § 16. 6. EA, AD. If, therefore, from any angle, &c. QED PROPOSITION D. THEOR. — The rectangle contained by the diagonals of a quadrilateral inscribed in a circle, is equal to both tlie rectangles contained by its opposite sides. Let ABCD be any quadrilateral inscribed in a... | |
 | Euclid, James Thomson - Geometry - 1845 - 380 pages
...is equal to the rectangle EA.AD. If, therefore, from an angle of a triangle, &c. PROP. E. THEOR. — 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 a quadrilateral inscribed in a circle,... | |
 | Euclides - 1846 - 292 pages
...BA, AC is equal to the rectangle EA, AD. Wherefore, If from any angle %c. QBP PROP. D. THEOn. Tin; rectangle, contained by the diagonals of a quadrilateral...inscribed in a circle, is equal to the sum of the rectangles contained by its opposite sides. Let ABCD be any quadrilateral inscribed in a circle, and... | |
 | Dennis M'Curdy - Geometry - 1846 - 138 pages
...Wherefore, if from any angle, &c. fiecite(o)p. 31, 3; (4) p. 21, 3 ; c)p. 4,6; . (d) p. lli, 6. QED D Th. 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 ABCD any quadrilateral inscribed in a circle... | |
 | John Playfair - Euclid's Elements - 1846 - 332 pages
...: and consequently the rectangle BA.AC is equal (16. 6.) to the rectangle EA.AD. JD PROP. D. THEOR. 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... | |
 | 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 inscribed in a circle, is equal to both the rectangles contained by its opposite sides. Let ABCD be any quadrilateral inscribed in a circle,... | |
 | 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 inscribed in a circle is equal to both the rectangles contained by its opposiie sides. LET abcd be any quadrilateral inscribed in a circle,... | |
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