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" 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 248
by Great Britain. Education Department. Department of Science and Art - 1899
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Elements of geometry: consisting of the first four,and the sixth, books of ...

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...
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Mathematical Tables: Containing the Common, Hyperbolic, and Logistic ...

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...
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

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...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

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,...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

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...
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Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ...

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...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

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...
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Elements of Geometry and Conic Sections

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...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

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,...
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The first six books of the Elements of Euclid, with numerous exercises

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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