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The rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to the sum of the two rectangles contained by its opposite sides.
A Treatise on Plane and Spherical Trigonometry: With Their Most Useful ... - Página v
por John Bonnycastle - 1806 - 419 páginas
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## The British Palladium: Or, Annual Miscellany of Literature and ..., Volumen7

1757
...the Figure is infcribed in a Circle. But the Recbngle of the two Diagonals of any Trapezium infcribed in a Circle is equal to the Sum of the Rectangles of the oppofite Sides : Therefore DExBC = DCXBE + DBXCE; the Half of which is (= 2880 Perches, or 18 Acres)...
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## A Course of Mathematics ...: Designed for the Use of the Officers ..., Volumen2

Isaac Dalby - 1806
...parallelogram, is equal to the squares on the four sides taken together. 241. THEOREM. The rectangle under the two diagonals of any quadrilateral inscribed in a circle, is equal to the sum of the two rectangles of the opposite sides : That is, AC x BD = AB x CD -f AD x BC. Suppose CP is drawn to...
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## Tracts on Mathematical and Philosophical Subjects: Comprising Among Numerous ...

Charles Hutton - 1812 - 485 páginas
...of the chord of an arc, 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, hitherto...
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## Dictionary of the Mathematical and Physical Sciences, According to the ...

James Mitchell - 1823 - 576 páginas
...equal to the internal and opposite angle. 7. Also, in this case, the rectangle of its two diagonals is equal to the sum of the rectangles of its opposite sides. TRAPEZOID, a quadrilateral figure, having two of its opposite sides parallel ; the area of which is...
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## Solutions of the Cambridge Problems: From 1800 to 1820, Volumen2

John Martin Frederick Wright - 1825 - 653 páginas
...the ratios of their sides. 3. The rectangle contained by the diagonals of any quadrilateral figure inscribed in a circle is equal to the 'sum of the rectangles contained by its opposite sides. 4. If the exterior angle of a triangle be bisected, and also one of...
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## Alma Mater: Or, Seven Years at the University of Cambridge

...the ratios of their sides. 3. The rectangle contained by the diagonals of any quadrilateral figure inscribed in a circle is equal to the sum of the rectangles contained by its opposite sides. 4. If the exterior angle of a triangle be bisected, and also one of...
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## Alma mater; or, Seven years at the University of Cambridge. By a Trinity-man ...

John Martin F. Wright - 1827
...the ratios of their sides. 3. The rectangle contained by the diagonals of any quadrilateral figure inscribed in a circle is equal to the sum of the rectangles contained by its opposite sides. 4. If the exterior angle of a triangle be bisected, and also one of...
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## Mathematical Tables: Containing the Common, Hyperbolic, and Logistic ...

Charles Hutton - 1834 - 368 páginas
...of the chord of an arc, 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...
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## Mathematical Tables: Containing the Common, Hyperbolic, and Logistic ...

Charles Hutton - 1842 - 368 páginas
...of the chord of an arc, 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...
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## The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846
...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 join AC,...
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