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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 Course of Mathematics ...: Designed for the Use of the Officers and Cadets ... - Page 238
by Isaac Dalby - 1806
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A Treatise on Plane and Spherical Trigonometry: With Their Most Useful ...

John Bonnycastle - Trigonometry - 1806 - 464 pages
...on this subject. He has also here proved, for the first time that we know of, that the rectangle of the two diagonals of any quadrilateral inscribed in a circle, is equal to the sum of the rectangles of its opposite sides (c). After the time of Ptolemy and his commentator Theon, little more...
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Mathematical Tables;: Containing the Common, Hyperbolic, and Logistic ...

Charles Hutton - Mathematics - 1811 - 574 pages
...chord of its supplement to a semicircle. 2. The rectangle under the two diagonals of any quadrilatéral 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 called the sine...
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A Course of Mathematics ...: Composed for the Use of the Royal Military ...

Charles Hutton - Mathematics - 1811 - 406 pages
...61). C^ ED THEOREM LXV. The Rectangle of the two Diagonals of any Quadrangle Inscribed in a Cirek, is equal to the sum of the two Rectangles of the Opposite Sides. LET ABCD be any quadrilateral inscribed in a circle, and AC, BD, its two diagonals : then the' rectangle...
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Tracts on Mathematical and Philosophical Subjects: Comprising Among Numerous ...

Charles Hutton - Bridges - 1812 - 514 pages
...sum of the squares 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...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 called the sine...
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A Course of Mathematics: For the Use of Academies as Well as Private Tuition

Charles Hutton - Mathematics - 1812 - 620 pages
...BE is = AD . DB (th. 61). q. E. D THEOREM LXV. The Rectangle of the two Diagonals of any Quadrangle Inscribed in a Circle, is equal to the sum of the two Rectangles of the Opposite Sides. LET ABCD be any quadrilateral inscribed in a circle, and AC, BD, its two diagonals : then the rectangle...
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A Philosophical and Mathematical Dictionary: Containing an ..., Volume 2

Charles Hutton - Astronomy - 1815 - 686 pages
...taken together, are equal to two right angles. And in this case the rectangle of the two diagonals is equal to the sum of the two rectangles of the opposite sides. For the properties of the particular species of quadrilaterals, see their respective names, SQUARE,...
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A Course of Mathematics: In Two Volumes. For the Use of Academies ..., Volume 1

Charles Hutton - Arithmetic - 1818 - 646 pages
...AD . DB (th. 61). «. ED THEOREM LXV. The Rectangle of the two Diagonals of any Quadrangle lnscribed in a Circle, is equal to the sum of the two Rectangles of the Opposite Sides. LET ABCD be any quadrilateral inscribed in a circle, and AC, BD, its two diagonals : then the rectangle...
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Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Volume 10

John Mason Good - 1819 - 910 pages
...taken together, are equal to two right angles. And in ibis case the rectangle of the two diagonals, is equal to the sum of the two rectangles of the opposite sides. For the properties of the particular specie» of quadrilaterals, see their respective names, SQUARE,...
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A Course of Mathematics: For the Use of Academies, as Well as Private ...

Charles Hutton - Mathematics - 1822 - 616 pages
...is = AD . DB (th. 61). «. E. ». THEOREM LXV. The Rectangle of the two Diagonals of any Quadrangle Inscribed in a Circle, is equal to the sum of the two Rectangles of the Opposite Sides. LET ABCD be any quadrilateral inscribed in a circle, and AC, BD, its two diagonals: then the rectangle...
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Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - Geometry - 1825 - 294 pages
...quadrilateral figure A BCD (fig. 135), the rectangle of the too diagonals AC, BD, is equal to the sum of the rectangles of the opposite sides ; that is, AC x BD = AB x CD .+ AD x BC. Demonstration. Take the arc CO = AD, and draw BO meeting the diagonal AC in /. The angle...
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