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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. Let ABCD be any quadrilateral inscribed in a circle... "
Elements of Euclid [selections from book 1-6] adapted to modern methods in ... - Page 206
by Euclides - 1874
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A Treatise on Plane and Spherical Trigonometry: With Their Most Useful ...

John Bonnycastle - Trigonometry - 1806 - 419 pages
...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 is known...
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A Course of Mathematics ...: Designed for the Use of the Officers ..., Volume 2

Isaac Dalby - Mathematics - 1806 - 526 pages
...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 - Bridges - 1812 - 514 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, hitherto...
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Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1813
...contained by the perpendicular and the diameter of the circle described about the triangle. 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. Book XI. Def. 1.— A solid is that wh.ich hath...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1819 - 333 pages
...BA.AC is equal (16. 6.) to the rectangle EA.AD. If, therefore, from an angle, &c. Q, ED 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...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - Geometry - 1821 - 514 pages
...AC is equal (16. 6.) to the rectangle1 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 equal to both the rectangles contained by its opposite sides.* Let ABCD be any quadrilateral inscribed in a...
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Solutions of the Cambridge Problems: From 1800 to 1820, Volume 2

John Martin Frederick Wright - Mathematics - 1825 - 798 pages
...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 the interior and opposite, the...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 372 pages
...rectangle BA, AC is equal (16. 6.) to the rectangle EA, AD. I f therefore from an angle, &c. QED PROB. D. THEOREM. The rectangle contained by the diagonals...a quadrilateral inscribed in a circle, is equal to both the rectangles contained by its opposite sides. Let ABCD be any quadrilateral inicribed in a circle,...
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Alma mater; or, Seven years at the University of Cambridge. By a Trinity-man ...

John Martin F. Wright - 1827 - 634 pages
...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 the interior and opposite, the...
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Alma Mater, Or, Seven Years at the University of Cambridge, Volume 1

John Martin Frederick Wright - 1827 - 344 pages
...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 the interior and opposite, the...
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