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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 Adapted to Modern Methods in Geometry - Page 204
by Euclid, James Bryce, David Munn (F.R.S.E.) - 1874 - 216 pages
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Littell's Living Age, Volume 159

1883 - 1060 pages
...the subject he gives there the theorem afterwards inserted in Euclid (Book VI. Prop. U.) relating to the rectangle contained by the diagonals of a quadrilateral inscribed in a circle. The Arabians made the improvement of using in place of the chord of an arc the sine, or half-chord...
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Annual Report

Canada. Topographical and Air Survey Bureau - 1908 - 758 pages
...CD equal to the arc AE. Show that the segment BAE equals one quarter of the area of the circle. ~j. The rectangle contained by the diagonals of a quadrilateral...is equal to the sum of the rectangles contained by pairs of opposite sides. 6. Construct a triangle having each of two angles double of the third angle....
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From Kant to Hilbert Volume 1: A Source Book in the Foundations of Mathematics

William Bragg Ewald - Mathematics - 2005 - 696 pages
...the subject he gives there the theorem afterwards inserted in Euclid (Book VI. Prop. D) relating to the rectangle contained by the diagonals of a quadrilateral inscribed in a circle. The Arabians made the improvement of using in place of the chord of an arc the sine, or half chord,...
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The Pythagorean Theorem: A 4,000-year History

Eli Maor - Mathematics - 2007 - 296 pages
...find the following result, known as Ptolemy's theorem: The rectangle contained by the diagonals of any quadrilateral inscribed in a circle is equal to the sum of the rectangles contained by the pairs of opposite sides. To understand this cryptic statement, we must again remember that the...
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Parliamentary Papers, Volume 17

Great Britain. Parliament. House of Commons - Bills, Legislative - 1871 - 902 pages
...about the same circle. 10. Triangles which have the same altitude are to one another as their bases. Hi The rectangle contained by the diagonals of a quadrilateral...of the rectangles contained by its opposite sides. ALGEBRA. Time allowed, 3 hours. 1. Reduce to their simplest forms — (a) 1 (0) a __ b __ «3 + fl»...
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Report of Her Majesty's Civil Service Commissioners: Together ..., Volumes 15-16

1870 - 964 pages
...the same circle. 10. Triangles which have the same altitude are to one another as their bases. 11. The rectangle contained by the diagonals of a quadrilateral...is equal to the sum of the rectangles contained by ite opposite sides. ALGEBRA. Time allowed, 3 hours. 1. Reduce to their simplest forms — (a) _1 _...
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The Bombay University Calendar, Volume 1

University of Bombay - 1907 - 940 pages
...rectangle contained by the perpendicular and the diameter of the circle described about the triangle. The rectangle contained by the diagonals of a quadrilateral...is equal to the sum of the rectangles contained by the two pairs of opposite sides. The ratio of the areas of similar triangles is equal to the ratio...
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The Bombay University Calendar, Volume 1

University of Bombay - 1910 - 1080 pages
...rectangle contained by the perpendicular and the diameter of the circle described about the triangle. Tha rectangle contained by the diagonals of a quadrilateral...is equal to the sum of the rectangles contained by the two pairs of opposite sides. The ratio of the areas of similar triangles is equal to the ratio...
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Calendar

University of St. Andrews - 1900 - 670 pages
...opposite angles, show that these lines will intersect on the median from the vertex of the triangle. 4. 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. If ABC be an equilateral triangle, and P any point...
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The Bombay University Calendar, Volume 1

University of Bombay - 1916 - 654 pages
...rectangle contained by the perpendicular acd the diameter of the circle described about tbe triangle. The rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to the sum of tbe rectangles contained by the two pain of opposite sides. The ratio of the areas of similar triangles...
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