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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

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...

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....

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,...

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...

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»...

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 _...

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...

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...