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" 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 circle, and join AC, BD ; the. "
The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by ... - Page 79
by Āryabhaṭa - 1878
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Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - Geometry - 1855 - 334 pages
...rectangle EA.AD. PROP. D. THEOR. The rectangle contained by the diagonals of a quadrilateral inscribed ma circle, is equal to both the rectangles, contained by its opposite sides. Let ABCD bo any quadrilateral inscribed in a circle, and let AC, BD be drawn ; the rectangle AC.BD is equal...
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Cambridge examination papers: a suppl. to the University calendar, 1856-59

Cambridge univ, exam. papers - 1856 - 252 pages
...similarly described figures upon the sides containing the right angle. 6. The rectangle contained by the diagonals of a quadrilateral figure inscribed in a...both the rectangles contained by its opposite sides. If the diagonals cut one another at an angle equal to one third of a right angle, the rectangles contained...
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National Society's Monthly Paper

1857 - 408 pages
...duplicate ratio of their homologous sides. 3. The rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to both the rectangles contained by its opposite sides. SECT. II, — 1. Describe a rhombus, of which one diagonal shall be double the other. 2. In a given...
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The Calendar for the Year ...

Royal University of Ireland - Universities and colleges - 1859 - 490 pages
...to the value of the real root of the equation xs — 6*= 100. 4. Prove that the rectangle under the diagonals of a quadrilateral figure inscribed in a circle is equal to the sum of the rectangles under the opposite sides ; and hence calculate the side of a regular quindecagon...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry, Plane - 1860 - 380 pages
...(Vi. 16.) If therefore from any angle, &c. QED PROPOSITION D. THEOREM. The rectangle contained by the diagonals of a quadrilateral figure inscribed in a...the rectangles contained by its opposite sides. Let AB CD be any quadrilateral figure inscribed in a circle, and join AC, BD. The rectangle contained by...
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The Elements of Euclid with Many Additional Propositions and Explanatory Notes

Eucleides - 1860 - 396 pages
...VI. 5. 6) III. 21 ) III. 31. ) VI. 4. e) VI. 16. PROPOSITION D. THEOREM. — The rectangle under the diagonals of a quadrilateral figure inscribed in a...both the rectangles contained by its opposite sides. DEMONSTRATION. Let ABCD he any quadrilateral figure inscribed in a circle, and join AC, BD : the rectangle...
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Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860 - 288 pages
...AD (VI. 16). I'JtorOSITJON D. THEOBEM. The rectangle contained by the diagonals of a quadrilateral inscribed in a circle, is equal to both the rectangles contained by its opposite sides. Given any quadrilateral ABCD inscribed in a circle, and join AC and BD ; to prove that the rectangle...
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Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ...

Euclides - 1861 - 464 pages
...other : ie BA . AC : EC . CA = AD : perp. from C. PROP. D. — THEOR. The rectangle contained by the diagonals of a quadrilateral figure inscribed in a...both the rectangles contained by its opposite sides. Cow. 23, 1. DEM. 21, Ш. 4, VI. 16, VI. 1, II. If there be two st. lines, one of which is divided into...
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Examination papers used at the examinations for direct commissions [&c.].

War office - 1861 - 714 pages
...touch the circle. VOLUNTARY PORTION. 1. The rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to both the rectangles contained by its opposite sides. 2. If two straight lines are at right angles to the same plane they shall be parallel to each other....
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Report on the examination for admission to the Royal military academy at ...

Woolwich roy. military acad - 1864 - 588 pages
...equilateral triangle, and compare the area of the hexagon so inscribed with the area of the triangle. a quadrilateral figure inscribed in a circle is equal...both the rectangles contained by its opposite sides. If the diagonals of the quadrilateral intersect at right angles, show that the sum of the squares of...
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