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" The rectangle contained by the diagonals of a quadrilateral ,figure inscribed in a circle, is equal to both the rectangles contained by i'ts opposite sides. "
Cambridge Problems: Being a Collection of the Printed Questions Proposed to ... - Page 112
1821 - 425 pages
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Report on the examination for admission to the Royal military academy at ...

Woolwich roy. military acad - 1868 - 426 pages
...circle in D, and if 0 be the centre of the circle inscribed in the triangle ABC, prove BD=DC = DO. 11. The rectangle contained by the diagonals of a quadrilateral...both the rectangles contained by its opposite sides. If the diagonals of a quadrilateral inscribed in a circle intersect at right angles, show that the...
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Dublin examination papers

Dublin city, univ - 1871 - 366 pages
...seeks its subjects in the past. JUNIOR FRESHMEN. glaibtmatirs. DR. STUBBS. 1 . 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~: 2. Find two lines which shall be to each other...
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874 - 342 pages
...to the rectangle EA, AD (VI. 16). If therefore from any angle, &c. QED PROPOSITION D. — Theorem. The rectangle contained by the diagonals of a quadrilateral...both the rectangles contained by its opposite sides. Let ABCD be any quadrilateral figure inscribed in a circle, and Then the rectangle contained by AC,...
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Euclidian Geometry

Francis Cuthbertson - Euclid's Elements - 1874 - 400 pages
...AC) = rectangle (AH, AR). THEOREM (h). The rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to both the rectangles contained by the opposite sides. Let FGHK be a quadrilateral figure inscribed in the a FGHK, and FH, GK its diagonals....
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the queens university calander

alexander thom - 1875 - 756 pages
...the equal angles were reciprocally proportional I Prove the propositions referred to. 4. Prove that the rectangle contained by the diagonals of a quadrilateral figure inscribed in a circle is equal to the sum of the rectangles contained by the opposite sides. 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 - 1876 - 446 pages
...equal to the rectangle EA, AD. (VI. 16.) If therefore from any angle, &c. QED PROPOSITION D. THEOREM. The rectangle contained by the diagonals of a quadrilateral...both the rectangles contained by its opposite sides. Let ^ .BCD be any quadrilateral figure inscribed in a circle, and join^C, BD. The rectangle contained...
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Modern geometry [ed.] with an appendix by W.B. Jack

Richard Wormell - 1876 - 268 pages
...the triangle. . . . . . . . . . . 240 D. The rectangle contained by the diagonals of a quadrilateral inscribed in a circle, is equal to both the rectangles contained by its opposite sides. . , 240 E. If a segment of a circle be bisected, and from the extremities of the base of the segment,...
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Solutions to the mathematical examination papers set for admission to the ...

D. Tierney - 1877 - 126 pages
...parallel to BD, then it may be readily proved that AB is divided as required in the points b, b', &c. 7. The rectangle contained by the diagonals of a quadrilateral...both the rectangles contained by its opposite sides. Euclid, Book VI., Prop. D. 8. Define the tangent of an angle, find the value of tan60, and prove...
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The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by ...

Āryabhaṭa - 1878 - 100 pages
...equiangular, and it is described about the circle. • PROP. H. THEOREM. The rectangle contained by Ihe diagonals of a quadrilateral figure inscribed in a...both the rectangles contained by its opposite sides. Let ABCD be any quadrilateral figure inscribed in a circle, -and join AC, BD : the rectangle contained...
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Report of Her Majesty's Civil Service Commissioners, Together ..., Volume 23

Great Britain. Civil Service Commission - 1879 - 622 pages
...drawn meeting the sides AB, AC in P and Q respectively. Show that it' PD=QD, then BP : CQ: :BA : CA. 9. The rectangle contained by the diagonals of a quadrilateral...both the rectangles contained by its opposite sides. PLANE TRIGONOMETRY. Time allowed, 3 hours. 1. Explain what is meant by the circular measure of an angle....
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