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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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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855 - 262 pages
...is equal to the rectangle E AA D (VI. 16). Therefore, if from any angle, &c. QED PROP. D. THEOREM. The rectangle contained by the diagonals of a quadrilateral...both the rectangles contained by its opposite sides. Let AB С D be any quadrilateral figure inscribed in a circle, and A С and BD its diagonals. The rectangle...
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Liber Cantabrigiensis, an account of the aids afforded to poor students, the ...

Robert Potts - 1855 - 1050 pages
...which makes BAE an isosceles triangle: shew that BC or DE is a mean proportional to BE and CD. 11. The rectangle contained by the diagonals of a quadrilateral...both the rectangles contained by its opposite sides. 13. If in the same circle there be inscribed two triangles of equal area, then the rectangle contained...
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The Elements of Euclid, with many additional propositions, and explanatory ...

Euclides - 1855 - 230 pages
...PROPOSITION D. (a) VI. 5. (6) III. 21 (c) III. 31. (<Z) VI. 4. (e) VI. 16. THEOREM.—The rectangle under the diagonals of a quadrilateral figure inscribed...both the rectangles contained by its opposite sides. DEMONSTRATION. Let ABCD be any quadrilateral figure inscribed in a circle, and join AC, BD : the rectangle...
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The Quarterly Journal of Pure and Applied Mathematics, Volume 1

Mathematics - 1857 - 478 pages
...ас Т* hence Oa.bc=0b.ac+0c. ab. Or, the rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to both the rectangles contained by its opposite sides; as we know by Euclid, book vi., prop. D. Again, it is known that if О be any point in the circumference...
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Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - Euclid's Elements - 1855 - 340 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 be any quadrilateral inscribed in a circle, and let AC, BD be drawn ; the rectangle AC.BD...
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Cambridge examination papers: a suppl. to the University calendar, 1856-59

Cambridge univ, exam. papers - 1856 - 200 pages
...a polygon of irregular shape, how would it have to be dealt with in the course of construction ? 6. The rectangle contained by the diagonals of a quadrilateral...both the rectangles contained by its opposite sides. EUCLID. BOOKS I. II. III.—(B.) For all Candidates for a SA Degree. 2. If a straight line fall upon...
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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
...Approximate 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
...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 AB CD be any quadrilateral figure inscribed in a circle, and join AC, BD. The rectangle contained...
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The Elements of Euclid with Many Additional Propositions and Explanatory Notes

Eucleides - 1860 - 396 pages
...a) 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...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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