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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. "
Science Examination Papers - Page 248
by Great Britain. Education Department. Department of Science and Art - 1899
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - Geometry - 1855 - 358 pages
...consequently the rectangle BA.AC is equal (16. 6.) to <be rectangle EA.AD. PROP. D. THEOR. The Ttttangl*. contained by the diagonals of a quadrilateral inscribed in a circle, is equal to both the rectangles, contained by ut opposite sides, I >et ABCD bo any quadrilateral inscribed in a...
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Elements of Plane and Solid Geometry: And of Plane and Spherical ...

Gerardus Beekman Docharty - Geometry - 1867 - 474 pages
...since CD . DE is= AD.DB(th. 21). QED THEOREM XXV. The rectangle of the two diagonal", of any quadrangle inscribed in a circle is equal to the sum of the two rectangles of the opposite sides. Let ABCD be any quadrilateral inscribed in a circle, and AC, BD its two diagonals...
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1868 - 338 pages
...multiplied by twice the diameter of the circumscribed circle. PROPOSITION XXXVIII. — THEOREM. 291. Tlie rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equivalent to the sum of the two rectangles of the opposite sides. Let ABCD be any quadrilateral inscribed...
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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - 1869 - 516 pages
...multiplied by twice the diameter of the circumscribed circle. PROPOSITION XXXVIII. — THEOREM. 291. The rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equivalent to the sum of the two rectangles of the opposite sides. Let ABCD be any quadrilateral inscribed...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Geometry - 1871 - 302 pages
...AD' + ADxDE But ADxDE = BDxDC (Prop. XXVII.); hence BAxAC=BDxDC+AD'. PROPOSITION XXX. THEOREM. Tke rectangle contained by the diagonals of a quadrilateral inscribed in a circle, is equivalent to the sum of the rectanglet if the opposite sides. Let ABCD be any quadrilateral in- B...
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The Calendar of Owens college, Manchester

Manchester univ - 1872 - 380 pages
...the base. 4. Similar polygons are to one another in the duplicate ratio of their homologous sides. 5. The 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. If from the vertices of an equilateral triangle straight...
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The Madras University Calendar

University of Madras - 1873 - 436 pages
...opposite angles of a quadrilateral inscribed in a circle are together equal to two right angles. IV. The rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to the sum of the rectangles contained l>y its opposite sides. V. Draw a straight line perpendicular to a plane from...
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Elements of Euclid [selections from book 1-6] adapted to modern methods in ...

Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 234 pages
...AC is less than the rectangle under BD and DC, by the square of AD. <Ji. E. D, PROP. B. — THEOREM. The 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 a quadrilateral inscribed in a circle. Join...
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Euclidian Geometry

Francis Cuthbertson - Euclid's Elements - 1874 - 400 pages
...equiangular; (i. 25) .-. BA : AHasAR : AC; (vi. 4) rectangle (BA, 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...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - Geometry - 1876 - 382 pages
...within the triangle, is equal to the rectangle contained by the two sides. PROPOSITION D. THEOREM. The 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. A Let ABCD be any quadrilateral inscribed in a . Join...
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