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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
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1863 - 504 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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A collection of elementary test questions in pure and mixed mathematics ...

James Robert Christie - Mathematics - 1866 - 428 pages
...= (a + x)'(2a — ж). E. • ' L GEOMETRY. 1. In a circle, the angle in a semicircle is <fec. 2. The rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to both the rectangles contained by its opposite sides. 3. If, in a circle, an equilateral polygon be...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - Geometry - 1855 - 350 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 Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1868 - 340 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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Dublin examination papers

Dublin city, univ - 1871 - 366 pages
...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 in the ratio of two given...
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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...of the rectangles contained by its opposite sides. If from the vertices of an equilateral triangle straight lines be drawn to any point on the circumference...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...sides. PROPOSITION D. THEOREM. The rectangle, contained. by the diagonals of a quadrilateral ^nscribed 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 0. Join AC, BD. Then rect. AC, BD=rect. AB, CD together...
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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...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 a given point above it....
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