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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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A Supplement to the Elements of Euclid

Daniel Cresswell - Geometry - 1819 - 410 pages
...AD. PROP. LVII. 66. THEOREM. The rectangle contained by the diagonals of a quadrilateral rectilineal figure, inscribed in a circle, is equal to both the rectangles contained by its opposite sides. Let ABCD be any quadrilateral rectilineal figure, inscribed in a circle ACB, and let AC, BD, be its...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Circle-squaring - 1819 - 348 pages
...from an angle, &c. Q, ED PROP. D. THEOR. 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 let AC, BD be drawn ; the rectangle AC.BD...
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A Supplement to the Elements of Euclid

Daniel Cresswell - Geometry - 1819 - 486 pages
...LVII. 66. THEOREM. The rectangle contained by the diagonals of a quadrilateral rectilineal Jigure, , inscribed in a circle, is equal to both the rectangles contained by its opposite sides. Let ABCD be any quadrilateral rectilineal figure, inscribed in a circle ACB, and let AC, BD, be its...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 317 pages
...from an angle, &c. Q, ED PROP. D. THEOR. The rectangle contained by tht diagonals of a quadrilateral inscribed in a circle, is equal to both the rectangles, contained by its opposite Let ABCD be any quadrilateral inscribed in a circle, and let AC. BD be drawn ; the rectangle AC.BD...
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Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1819 - 740 pages
...described about the triangle. Prop. D. Theor. The rectangle contained by the diagonals of a quadrilateral inscribed in a circle, is equal to both the rectangles contained by it» opposite sides. Book XI. Def. 1. — A solid is that which hath length, breadth, and thickness....
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Solutions of the Cambridge Problems: From 1800 to 1820, Volume 2

John Martin Frederick Wright - Mathematics - 1825 - 798 pages
...base, the vertical angle, and the sum of the two remaining sides of a triangle ; to construct it. 19. The rectangle contained by the diagonals of a quadrilateral...both the rectangles contained by its opposite sides. GEOMETRY. 1. How many sides has that polygon whose interior angles equal ten right angles ? 2. In any...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 372 pages
...from an angle, &c. QED PROB. D. THEOREM. 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 inicribed in a circle, and join AC, BD ; the rectangle contained by AC,...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 513 pages
...BA, AC is equal* to the rectangle EA, AD. If therefore from an angle, &c. QED PROP. D. THEOR. See N. 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 join AC, BD : the rectangle contained...
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - Geometry - 1829 - 186 pages
...angles at the centres are to one another as the circumferences of the circles. The rectangle under the diagonals of a quadrilateral figure inscribed in a circle is equal to both the rectangles under its two opposite sides. The homologous sides, and also the perimeters of similar polygons inscribed...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 pages
...angle," &c. QED PROP. D. THEOR. The rectangle contained by the diagonals of a See N. 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 rectangle contained by AC,...
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