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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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An Elementary Geometry: Plane, Solid and Spherical

William Frothingham Bradbury - Geometry - 1880 - 260 pages
...equal to the product of its three sides divided by twice the diameter of the circumscribed circle. 104. The rectangle contained by the diagonals of a quadrilateral...equal to the sum of the two rectangles contained by the opposite sides. 105. If a perpendicular is drawn from the vertex of a triangle ABC, to the base...
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Report of Her Majesty's Civil Service Commissioners, Together ..., Volume 24

Great Britain. Civil Service Commission - 1880 - 660 pages
...Enclid's definition of proportion, and from it deduce the Algebraical definition of proportion. 2. Prove that 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. Prove, by geometry, that the geometrical mean...
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A Synopsis of Elementary Results in Pure and Applied ..., Volume 1, Part 1

George Shoobridge Carr - Mathematics - 1880
...base and the diameter of the circumscribing circle. VI. D. — Ptolemy's Theorem. The rectangle of the diagonals of a quadrilateral inscribed in a circle is equal to both the rectangles under the opposite sides. BOOK XL XI. 4. — A right line perpendicular to two...
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Elements of Geometry

George Albert Wentworth - 1881 - 266 pages
....a*. 278 EA AC :.BA X AC = EA X AD. QED PROPOSITION XX. THEOREM. 301. The product of the two diagonals of a quadrilateral inscribed in a circle is equal to the sum of the products of its opposite sides. J3 Let ABC D be any quadrilateral inscribed in a circle, AC and BD...
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Geometrical Exercises for Beginners

Samuel Constable - Geometry - 1882 - 222 pages
...triangle, the base, vertical angle, and the rectangle contained by the sides: construct it. PROP. 95. The rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to the sum of the rectangles contained by the opposite sides. Let ABCD be a quadrilateral inscribed in a circle : then...
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Science, Volume 2

John Michels (Journalist) - Science - 1883 - 880 pages
...subject, he gives there the theorem, afterwards inserted in Euclid (book vi. prop. D), relating to the rectangle contained by the diagonals of a quadrilateral inscribed in a circle. The Arabians made the improvement of using, in place of the chord of an are, the sine, or half chord...
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The Elements of Euclid, books i. to vi., with deductions, appendices and ...

Euclides - 1884 - 434 pages
...8. In the same figure prove AB . AD + CB . CD : BA . BC + DA . DC = AC:BD. PROPOSITION D.* THEOREM. The rectangle contained by the diagonals of a quadrilateral...the two rectangles contained by its opposite sides. A Let ABCD be a quadrilateral inscribed in a circle, and AC, BD its two diagonals : it is required...
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A Short History of Greek Mathematics

James Gow - Mathematics - 1884 - 350 pages
...Some of these Ptolemy first sets out. He next proves the proposition, now appended to Euclid vi. (D), that " the rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to both the rectangles contained by its opposite sides1", and then proceeds to shew how from the chords...
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English Mechanic and World of Science: With which are ..., Volume 38

Industrial arts - 1884 - 594 pages
...the subject he gives there the theorem afterwards inserted in Euclid (Book VI. Prop. D) relating to the rectangle contained by the diagonals of a quadrilateral inscribed in a circle. The Arabians made the improvement of using in place of the chord of an arc the sine, or half chord...
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A treatise on spherical trigonometry, by W.J. M'Clelland and T. Preston, Part 1

William John M'Clelland - 1885 - 182 pages
...angles of a triangle are equal, the triangle is isosceles. (4). The sum of one pair of opposite angles of a quadrilateral inscribed in a circle is equal to the sum of the remaining pair. For, join the pole of the circle to the angles of the quadrilateral forming four isosceles...
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