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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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National Society's Monthly Paper

1857 - 408 pages
...another. 2. Similar triangles are to one another in the 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...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1858 - 256 pages
...BDxDC (Prop. XXVII.) ; hence BAxAC=BDxDC+AD'. Therefore, if an angle, &c. PROPOSITION XXX. THEOREM. The rectangle contained by the diagonals of a quadrilateral inscribed in a circle, is equivalent to the sum of the rectangles of the opposite sides. Let ABCD be any quadrilateral inscribed...
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A Treatise on Plane and Spherical Trigonometry, and on Trigonometrical ...

John Hymers - Logarithms - 1858 - 292 pages
...COB FO cosFG ' cos CH+ cos FH~ cos AO + cos FQ* or 4. The product of the sines of the semi-diagonals of a quadrilateral inscribed in a circle, is equal to the sum of the products of the sines of half the opposite sides. Let the dotted lines (fig. 24) represent the chords...
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Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860 - 288 pages
...consequently the rectangle BA • AC is equal to the rectangle EA • AD (VI. 16). I'JtorOSITJON D. THEOBEM. The rectangle contained by the diagonals of a quadrilateral inscribed in a circle, is equal to both the rectangles contained by its opposite sides. Given any quadrilateral ABCD inscribed in a circle,...
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Examination papers used at the examinations for direct commissions [&c.].

War office - 1861 - 714 pages
...square of the line which meets it, the line which meets shall touch the circle. VOLUNTARY PORTION. 1. The rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to both the rectangles contained by its opposite sides. 2. If two straight lines are at right angles to...
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Elementary Trigonometry: With a Collection of Examples

Thomas Percy Hudson - Trigonometry - 1862 - 200 pages
...(fj+y) = sin a sin 7+ sin /3 sin(a + j3+7), and apply this formula to shew that the rectangle under the diagonals of a quadrilateral inscribed in a circle is equal to the sum of the rectangles under the opposite sides. sin (a +/3) sin (j3 +7) ={cos (a - 7) - cos (0 + 2/8 + 7)} =...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1861 - 628 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 and Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 520 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 quadrilatoral inscribed...
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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 - 426 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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