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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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A Treatise on Statics: With Applications to Physics, Volume 1

George Minchin Minchin - Statics - 1890 - 430 pages
...regard to the circumstances of given systems of forces. Thus, Ptolemy's theorem that the rectangle under the diagonals of a quadrilateral inscribed in a circle is equal to the sum of the rectangles under the opposite pairs of sides follows (see example 1 3, p. 1 9) from the fact that, if ABCD is...
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The Elements of Plane and Solid Geometry: With Numerous Exercises

Edward Albert Bowser - Geometry - 1890 - 420 pages
...circle circumscribed about a triangle when the three sides are known. EXERCISE. 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. SUGGESTION.— Make /DAE = /BAC. Then in the similar is DAE, CAB, AD...
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Report of the Secretary for Public Instruction ...

Queensland. Department of Public Instruction - Education - 1890 - 526 pages
...to the area of the triangle. 7. The rectangle contained by the diagonals of a quadrilateral figure inscribed in a circle is equal to the sum of the rectangles contained by pairs of opposite sides. If the quadrilateral cannot be inscribed in a circle, will this ram be greater...
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The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...exercise to the student. Ex. 758.— If the rectangle contained by the diagonals of a quadri_ lateral is equal to the sum of the rectangles contained by its opposite sides, a circle can be described about it. Ex. 759.— Enunciate the contrapositive of Ptolemy's theorem (see...
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Annual Report of the Chief Superintendent of Education

1891 - 718 pages
...equal to the similar and similarly described figures upon the sides containing the right angle. 2. The rectangle contained by the diagonals of a quadrilateral...of the rectangles, contained by its opposite sides. 3. If two planes cut one another, their common section must be a straight line. 4. If two planes which...
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Examinations Papers

1891 - 718 pages
...two sides on two parallel straight lines are to one another as the sums of their parallel sides. 3. The rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to the sum of the two rectangles contained by its opposite sides. What does this proposition become when the diagonals...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - Geometry - 1892 - 460 pages
...:: EA : AC; vI. 4. .'. the rect. BA, AC'^the rect. EA, AD. vi. 16. QED PROPOSITION D. THEOREM. Tlie rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to the sum of the two rectangles contained by its opposite sides. Let ABCD be a quadrilateral inscribed in a circle,...
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Euclid's Elements of Geometry, Books 1-6

Henry Martyn Taylor - 1893 - 486 pages
...Wherefore, if two triangles &o. PROPOSITION 37 B. The rectangle contained by the diagonals of a convex quadrilateral inscribed in a circle is equal to the sum of the rectangles contained by pairs of opposite sides*. Let ABCD be a quadrilateral inscribed in a circle and AC, BD be its diagonals...
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Euclid's Elements of Geometry, Books 1-6; Book 11

Henry Martyn Taylor - Euclid's Elements - 1895 - 708 pages
...Wherefore, if two triangles &c. PROPOSITION 37 B. The rectangle contained by the diagonals of a convex quadrilateral inscribed in a circle is equal to the sum of the rectangles contained by pairs of opposite sides*. Let ABCD be a quadrilateral inscribed in a circle and AC, BD be its diagonals...
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Calendar, for the Year ...

1896 - 154 pages
...pair of opposite sides is equal to the rectangle contained by the perpendiculars on the diagonals. 3. The rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to the sum of the two rectangles contained by the opposite sides. In a quadrilateral inscribed in a circle, the rectangle...
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