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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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Sessional Papers, Volume 37, Part 4

Ontario. Legislative Assembly - Ontario - 1905 - 1096 pages
...described about the triangle. The rectangle contained by the diagonals of a quadrilateral inscribed ii a circle is equal to the sum of the two rectangles contained by its opposM sides. Two similar polygons may be so placed that the lines joining correi ponding points are...
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Calendar of Queen's College and University, Kingston, Canada for the Year ...

Queen's University (Kingston, Ont.) - 1906 - 314 pages
...rectangle contained by the perpendicular and the diameter of the circle described about the triangle. The rectangle contained by the diagonals of a. quadrilateral...the two rectangles contained by its opposite sides. Two similar polygons may be so placed that the lines joining corresponding points are concurrent.....
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Books 3-9

Euclid - Mathematics, Greek - 1908 - 456 pages
...rav (v ru> KVK\.W The theorem may be enunciated thus. The rectangle contained by the diagonals of any quadrilateral inscribed in a circle is equal to the sum of the rectangles contained by the pairs of opposite sides. I shall give the proof in Ptolemy's words, with...
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Annual Report, Volumes 2-3

Civil Service Commission of Canada - Civil service - 1910 - 238 pages
...segments. Find a square whose area is equal to that of a given triangle. 10. The rectangle contained hy the diagonals of a quadrilateral inscribed in a circle is equal to the sum of the rectangles contained by the opposite sides. By taking the diagonals perpendicular to each other, deduce...
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Journal of Education

Education - 1911 - 1330 pages
...externally into segments which have the same ratio as the other sides of the triangle. Euclid, VI. 3rd. 2. The rectangle contained by the diagonals of a quadrilateral...the two rectangles contained by its opposite sides. 3. In a convex solid angle, the sum of the face angles is less than four right angles. 4. Draw an isoseceles...
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Regulations and Courses of Study of the Continuation Schools ...

Ontario. Dept. of Education - 1913 - 128 pages
...rectangle contained by the perpendicular and the diameter of the circle described about the triangle. The rectangle contained by the diagonals of a quadrilateral...the two rectangles contained by its opposite sides. Two similar polygons may be so placed that the lines joining corresponding points are concurrent. If...
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Sessional Papers - Legislature of the Province of Ontario, Volume 6

Ontario. Legislative Assembly - Ontario - 1914 - 998 pages
...rectangle contained by the perpendicular and the diameter of the circle described about the triangle. The rectangle contained by the diagonals of a quadrilateral...the two rectangles contained by its opposite sides. Two similar polygons may be so placed that the lines joining corresponding points are concurrent. If...
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Report of the Secretary for Public Instruction ..., Volume 40

Queensland. Department of Public Instruction - Education - 1916 - 244 pages
...exterior to the circumference. For Admission as Teacher of the Second Class. (THREE HOURS ALLOWED.) 1. The rectangle contained by the diagonals of a quadrilateral...the two rectangles contained by its opposite sides. 2. Areas of triangles of equal altitude are to one another as their bases. Prove by this theorem that...
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Advanced Geometry for High Schools ...

Alexander H. McDougall - Geometry - 1919 - 232 pages
...DE) = AD2 + AD. DE = AD2+ BD. DC. Л rect. BA . AC = rect. BD . DC + AD5. 15. Ptolemy's Theorem :— The 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. This theorem is a particular case ofthat o/ 16. ABCD...
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Littell's Living Age, Volume 159

1883 - 1060 pages
...the subject he gives there the theorem afterwards inserted in Euclid (Book VI. Prop. U.) 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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