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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 Text-book of Euclid's Elements for the Use of Schools, Book 1

Euclid - Euclid's Elements - 1904 - 488 pages
....-. BA : AD :: EA : AC; VI. 4. .-. the rect. BA, AC = the rect. EA, AD. VI. 16. QED PROPOSITION D. THEOREM. The rectangle contained by the diagonals...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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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 inscribed in a circle is equal to the sum of the two rectangles contained by its opposite sides. Two similar polygons may be so placed that the lines...
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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 the addition only, in...
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Annual Report, Volumes 2-3

Civil Service Commission of Canada - Civil service - 1910 - 240 pages
...stand. 3. Similar triangles are to one another in the duplicate ratio of their homologous sides. 4. 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. 5. The locus of a point, the ratio of whose distances...
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Annual Calendar of McGill College and University

McGill University - 1883 - 404 pages
...the two other sides produced. .10. The rectangle contained by the diagonals of a quadrilateral figure inscribed in a circle is equal to the sum of the rectangles contained by its opposite sides. 1 1. Find the areas of the square and regular hexagon inscribed in a circle of 2 inches radius. 12....
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Journal of Education

Education - 1911 - 1334 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...inscribed in a circle, is equal to the sum of the two rectangles contained by its opposite sides. 3. In a convex solid angle, the sum of the face angles...
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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 inscribed in a circle is equal to the sum of the two rectangles contained by its opposite sides. Two similar polygons may be so placed that the lines...
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Sessional Papers - Legislature of the Province of Ontario, Volume 6

Ontario. Legislative Assembly - Ontario - 1914 - 996 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 inscribed in a circle is equal to the sum of the two rectangles contained by its opposite sides. Two similar polygons may be so placed that the lines...
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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 inscribed in a circle is equal to the sum of the two rectangles contained by its opposite sides. 2. Areas of triangles of equal altitude are to one...
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Advanced Geometry for High Schools ...

Alexander H. McDougall - Geometry - 1919 - 232 pages
...= AD (AD + 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 the rectangles contained by its opposite sides. This theorem is a particular case ofthat o/ 16. ABCD is a quadrilateral inscribed in a circle. To...
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