 | Samuel Constable - Geometry - 1882 - 222 pages
...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 AC.BD = AB.CD... | |
 | Euclides - 1884 - 434 pages
...: BA . BC + DA . DC = AC:BD. PROPOSITION D.* THEOREM. 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. A Let ABCD be a quadrilateral inscribed in a circle,... | |
 | William John M'Clelland - 1885 - 182 pages
...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... | |
 | New Brunswick. Board of Education - Education - 1889 - 1004 pages
...figures upon the sides containing the right angle. 2. 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. 3. If two planes cut one another, their common section must be a straight... | |
 | George Minchin Minchin - Statics - 1890 - 430 pages
...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... | |
 | Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...their circum-circles are equal. PROPOSITION D. 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. Let ABCD be a cyclic quadl., AC and BD its diagls. ; then rect. AC,... | |
 | Edward Albert Bowser - Geometry - 1890 - 420 pages
...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... | |
 | 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... | |
 | 1891 - 718 pages
...figures upon the sides containing the right angle. 2. 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. 3. If two planes cut one another, their common section must be a straight... | |
 | 1891 - 718 pages
...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 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. 
