 | Isaac Dalby - Mathematics - 1806 - 526 pages
...four sides taken together. 241. THEOREM. The rectangle under the two diagonals of any quadrilateral inscribed in a circle, is equal to the sum of the two rectangles of the opposite sides : That is, AC x BD = AB x CD -f AD x BC. Suppose CP is drawn to make the angle... | |
 | Charles Hutton - Bridges - 1812 - 514 pages
...of its supplement to a semicircle.—2. The rectangle under the two diagonals of any quadrilateral inscribed in a circle, is equal to the sum of the two rectangles under the opposite sides.—3. The sum of the squares of the sine and cosine, hitherto called the sine of the complement,... | |
 | Charles Hutton - Mathematics - 1812 - 620 pages
...BE is = AD . DB (th. 61). q. E. D THEOREM LXV. The Rectangle of the two Diagonals of any Quadrangle Inscribed in a Circle, is equal to the sum of the two Rectangles of the Opposite Sides. LET ABCD be any quadrilateral inscribed in a circle, and AC, BD, its two diagonals... | |
 | Charles Hutton - Arithmetic - 1818 - 646 pages
...AD . DB (th. 61). «. ED THEOREM LXV. The Rectangle of the two Diagonals of any Quadrangle lnscribed in a Circle, is equal to the sum of the two Rectangles of the Opposite Sides. LET ABCD be any quadrilateral inscribed in a circle, and AC, BD, its two diagonals... | |
 | Charles Hutton - Mathematics - 1822 - 616 pages
...is = AD . DB (th. 61). «. E. ». THEOREM LXV. The Rectangle of the two Diagonals of any Quadrangle Inscribed in a Circle, is equal to the sum of the two Rectangles of the Opposite Sides. LET ABCD be any quadrilateral inscribed in a circle, and AC, BD, its two diagonals:... | |
 | Charles Hutton - Logarithms - 1834 - 466 pages
...chord of its supplement to a semicircle. 2. The rectangle under the two diagonals of any quadrilateral inscribed in a circle, is equal to the sum of the...sides. 3. The sum of the squares of the sine and cosine (often called the sine of the complement), is equal to the square of the radius 4. The difference between... | |
 | Charles Hutton - Logarithms - 1842 - 450 pages
...chord of its supplement to a semicircle. 2. The rectangle under the two diagonals of any quadrilateral inscribed in a circle, is equal to the sum of the...sides. 3. The sum of the squares of the sine and cosine (often called the sine of the complement), is equal to the square of the radius. 4. The difference... | |
 | Charles Hutton - Logarithms - 1855 - 462 pages
...supplement to a semicircle. 2. The rectangle under the two diagonals of any quadrilateral inscribed in в circle, is equal to the sum of the two rectangles under the opposite sides. 3. 1Ъе sum of the squares of the sine and cosine (often called the sine of the complement), is equal... | |
 | Gerardus Beekman Docharty - Geometry - 1867 - 474 pages
...since CD . DE is= AD.DB(th. 21). QED THEOREM XXV. The rectangle of the two diagonal", of any quadrangle inscribed in a circle is equal to the sum of the two rectangles of the opposite sides. Let ABCD be any quadrilateral inscribed in a circle, and AC, BD its two diagonals... | |
 | William Frothingham Bradbury - Geometry - 1877 - 262 pages
...diameter of the circumscribed circle. 104. 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. 105. If a perpendicular is drawn from the vertex of a triangle ABC,... | |
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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. 
