| Almanacs, English - 1757
...the Figure is infcribed in a Circle. But the Recbngle of the two Diagonals of any Trapezium infcribed **in a Circle is equal to the Sum of the Rectangles of** the oppofite Sides : Therefore DExBC = DCXBE + DBXCE; the Half of which is (= 2880 Perches, or 18 Acres)... | |
| Isaac Dalby - Mathematics - 1806 - 526 pages
...parallelogram, is equal to the squares on the 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... | |
| Charles Hutton - Bridges - 1812 - 514 pages
...of the chord of an arc, and of the 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** two rectangles under the opposite sides.—3. The sum of the squares of the sine and cosine, hitherto... | |
| James Mitchell - Mathematics - 1823 - 684 pages
...equal to the internal and opposite angle. 7. Also, in this case, the rectangle of its two diagonals **is equal to the sum of the rectangles of its opposite sides.** TRAPEZOID, a quadrilateral figure, having two of its opposite sides parallel ; the area of which is... | |
| John Martin Frederick Wright - Mathematics - 1825 - 798 pages
...the ratios of their sides. 3. The rectangle contained by the diagonals of any quadrilateral figure **inscribed in a circle is equal to the 'sum of the rectangles** contained by its opposite sides. 4. If the exterior angle of a triangle be bisected, and also one of... | |
| John Martin Frederick Wright - 1827 - 344 pages
...the ratios of their sides. 3. The rectangle contained by the diagonals of any quadrilateral figure **inscribed in a circle is equal to the sum of the rectangles** contained by its opposite sides. 4. If the exterior angle of a triangle be bisected, and also one of... | |
| John Martin F. Wright - 1827 - 638 pages
...the ratios of their sides. 3. The rectangle contained by the diagonals of any quadrilateral figure **inscribed in a circle is equal to the sum of the rectangles** contained by its opposite sides. 4. If the exterior angle of a triangle be bisected, and also one of... | |
| Charles Hutton - Logarithms - 1834 - 368 pages
...of the chord of an arc, and of the 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** two rectangles under the opposite sides. 3. The sum of the squares of the sine and cosine (often called... | |
| Charles Hutton - Logarithms - 1842 - 456 pages
...of the chord of an arc, and of the 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** two rectangles under the opposite sides. 3. The sum of the squares of the sine and cosine (often called... | |
| Euclides - 1846 - 292 pages
...Wherefore, If from any angle %c. QBP PROP. D. THEOn. 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, and join AC,... | |
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