| John Bonnycastle - Trigonometry - 1806 - 464 pages
...on this subject. He has also here proved, for the first time that we know of, that the rectangle of the two diagonals of any quadrilateral inscribed in a circle, is equal to the sum of the rectangles of its opposite sides (c). After the time of Ptolemy and his commentator Theon, little more... | |
| Charles Hutton - Mathematics - 1811 - 574 pages
...chord of its supplement to a semicircle. 2. The rectangle under the two diagonals of any quadrilatéral 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... | |
| Charles Hutton - Mathematics - 1811 - 406 pages
...61). C^ ED THEOREM LXV. The Rectangle of the two Diagonals of any Quadrangle Inscribed in a Cirek, 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 : then the' rectangle... | |
| Charles Hutton - Bridges - 1812 - 514 pages
...sum of the squares 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...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... | |
| 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 : then the rectangle... | |
| Charles Hutton - Astronomy - 1815 - 686 pages
...taken together, are equal to two right angles. And in this case the rectangle of the two diagonals is equal to the sum of the two rectangles of the opposite sides. For the properties of the particular species of quadrilaterals, see their respective names, SQUARE,... | |
| 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 : then the rectangle... | |
| John Mason Good - 1819 - 910 pages
...taken together, are equal to two right angles. And in ibis case the rectangle of the two diagonals, is equal to the sum of the two rectangles of the opposite sides. For the properties of the particular specie» of quadrilaterals, see their respective names, SQUARE,... | |
| 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: then the rectangle... | |
| Charles Hutton - Logarithms - 1834 - 466 pages
...the sum of the squares 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...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 the sine of... | |
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