 | Isaac Dalby - 1806 - 526 σελίδες
...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 make the angle... | |
 | John Bonnycastle - 1806 - 464 σελίδες
...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 - 1811 - 574 σελίδες
...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 - 1812 - 514 σελίδες
...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 called the sine... | |
 | Charles Hutton - 1812 - 620 σελίδες
...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... | |
 | John Mason Good - 1813 - 714 σελίδες
...contained by the perpendicular and the diameter of the circle described about the triangle. Prop. D. Theor. The rectangle contained by the diagonals of a quadrilateral inscribed in a circle, is equal to both the rectangles contained by its opposite sides. Book XI. Def. 1.— A solid is that wh.ich hath... | |
 | Charles Hutton - 1818 - 646 σελίδες
...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... | |
 | John Playfair - 1819 - 350 σελίδες
...BA.AC is equal (16. 6.) to the rectangle EA.AD. If, therefore, from an angle, &c. Q, ED PROP. D. THEOR. The rectangle contained by the diagonals of a quadrilateral inscribed in a circle, is equal to both the rectangles, contained by its opposite . sides. Let ABCD be any quadrilateral inscribed in... | |
 | Euclid, Robert Simson - 1821 - 514 σελίδες
...AC is equal (16. 6.) to the rectangle1 EA, AD. If therefore, from an angle, &c.' QED PROP. D. THEOR. THE rectangle contained by the diagonals of a quadrilateral inscribed in a circle, is equal to both the rectangles contained by its opposite sides.* Let ABCD be any quadrilateral inscribed in a... | |
 | Charles Hutton - 1822 - 616 σελίδες
...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:... | |
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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. 
