 | John Bonnycastle - Trigonometry - 1806 - 464 pages
...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 is known... | |
 | Isaac Dalby - Mathematics - 1806 - 526 pages
...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
...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... | |
 | John Mason Good - 1813 - 714 pages
...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... | |
 | John Playfair - Circle-squaring - 1819 - 350 pages
...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... | |
 | Euclides - 1821 - 294 pages
...•'• &c. Cor. 4. In a quadrilateral figure inscribed in a circle, the rectangle under the diagonals is equal to the sum of the rectangles under the opposite sides. figure, an -£1 = to the lenn: that line will divide the diagonal on which it falls into segments,... | |
 | Euclid, Robert Simson - Geometry - 1821 - 514 pages
...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... | |
 | Euclid - 1822 - 222 pages
...In any quadrilateral figure ABCD inscribed in a circle, the rectangle under the diagonals AC and BD is equal to the sum of the rectangles under the opposite sides, under AB and CD, and under BC and AD. Make the angle ABE equal to CBD, and since the angles ABE and... | |
 | Peter Nicholson - Mathematics - 1825 - 1046 pages
...rectangle EA, AD. I f therefore from an angle, &c. QED PROB. D. THEOREM. 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 inicribed in a circle,... | |
 | 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... | |
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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. 
