| 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
...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... | |
| John Playfair - Circle-squaring - 1819 - 350 pages
...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 - Geometry - 1821 - 514 pages
...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... | |
| 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 the interior and opposite, the... | |
| Peter Nicholson - Mathematics - 1825 - 1046 pages
...rectangle BA, AC is equal (16. 6.) to the rectangle EA, AD. I f therefore from an angle, &c. QED PROB. D. **THEOREM. The rectangle contained by the diagonals...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 F. Wright - 1827 - 632 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 the interior and opposite, the... | |
| 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 the interior and opposite, the... | |
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