 | 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... | |
 | Charles Hutton - Mathematics - 1811 - 574 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... | |
 | Isaac Dalby - Mathematics - 1813 - 538 pages
...squares on the four sides taken together. 244. 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, ACxBD=:ABxCDi-ADxBC. Suppose CP is drawn to make the... | |
 | William Shepherd, Jeremiah Joyce, Lant Carpenter - Education - 1817 - 606 pages
...is said to have been the author of the proposition " 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." After Ptolemy, and his commentator Theon, little more is known on this subject,... | |
 | 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... | |
 | John Mason Good - 1819 - 800 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 it» opposite sides. Book XI. Def. 1.—A solid is that which hath... | |
 | John Playfair - 1819 - 354 pages
...BA.AC is equal (16. 6.) to the rectangle 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, Robert Simson - Geometry - 1821 - 514 pages
...is equal (16. f>.) to the rectangle 1 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 equaf to both the rectangles contained by its opposite sides.* Let ABCD be any quadrilateral inscribed... | |
 | Peter Nicholson - Mathematics - 1825 - 1046 pages
...AC is equal (16. 6.) to the rectangle EA, AD. If 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,... | |
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Show that the rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to the sum of the rectangles contained by the opposite sides. 
