 | 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 is known... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | John Martin Frederick Wright - 1825 - 798 σελίδες
...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 - 1825 - 1046 σελίδες
...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 σελίδες
...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 σελίδες
...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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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. Let ABCD be any quadrilateral inscribed in a circle... 
