 | 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... | |
 | 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... | |
 | Charles Hutton - Logarithms - 1834 - 466 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 (often called... | |
 | Charles Hutton - Logarithms - 1842 - 450 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 (often called... | |
 | Euclides - 1846 - 292 pages
...AD. Wherefore, If from any angle %c. QBP PROP. D. THEOn. 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, and... | |
 | George Roberts Perkins - Geometry - 1847 - 326 pages
...quadrant, which is the measure of a right angle (B. Ill, Prop, vii, Cor. 2)Cor. 4. The sum of any two opposite angles of a quadrilateral inscribed in a circle, is equal to two right angles ; for, as each inscribed angle is measured by half the arc on which it stands, it... | |
 | George Roberts Perkins - Geometry - 1850 - 332 pages
...quadrant, which is the measure of a right-angle, (B. Ill, Prop, vi, Cor. 2.) Cor. 4. The sum of any two opposite angles of a quadrilateral inscribed in a circle, is equal to two rightangles ; for, as each inscribed angle is measured by half the arc which subtends it, it follows... | |
 | John Hymers - Logarithms - 1858 - 292 pages
...COB FO cosFG ' cos CH+ cos FH~ cos AO + cos FQ* or 4. The product of the sines of the semi-diagonals of a quadrilateral inscribed in a circle, is equal to the sum of the products of the sines of half the opposite sides. Let the dotted lines (fig. 24) represent the chords... | |
 | Thomas Percy Hudson - Trigonometry - 1862 - 202 pages
...sin 7+ sin /3 sin(a + j3+7), and apply this formula to shew that the rectangle under the diagonals of a quadrilateral inscribed in a circle is equal to the sum of the rectangles under the opposite sides. sin (a +/3) sin (j3 +7) =£{cos (a - 7) - cos (0 + 2/8 + 7)} =... | |
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The rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to the sum of the two rectangles contained by its opposite sides. 
