 | 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... | |
 | Euclid - Geometry - 1845 - 218 pages
...to the rectangle § 16. 6. EA, AD. If, therefore, from any angle, &c. QED PROPOSITION D. THEOR. — The rectangle contained by the diagonals of a quadrilateral inscribed in a circle, is equal to both tlie rectangles contained by its opposite sides. Let ABCD be any quadrilateral inscribed in a... | |
 | Euclid, James Thomson - Geometry - 1845 - 382 pages
...is equal to the rectangle EA.AD. If, therefore, from an angle of a triangle, &c. PROP. E. 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 a quadrilateral inscribed in a circle,... | |
 | Euclides - 1846 - 292 pages
...BA, AC is equal to the rectangle EA, AD. Wherefore, If from any angle %c. QBP PROP. D. THEOn. Tin; rectangle, contained by the diagonals of a quadrilateral...rectangles contained by its opposite sides. Let ABCD be any quadrilateral inscribed in a circle, and join AC, BD : the rectangle contained by AC, BD is equal... | |
 | Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...: and consequently the rectangle BA.AC is equal (16. 6.) to the rectangle EA.AD. JD 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... | |
 | Dennis M'Curdy - Geometry - 1846 - 166 pages
...Wherefore, if from any angle, &c. fiecite(o)p. 31, 3; (4) p. 21, 3 ; c)p. 4,6; . (d) p. lli, 6. QED D Th. The rectangle contained by the diagonals of a quadrilateral inscribed in a circle, is equal to both the rectangles contained by its opposite sides. Given ABCD any quadrilateral inscribed in a circle... | |
 | Thomas Gaskin - Geometry, Analytic - 1847 - 301 pages
...COLLEGE. DEC. 1841. (No. XII.) 1. THE rectangle contained by the diagonals of a quadrilateral figure inscribed in a circle is equal to the sum of the rectangles contained by its opposite sides. 2. Four circles are drawn, of which each touches one side of a quadrilateral figure and the adjacent... | |
 | Elias Loomis - Conic sections - 1849 - 252 pages
...+ ADxDE. But ADxDE=BDxDC (Prop. XXVII.); hence BA x AC=BD x DC+AD'. BAxAC=:ApxAE. PROPOSITION XXX. THEOREM. The rectangle contained by the diagonals of a quadrilateral inscribed in a circle, is equivalent to the sum of the rectangles of the opposite sides. Let ABCD be any quadrilateral inscribed... | |
 | Education - 1851 - 502 pages
...triangles are proportionals. 3. The rectangle contained by the diagonals of a quadrilateral figure inscribed in a circle is equal to the sum of the rectangles contained by its opposite sides. 2. If one diagonal of a quadrilateral bisects the other, it divides the quadrilateral into four equal... | |
 | Euclides - Geometry - 1853 - 176 pages
...is equal (vi. 16) to the rectangle ea, a d. If therefore from an angle, &c. QED PROPOSITION D. — THEOREM. The rectangle contained by the diagonals...a quadrilateral inscribed in a circle is equal to both the rectangles contained by its opposiie sides. LET abcd be any quadrilateral inscribed in a circle,... | |
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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... 
