 | John Mason Good - 1819 - 800 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...circle, is equal to both the rectangles contained by it» opposite sides. Book XI. Def. 1. — A solid is that which hath length, breadth, and thickness.... | |
 | John Playfair - 1832 - 358 σελίδες
...equal (16. 6. ) to the rectangle E A. AD. If, there- ^ fore, from an angle, &c. QED PROP. D. TIJEOR. The rectangle contained by the diagonals of a quadrilateral...inscribed in a circle, is equal to both the rectangles, contai, by its opposite sides. Let ABCD be any quadrilateral inscribed in a circle, and let AC, BD... | |
 | John Playfair - 1835 - 336 σελίδες
...: and consequently the rectangle BA.AC is equal (16. 6.) to the rectangle EA.AD. x, PROP. D. THEOR. The rectangle contained by the diagonals of a quadrilateral inscribed in a circle, is equal tf both the rectangles, contained by its opposite sides. Let ABCD be any quadrilateral inscribed in... | |
 | John Playfair - 1837 - 332 σελίδες
...rectangle BA.AC is equal (16. 6.) to the rectangle EA.AD. 15Q c. I" ELEMENTS * ^ ,,' PROP. D. THEOR. The rectangle contained by the diagonals of a quadrilateral inscribed in a circle, is equal to loth the rectangles, contained by its opposite sides. Let ABCD be any quadrilateral inscribed in a... | |
 | Euclides - 1842 - 316 σελίδες
...equivalent (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 equivalent to both the rectangles contained by its opposite sides. Let ABC D be any quadrilateral inscribed... | |
 | Euclid - 1845 - 218 σελίδες
...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 circle,... | |
 | Euclides - 1846 - 292 σελίδες
...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 inscribed in a circle, is equal to the sum of the rectangles contained by its opposite sides. Let ABCD be any quadrilateral inscribed... | |
 | Elias Loomis - 1849 - 252 σελίδες
...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... | |
 | Elias Loomis - 1858 - 256 σελίδες
...BDxDC (Prop. XXVII.) ; hence BAxAC=BDxDC+AD'. Therefore, if an angle, &c. 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... | |
 | Benjamin Greenleaf - 1861 - 638 σελίδες
...multiplied by twice the diameter of the circumscribed circle. PROPOSITION XXXVIII. — THEOREM. 291. The rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equivalent to the sum of the two rectangles of the opposite sides. Let ABCD be any quadrilateral inscribed... | |
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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. 
