 | Francis Cuthbertson - Euclid's Elements - 1874 - 400 pages
...equiangular; (i. 25) .-. BA : AHasAR : AC; (vi. 4) rectangle (BA, AC) = rectangle (AH, AR). THEOREM (h). The rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to both the rectangles contained by the opposite sides. Let FGHK be a quadrilateral figure inscribed in... | |
 | alexander thom - 1875 - 758 pages
...propositions referred to. 4. Prove that the rectangle contained by the diagonals of a quadrilateral figure inscribed in a circle is equal to the sum of the rectangles contained by the opposite sides. Hence calculate the side of a regular quindecagon inscribed in a given circle.... | |
 | Euclides, James Hamblin SMITH - 1876 - 382 pages
...part of it within the triangle, is equal to the rectangle contained by the two sides. PROPOSITION D. THEOREM. The rectangle, contained by the diagonals...of the rectangles, contained by its opposite sides. A Let ABCD be any quadrilateral inscribed in a ©. Join AC, BD. Then rect. AC, BD=rect. AB, CD together... | |
 | Richard Wormell - 1876 - 268 pages
...perpendicular and the diameter of the circle described about the triangle. . . . . . . . . . . 240 D. The rectangle contained by the diagonals of a quadrilateral inscribed in a circle, is equal to both the rectangles contained by its opposite sides. . , 240 E. If a segment of a circle be bisected,... | |
 | William Frothingham Bradbury - Geometry - 1877 - 262 pages
...equal to the product of its three sides divided by twice the diameter of the circumscribed circle. 104. The rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to the sum of the two rectangles contained by the opposite sides. 105. If a perpendicular is drawn from the vertex of... | |
 | Elias Loomis - Conic sections - 1877 - 458 pages
...have AB:AE::AD:AC; and hence AB x AC = AE x AD. Therefore, in any triangle, etc. PROPOSITION XXXII. 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. I.et ABCD be any quadrilateral inscribed... | |
 | George Albert Wentworth - Geometry - 1877 - 416 pages
...other ; BA AD EA AC -. BA X AC = EA XAD. § 278 PROPOSITION XX. THEOREM. 301. The product of the two diagonals of a quadrilateral inscribed in a circle is equal to the sum of the products of its opposite sides. Let ABC D be any quadrilateral inscribed in a circle, AC and BD its... | |
 | Euclides - 1878 - 398 pages
...part of it within the triangle, is equal to the rectangle contained by the two sides. PROPOSITION D. THEOREM. The rectangle, contained by the diagonals...rectangles, contained by its opposite sides. Let ABCD be any quadrilateral inscribed in a ®. Join AC, BD. Then reet. AC, BD=rect. AB, CD together with rect.... | |
 | James White - Conic sections - 1878 - 160 pages
...Then there are two similar triangles formed, as in previous proposition. XXVIII. The rectangle under the diagonals of a quadrilateral inscribed in a circle is equal to the sum of the rectangles under the opposite sides.. XXIX. If from any point on the circumference of a circle perpendiculars... | |
 | James McDowell - 1878 - 310 pages
...under the whole produced bisector and its produced part ................ 61 93. The rectangle under the diagonals of a quadrilateral inscribed in a circle is equal to the sum of the rectangles under its opposite sides (VI. D) ................ 61 94. If perpendiculars be drawn from the extremities... | |
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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... 
