 | George Shoobridge Carr - Mathematics - 1880
...tho base and the diameter of the circumscribing circle. VI. D.—Ptolemy's Theorem. The rectangle of the diagonals of a quadrilateral inscribed in a circle is equal to both the rectangles under the opposite sides. BOOK XL XI. 4.—A right line perpendicular to two others... | |
 | George Albert Wentworth - 1881 - 266 pages
...nrc, - - . EA AG -. В A X Л (7 = EA X AD. I 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 Б D its... | |
 | Samuel Constable - Geometry - 1882 - 222 pages
...triangle, the base, vertical angle, and the rectangle contained by the sides: construct it. PROP. 95. The rectangle contained by the diagonals of a quadrilateral...of the rectangles contained by the opposite sides. Let ABCD be a quadrilateral inscribed in a circle : then AC.BD = AB.CD + BC.AD, where AC, BD are the... | |
 | George Albert Wentworth - Geometry - 1882 - 442 pages
...AD о 97S EA AC .-. В А У. АС = ЕА X AD. PBOPOSITION XX. THEOBEM. 301. The product of the two diagonals of a quadrilateral inscribed in a circle is equal to the sum of the product» of it» opposite sides. J3 Let ABC D Ъе any quadrilateral inscribed in a circle, AG and... | |
 | George Albert Wentworth - Geometry, Modern - 1882 - 268 pages
...=. §278 .-.BA X AC = EA X AD. Q. ED PROPOSITION XX. THEOREM. 301. The product of the two diagonal» of a quadrilateral inscribed in a circle is equal to the sum of the products of it» opposite sides. Let А В С D be any quadrilateral inscribed in a circle, AG and... | |
 | Euclid - Euclid's Elements - 1882 - 434 pages
...greater than the tecXiHv^a AC, BD. 33. If the rectangle contained by the diagonals of a quadrilateral be equal to the sum of the rectangles contained by the opposite sides, a circle can be described round the quadrilateral. This is the converse of VI. D; it can be demonstrated... | |
 | Euclides, James Hamblin Smith - 1883 - 376 pages
...equal to the rectangle contained by the toio EUCLID'S ELEMENTS. PROPOSITION D. THEOREM. [Book VI. j; The, rectangle, contained by the diagonals of a quadrilateral...is equal to the sum of the rectangles, contained by its opposite sides. Let ABCD be any quadrilateral inscribed in a 0. Join AC, BD. Then net. AC, BD=rect.... | |
 | John Michels (Journalist) - Science - 1883 - 880 pages
...subject, he gives there the theorem, afterwards inserted in Euclid (book vi. prop. D), relating to the rectangle contained by the diagonals of a quadrilateral inscribed in a circle. The Arabians made the improvement of using, in place of the chord of an arc, the sine, or half chord... | |
 | Euclides - 1884 - 434 pages
...same figure prove AB • AD + CB • CD : BA • BC + DA • DC = AG-.BD. PROPOSITION D.* THEOREM. 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. A Let ABCD be a quadrilateral inscribed in a circle,... | |
 | James Gow - Mathematics - 1884 - 350 pages
...Some of these Ptolemy first sets out. He next proves the proposition, now appended to Euclid VI. (D), that " the rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to both the rectangles contained by its opposite sides 1 ", and then proceeds to shew how from the chords... | |
| |
Show that the rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to the sum of the rectangles contained by the opposite sides. 
