 | Oxford univ, local exams - 1880 - 396 pages
...drawn parallel to the base. 11. 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. 12. If a straight line stand at right angles to each of two straight... | |
 | George Albert Wentworth - 1881 - 266 pages
...££.a*. §278 EA AC :.BA X AC = EA X AD. QED 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. J3 Let ABC D be any quadrilateral inscribed in a circle, AC and BD... | |
 | Samuel Constable - Geometry - 1882 - 222 pages
...angle, and the rectangle contained by the sides: construct it. PROP. 95. 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. Let ABCD be a quadrilateral inscribed in a circle : then AC.BD = AB.CD... | |
 | Euclides - 1884 - 434 pages
...AB . AD + CB . CD : BA . BC + DA . DC = AC: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
...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 sides1", and then proceeds to shew how from the chords... | |
 | William John M'Clelland - 1885 - 182 pages
...angles of a triangle are equal, the triangle is isosceles. (4). The sum of one pair of opposite angles of a quadrilateral inscribed in a circle is equal to the sum of the remaining pair. For, join the pole of the circle to the angles of the quadrilateral forming four isosceles... | |
 | George Shoobridge Carr - Mathematics - 1886 - 1036 pages
...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 XI. XI. 4. — A right line perpendicular to two... | |
 | Encyclopedias and dictionaries - 1888 - 916 pages
...called after him, concerning a quadrilateral inscribed in a circle : Tho rectangle under tho diagonals is equal to the sum of the rectangles under the opposite sides. By means of this theorem the chord of the sura or of the difference of two arcs whose chords are given... | |
 | New Brunswick. Board of Education - Education - 1889 - 1004 pages
...similarly described figures upon the sides containing the right angle. 2. The 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. 3. If two planes cut one another, their common section must be a straight... | |
 | George Minchin Minchin - Statics - 1890 - 430 pages
...considerations with regard to the circumstances of given systems of forces. Thus, Ptolemy's theorem that the rectangle under the diagonals of a quadrilateral...equal to the sum of the rectangles under the opposite pairs of sides follows (see example 1 3, p. 1 9) from the fact that, if ABCD is such a quadrilateral,... | |
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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. 
