 | 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... | |
 | 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... | |
 | John Hymers - Logarithms - 1858 - 292 pages
...cosFG ' cos CH+ cos FH~ cos AO + cos FQ* or 4. The product of the sines of the semi-diagonals of a quadrilateral inscribed in a circle, is equal to the sum of the products of the sines of half the opposite sides. Let the dotted lines (fig. 24) represent the chords... | |
 | Royal University of Ireland - Universities and colleges - 1859 - 490 pages
...equation xs — 6*= 100. 4. Prove that the rectangle under the diagonals of a quadrilateral figure inscribed in a circle is equal to the sum of the rectangles under the opposite sides ; and hence calculate the side of a regular quindecagon inscribed in a given... | |
 | Thomas Percy Hudson - Trigonometry - 1862 - 218 pages
...=sin a sin 7+ sin 3 riu and apply this formula to shew that the rectangle under- the diagonals of a quadrilateral inscribed in a circle is equal to the sum of the rectangles under the opposite sides. = j{cos (o -7) -cos (0+7) + C08 (0+7) -cos(a+i/J+7)! = sina sin 7 + sin j3... | |
 | Dublin city, univ - 1871 - 366 pages
...FRESHMEN. glaibtmatirs. DR. STUBBS. 1 . The rectangle under the diagonals of a quadrilateral figure inscribed in a circle is equal to the sum of the rectangles under the opposite sides~: 2. Find two lines which shall be to each other in the ratio of two given... | |
 | Manchester univ - 1872 - 380 pages
...in the duplicate ratio of their homologous sides. 5. 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. If from the vertices of an equilateral triangle straight lines be... | |
 | University of Madras - 1873 - 436 pages
...a circle are together equal to two right angles. IV. The rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to the sum of the rectangles contained l>y its opposite sides. V. Draw a straight line perpendicular to a plane from a given point... | |
 | Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 236 pages
...by the square of AD. <Ji. E. D, PROP. B. — THEOREM. 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. Let ABCD be a quadrilateral inscribed in a circle. Join AC, BD. The... | |
 | 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... | |
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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. 
