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" The opposite angles of a quadrilateral inscribed in a circle are together equal to two right angles, with converse. "
Calendar - Page 286
by University of St. Andrews - 1896
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Elements of Geometry: With Notes

John Radford Young - Euclid's Elements - 1827 - 228 pages
...inscribed angle subtended by the difference of the opposite intercepted arcs. PROPOSITION XVII. THEOREM. The opposite angles of a quadrilateral inscribed in...a circle, are together equal to two right angles. The opposite angles A, C, or ABC, ADC, of the inscribed quadrilateral ABCD, are together equal to two...
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Hirsch's Collection of Examples Formulae and Calculations on the Literal ...

Hirsch - Algebra - 1827 - 690 pages
...324', 6 = 137', с = 431', d = 122', then q = 44079-76 D'. SECTION XXXI. Рвов. All the sides of a quadrilateral, whose opposite angles are together equal to two right angles (about which, consequently, a circle may be described), are given: required to find its area. SOLUT....
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Hirsch's Geometry: Or, A Sequel to Euclid

Meyer Hirsch - Geometry - 1827 - 288 pages
...324', b = 137', с = 431х, d = 122х, then q = 44079-76 Dх. ' SECTION XXXI. PHOB. All the sides of a quadrilateral, whose opposite angles are together equal to two right angles (about which, consequently, a circle may be described), are given: required to ßnd us area. SOLUT....
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The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ...

Euclides - 1833 - 304 pages
...other given angle, to which it is external or internal, contrary to prop. 16, b. 1. PROP. 22. THEOR. The opposite angles of a quadrilateral inscribed in a circle, are together equal to two rig/it angles. For of either triangle, into which one of the diagonals resolves the quadrilateral,...
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The British Annals of Education for ...: Being The Scholastic ..., Volumes 1-2

Education - 1844 - 688 pages
...which joins their centres, shall pass through the point of contact. 10. The opposite angles of any quadrilateral inscribed in a circle, are together equal to two right angles. 11. If a straight line touch a circle, and from the point of contact a straight line be drawn cutting...
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Papers for the schoolmaster, Volume 3

1867 - 336 pages
...the difference of the angles BDE, ADE, will be invariable. SECTION III. 1. The opposite angles of Buy quadrilateral inscribed in a circle, are together equal to two right angles. No parallelogram can be inscribed in a circle, unless it be rectangular. 2. In equal circles the angles...
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Liber Cantabrigiensis, an account of the aids afforded to poor students, the ...

Robert Potts - 1855 - 1050 pages
...the square on the other part. Deduce the same from the preceding propositions of the Second Book. 6. The opposite angles of a quadrilateral inscribed in...a circle, are together equal to two .right angles. Shew that no parallelogram, except a rectangle, can be inscribed in a circle. 7. If a straight line...
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Lessons on plane trigonometry

Edward Butler (A.M.) - 1862 - 154 pages
...will become Q=i&2 sec20 secsx t»n Q5 which is calculable by logarithms. 73. Given the four sides of a quadrilateral whose opposite angles are together equal to two right angles, to find the angles and the area. Let the sides AB, BC, CD, and DA, of the quadrilateral be represented...
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Liber Cantabrigiensis: An Account of the Aids Afforded to Poor ..., Volume 2

Robert Potts - 1863 - 482 pages
...the squares of the lines joining the angular points with the middle points of the opposite sides. 12. The opposite angles of a quadrilateral inscribed in...a circle are together equal to two right angles. A segment of a circle rolls upon a plane from one end of its circumference to the other. Shew that the...
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Calendar of the McGill University, Montreal

McGill University - 1865 - 332 pages
...square of half the line is equal to the square of the line made up of the half and the produced part. 3. The opposite angles of a quadrilateral inscribed in a circle are together equal to two right angles. o. If the opposite angles of a quadrilateral are together equal to two right angles, the quadrilateral...
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