| Mathematics - 1836
...two, the plane which passes through them, is parallel to the plane passing through the others. 1831 9. **The opposite angles of any quadrilateral figure inscribed...in a circle are together equal to two right angles.** 10. Describe an equilateral and equiangular pentagon about a given circle. 11. Triangles and parallelograms... | |
| John Playfair - Geometry - 1836 - 114 pages
...equal angles are similar. PROP. XIV. THEOR. The opposite angles of any quadrilateral figure described **in a circle, are together equal to two right angles. Let ABCD be a quadrilateral figure** in the circle ABCD ; any two of its opposite angles are together equal to two right angles. Join AC,... | |
| George Darley - Geometry - 1836 - 128 pages
...circle from any one point but the centre, ibid. ART. 69. The opposite angles of a four-sided rectilineal **figure inscribed in a circle are together equal to two right angles,** 53. ART. 70. The angles in the same segment of a circle are equal, 55. AIIT. 71. The angle in the segment... | |
| Eugenius Nulty - Geometry - 1836 - 220 pages
...OF THE ANGLES AND SIDES OF INSCRIBED FIGURES. THEOREM I. 26. The opposite angles of a quadrilatéral **inscribed in a circle, are together equal to two right angles. Let** AB С D be a quadrilateral inscribed in the circle A С D ; the opposite angles AB С, AD С are together... | |
| Euclides - 1837
...BEC, 2. that, similarly, Z CAD, =: Z CED, 3. that .'. whole Z BAD — whole Z BED. PROPOSITION XXII. **Theorem. The opposite angles of any quadrilateral...in a circle are together equal to two right angles.** Steps of the Demonstration. 1. Prove that whole Z ADC = Zs BAG + ACB, 2. that Zs ADC + CBA = the 3... | |
| Charles Reiner - 1837
...intersect each other at right angles, the four straight lines joining their extremities form a square. 15. **The opposite angles of any quadrilateral figure inscribed...in a circle are together equal to two right angles.** 16. A square,—a rectangle,—and a trapezium of which the opposite angles are together equal to two... | |
| Andrew Bell - Euclid's Elements - 1837 - 240 pages
...whole angle BED. PROPOSITION XXII. THEOREM. The opposite angles of any quadrilateral figure described **in a circle, are together equal to two right angles. Let ABCD be a quadrilateral figure** in the circle ABCD ; any two of its opposite angles are together equal to two right angles. Join AC,... | |
| Euclid - Geometry - 1837 - 390 pages
...segment, &c. * PROP. XXII. THEOR. THE opposite angles of any quadrilateral figure described in a circle, t **are together equal to two right angles. Let ABCD be a quadrilateral figure** in the circle ABCD ; any two of its opposite angles are together equal to two right angles. Join AC,... | |
| Euclides - 1838
...equal to the whole angle BED. Therefore the angles in the same segment, &c. QE n. PROP. XXII. THEOR. **The opposite angles of any quadrilateral figure inscribed...two right angles. Let ABCD be a quadrilateral figure** in the circle ABCD; any two of its opposite angles shall together be equal to two right angles. Join... | |
| Euclides - 1840
...XXI. THEOR. All angles in the same segment of a circle are equal to one another. PROP. XXII. THEOR. **The opposite angles of any quadrilateral figure inscribed...a circle, are together equal to two right angles.** PROP. XXIII. THEOR. Upon the same straight line, and upon the same side of it, there cannot be two... | |
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