 | Robert Simson - 1827 - 546 σελίδες
...t2Ax. to the whole angle BED. Wherefore the angles in the same segment, &c. QED PROP. XXII. THEOR. The opposite angles of any quadrilateral .figure inscribed...a circle, are together equal to two right angles. 1 20. 3. Let ABCD be a quadrilateral figure in the circle ABCD; any two of its opposite angles shall... | |
 | 1828 - 524 σελίδες
...the solidity. 10 70. Parallelograms upon equal bases and between the same parallels are equal. 80. The opposite angles of any quadrilateral figure, inscribed...a circle, are together equal to two right angles. 81. If two triangles have one angle in one equal to one angle in the other, and the sides about the... | |
 | University of Cambridge - 1831 - 552 σελίδες
...Caius. FRIDAY MORNING, January 14, 1831. 9 o'clock, to 11. First, Second, Third and Fourth Classes. 1. THE opposite angles of any quadrilateral figure inscribed...in a circle are together equal to two right angles. 2. Describe an equilateral and equiangular pentagon about a given circle. 3. What sum must be paid... | |
 | John Playfair - 1835 - 336 σελίδες
...CAD, CED are equal ; Therefore the whole angle BAD is equal to the whole angle BED. PROP. XXII. THEOR. The opposite angles of any quadrilateral figure inscribed...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... | |
 | 1836 - 366 σελίδες
...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... | |
 | George Darley - 1836 - 172 σελίδες
...situated in the circumference of that circle. ART. 69. The opposite angles of a four-sided rectilineal figure inscribed in a circle, are together equal to two right angles. Let ABCD be a four-sided rectilineal figure inscribed in the circle ACD. Then the angles ABC, ADC,... | |
 | Euclides - 1837 - 112 σελίδες
...that, similarly, Z CAD, =: Z CED, 3. that .'. whole Z BAD — whole Z BED. PROPOSITION XXII. Theorem. The opposite angles of any quadrilateral figure inscribed...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 - 254 σελίδες
...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... | |
 | Euclides - 1838 - 264 σελίδες
...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...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 shall together... | |
 | Euclides - 1840 - 82 σελίδες
...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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The opposite angles of any quadrilateral figure inscribed in a circle, are together equal to two right angles. 
