| Robert Simson - Trigonometry - 1827 - 513 pages
...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... | |
| Science - 1828
...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
...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 - Euclid's Elements - 1835 - 316 pages
...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... | |
| 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... | |
| George Darley - Geometry - 1836 - 128 pages
...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
...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
...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
...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
...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... | |
| |