 | Euclides - Euclid's Elements - 1837 - 112 pages
...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 - Geometry - 1837 - 254 pages
...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 pages
...whole angle BAD is 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...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 - 192 pages
...that is to say, they are equal to two right angles. In like manner it may be shown that Zs BAC and BDC are together equal to two right angles. PROP. XXIII. THEOR. Upon the same straight line (AB), and upon the same side of it, there cannot be two similar segments 'of circles not coinciding... | |
 | Euclides - Geometry - 1841 - 378 pages
...angle BAD is equal * to the whole angle BED. Wherefore, the *2 Ax. angles in the same segment, &c. QED PROP. XXII. THEOR. The opposite angles of any quadrilateral...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 - 1842 - 316 pages
...whole angle BAD is equal to the whole angle BED. Wherefore the angles in the same segment, &c. QED PROP. XXII. THEOR. THE opposite angles of any quadrilateral...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... | |
 | Euclides - 1845 - 546 pages
...whole angle BED. (ax. 2.) Wherefore the angles in the same segment, &c. QED PROPOSITION XXII. THEOREM. 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. Then any two of its opposite angles shall together... | |
 | Scottish school-book assoc - 1845 - 444 pages
...arc on which it stands. (Prop. 1. cor. 3.) PROPOSITION XLVIII. — THEOREM. The opposite angles of a quadrilateral figure inscribed in a circle are together equal to two right angles. For the three is of the A ABC, namely ABC, BCA, and CAB, are together equal to two right angles, (Prop.... | |
 | Euclides - 1848 - 52 pages
...THEOREM. The angles in the same segment of a circle are equal to one another. PROP. XXII. THEOREM. The opposite angles of any quadrilateral figure inscribed...are together equal to two right angles. PROP. XXIII. THEOREM. Upon the same straight line, and upon the same side of it, there cannot be two similar segments... | |
 | Euclid, Thomas Tate - 1849 - 120 pages
...But if the segment BAED be not greater than a semicircle, let BAD, BED be angles in it; these also AE PROP. XXII. THEOR. The opposite angles of any quadrilateral...a circle, are together equal to two right angles. LetABCobe a quadrilateral figure in the circle ABCD; any two of its opposite angles are together equal... | |
| |
The opposite angles of any quadrilateral figure inscribed in a circle, are together equal to two right angles. 
