 | Euclid - 1835 - 540 pages
...semicircle ; and the angles in it BAG, BEC are equal, by the first case : For the same reason, because CBED is greater than a semicircle, the angles CAD, CED...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... | |
 | Robert Simson - Trigonometry - 1835 - 544 pages
...semicircle ; and the angles in it B AC, BEC are equal, by the first case : For the same reason, because CBED is greater than a semicircle, the angles CAD, CED...XXII. THEOR. The opposite angles of any quadrilateral Jiyure described in a circle, are together equal to two right angles. Let ABCD be a quadrilateral figure... | |
 | John Playfair - Euclid's Elements - 1835 - 336 pages
...semicircle ; and the angles in it, BAC, EEC are equal, by the first case : For the same reason, because CBED is greater than a semicircle, the angles CAD, CED...the whole angle BAD is equal to the whole angle BED. PROP. XXII. THEOR. The opposite angles of any quadrilateral figure inscribed in a circle, are together... | |
 | John Playfair - Geometry - 1836 - 148 pages
...semicircle ; and the angles in it, BAC, BEC are equal, by the first case ; for the same reason, because CBED is greater than a semicircle, the angles CAD, CED...Wherefore the angles in the same segment, &c. QED COR. Segments of circles which contain equal angles are similar. PROP. XIV. THEOR. The opposite angles... | |
 | John Playfair - Euclid's Elements - 1836 - 488 pages
...; and the angles in it, ' BAC, BEC are equal, by the first case: For the same reason, because CBED is greater than a semicircle, the angles CAD, CED...therefore the whole angle BAD is equal to the whole anglo BED. Wherefore the angles in the same segment, &c, QED T--X i • '" • PROP. XXI L THEOR. The... | |
 | Mathematics - 1836 - 366 pages
...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 - Euclid's Elements - 1837 - 332 pages
...semicircle ; and the angles in it, BAG, EEC are equal, by the first case : for the same reason, because CBED is greater than a semicircle, the angles CAD, CED...the whole angle BAD is equal to the whole angle BED. PROP. XXII. THEOR. The opposite angles of any quadrilateral figure described in a circle, are together... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...semicircle ; and the angles in it BAG, BEC, are equal, by the first case. For the same reason, because CBED is greater than a ' semicircle, the angles CAD, CED,...the whole angle BAD is equal to the whole angle BED. PROPOSITION XXII. THEOREM. The opposite angles of any quadrilateral figure described in a circle, are... | |
 | 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... | |
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CBED is greater than a semicircle, the angles CAD, CED are equal : therefore the whole angle BAD is, equal to the whole angle BED. 
