 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...BEC. In the same manner, it might be shown that the angles CAD, CED are equal. Therefore (1 ax. 2.) the whole angle BAD is equal to the whole angle BED. Wherefore angles in the same segment, &c. * PROP. XXII. THEOR. THE opposite angles of any quadrilateral figure... | |
 | Robert Simson - Geometry - 1838 - 434 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...BED. Wherefore the angles in the same segment, &c. Q. °ED PROP. XXII. THEOR. THE opposite angles of any quadrilateral figure described in a circle, are... | |
 | Euclides - 1838 - 264 pages
...BAC to BEC. In like manner it may be demonstrated that the angle CAD *i AX is equal to tne "Dgle CED. Therefore* the 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... | |
 | Euclides - 1840 - 82 pages
...the same arch. PROP. 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...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... | |
 | Euclides - Geometry - 1841 - 378 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...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... | |
 | John Playfair - Euclid's Elements - 1842 - 332 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...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... | |
 | Euclid - Geometry - 1845 - 218 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...Wherefore, the angles in the same segment, &c. QED PROPOSITION XXII. THEOR. — The opposite angles of any quadrilateral figure described in a circle,... | |
 | Euclides - 1845 - 546 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,...the whole angle BAD is equal to the whole angle BED. (ax. 2.) Wherefore the angles in the same segment, &c. QED PROPOSITION XXII. THEOREM. The opposite... | |
 | Euclid, James Thomson - Geometry - 1845 - 382 pages
...BkC. In the same manner, it might oe shown that the angles CAD, CED are equal. Therefore (I. ax. 2) the whole angle BAD is equal to the whole angle BED. Wherefore angles, &c.f PROP. XXII. THKOR. — The opposite angles of any quadrilateral figure described in a... | |
 | Euclides - 1846 - 292 pages
...angles in it, BAC, BEC, are equal, by the first case : For the same reason, because the segment CAED is greater than a semicircle, the angles CAD, CED...angle BED. Wherefore, The angles in the same segment ffc, QK l>. PROP. XXII. THEOE. The opposite angles of any quadrilateral fffure inscribed in a circle... | |
| |
CBED is greater than a semicircle, the angles CAD, CED are equal : therefore the whole angle BAD is, equal to the whole angle BED. 
