 | Euclides - Euclid's Elements - 1837 - 112 pages
...3. that similarly 2 Z GDB = Z GEB, 4. that :. remaining /_ BEC = 2 remaining Z BDC. PROPOSITION XXI. Theorem. The angles in the same segment of a circle are equal to one another. Steps of the Demonstration to Case ^st, In which the segment is > ^ © . 1. Prove that Z BFD = 2 Z... | |
 | Robert Simson - Geometry - 1838 - 434 pages
...is double of the remaining angle BDC. Therefore the angle at the centre, &c. QED PROP. XXI. THEOR. THE angles in the same segment of a circle are equal...to one another.* Let ABCD be a circle, and BAD, BED AE angles in the same segment BAED : the angles BAD, BED are equal to one another. Take F the centre... | |
 | Euclid - Geometry - 1838 - 470 pages
...double of the remaining angle BDC. Therefore the angle at the centre, &c. ( l. ED PROP. XXI. THEOR. THE angles in the same segment of a circle are equal to one another.* r. Let ABCD be. a circle, and BAD, BED angles in the same segment BAED : the angles BAD, BED are equal... | |
 | Euclides - 1838 - 264 pages
...circumference. PROP. XXI. THEOR. The angles in the same segment of a circle are ejual to one another. Let A BCD be a circle, and BAD, BED angles in the same segment BAED; these angles ahull be equal to one another. Take F the centre of the circle,* draw BF, FD, as also... | |
 | Euclides - 1840 - 82 pages
...circle, is double of the angle at the circumference, standing on 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 figure inscribed in a circle, are together... | |
 | Euclides - Geometry - 1841 - 378 pages
...angle at the centre, &c. QED PROP. XXI. THEOR. The angles in the same segment of a circle are eqv.al to one another. Let ABCD be a circle, and BAD, BED...angles in the same segment BAED: the angles BAD, BED shall be equal to one another. First, let the segment BAED be greater than a semicircle; find F the... | |
 | Euclides - 1842 - 316 pages
...Therefore the angle at the centre, &c. QED for the same EUC. B. III. OF GEOMETRY. PROP. XXI. THEOR. THE angles in the same segment of a circle are equal...same segment BAED: the angles BAD, BED are equal to one another. Take F, the centre of the circle ABCD. and, first, let the segment BAED be greater than... | |
 | John Playfair - Euclid's Elements - 1842 - 332 pages
...the other ; therefore the remaining angle BDC is double of the remaining angle BAC. PROP. XXI. THEOR. The angles in the same segment of a circle are equal...same segment BAED : the' angles BAD, BED are equal to one another. Take F the centre of the circle ABCD : And, first, let the segment BAED be greater than... | |
 | Christian - 1843 - 412 pages
...you here seem to confound it. We know that the whole is greater than its part ; and we know, that all the angles in the same segment of a circle are equal to each other. We have intuition and demonstration as grounds of this knowledge ; but is there no ground... | |
 | Euclid - Geometry - 1845 - 218 pages
...of the remaining angle BDC. Therefore the angle at the centre, &c. QED PROPOSITION XXI. THEOR. — The angles in the same segment of a circle are equal...same segment BAED : the angles BAD, BED are equal to one another. * i. 3. Take* F, the centre of the circle ABCD : and, first, let the segment BAED be greater... | |
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The angles in the same segment of a circle are equal to one another. 
