 | Mathematics - 1835 - 684 pages
...the circumference are as the arcs upon which they stand. (13. and II. 17.) I»EOP. 15. (EUC. Ш. 21.) Angles in the same segment of a circle are equal to one another. For they are halves of the same angle, viz. the angle at the centre which stands upon their common... | |
 | John Playfair - Geometry - 1836 - 148 pages
...double of the remaining angle BDC. Therefore, the angle at the centre, &c. QED PROP. XIII. THEOR. The angles in the same segment of a circle are equal to...; and first, let the segment BAED be greater than a semicircle, and join BF, FD ; and because the angle BFD is at the cantre, and the angle BAD at the... | |
 | John Playfair - Euclid's Elements - 1836 - 488 pages
...the remaining ^cx C angle BAC. Therefore the angle at the centre, &c. Q. E, D PROP, XXI. THEOR. The angles in the same segment of a circle are ^ equal...are equal to one another. Take F the centre of the eircle ABCD: And, first, let the segment BAED be greater than a semicircle, and join BF, FD : And because... | |
 | Mathematics - 1836 - 488 pages
...the circumference, upon the same base, that is, upon the same point of the circumference. XXI. The angles in the same segment of a circle are equal to one another. XXII. The opposite angles of any quadrilateral figure described in a circle, are together equal to... | |
 | John Playfair - Euclid's Elements - 1837 - 332 pages
...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 to...ABCD: And, first, let the segment BAED be greater than a semicircle, and join BF, FD : and because the angle BFD is at the centre, and the angle BAD at the... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...therefore the remaining angle BDC is double of the remaining angle BAG. PROPOSITION XXI. TIIEOREM. The angles in the same segment of a circle are equal to...; and, first, let the segment BAED be greater than a semicircle, and join BF, FD. And because the angle BFD is at the centre, and the angle BAD at the... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...this case is not given in a separate form, its proof is contained in that of either of the others. ANGLES in the same segment of a circle are equal to...circle, and BAD, BED angles in the same segment BAED : these angles are equal. Take (111. 1.) F the centre of the circle ABCD ; and join BF, FD : draw also... | |
 | Euclides - Euclid's Elements - 1837 - 112 pages
...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
...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... | |
 | 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... | |
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The angles in the same segment of a circle are equal to one another. 
