| Frederick Walter Simms - Leveling - 1856 - 258 pages
...as compared with its extent, and is deduced from the well-known theorem, that all angles contained **in the same segment of a circle are equal to one another.*** The method is as follows: — Place a theodolite at B and another at C (figure 5, plate 7), the two... | |
| War office - 1858 - 578 pages
...with twice the rectangle contained by the parts. 4. What is the angle in a segment of a circle ? The **angles in the same segment of a circle are equal to one another.** VOLUNTARY PORTION. 1. Give Euclid's construction for describing an isosceles triangle having each of... | |
| John Playfair - Geometry - 1860 - 334 pages
...remaining angle BDC is double of the remaining angle BAC. PROP. XXI. THEOR. The angles in the sam$ **segment of a circle are equal to one another. Let...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... | |
| Robert Potts - Geometry, Plane - 1860 - 380 pages
...of the remaining angle BAC. Therefore the angle at the center, &c. QED PROPOSITION XXI. THEOREM. The **angles in the same segment of a circle are equal to...circle, and BAD, BED angles in the same segment BAED.** Then the angles BAD, BED shall be equal to one another. First, let the segment BAED be greater than... | |
| Euclides - 1860 - 288 pages
...double of the remaining angle BAC. %* See Appendix — Proposition (c). PltOrOSITIOX XXI. THEOREM. The **angles in the same segment of a circle are equal to one another.** Given a. circle ABCD, and BAD, BED angles in the same segment BAED ; to prove that the angles BAD and... | |
| War office - 1861 - 260 pages
...7. Parallelograms upon the same base and between the same parallels are equal to one another. 8. The **angles in the same segment of a circle are equal to one another.** 9. Inscribe an equilateral and equiangular quindecagon in a given circle. 10. When are two rows of... | |
| Euclides - 1861 - 464 pages
...the centre of the orbit is taken double the angle at the circumference. PИОP. 21.— ТНEOK. The **angles in the same segment of a circle are equal to one another.** Con. 1, Ш. Pet. 1 and 2. DEM. 20, IIL Ax. 7. Ax. 2. EI Hyp. Cone. In 0 ABCD, let BAD, BED be że in... | |
| Euclides - 1862 - 140 pages
...tame segment of a circle are equal to one another. (References— Prop. IIL 1, 20.) Hypothesis.— **Let ABCD be a circle, and BAD, BED, angles in the same segment BAED.** Sequence. — The angles BAD, BED, shall be equal to one another. Case I.— First, let the segment... | |
| Euclides - 1862 - 172 pages
...of the r< malnlng angle BAC. Therefore, the angie at the centre, &c. QED PROP. XXI.— THEOREM. The **angles in the same segment of a circle are equal to one another.** (References — Prop. m. 1, 20.) Let ABCD be a circle, and BAD, BED, angles in the same segment BAED.... | |
| Euclides - 1863 - 122 pages
...&c. QED Pltor. XXI. (THEonEM.)—The angles (BAD and BED) in the same segment of a circle (AB (J LJ) **are equal to one another. Take F, the centre of the circle ABCD** (III. 1), and join BF and I'D.. Next, let the segment BAED be not greater than a semicircle. Because... | |
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