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" The angles in the same segment of a circle are equal to one another. "
The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... - Page 81
by Euclid, Robert Simson - 1829 - 516 pages
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A Treatise on the Principles and Practice of Levelling, Showing Its ...

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...
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Examination papers used at the examinations for direct commissions [&c.].

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...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

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...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

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...
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Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

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...
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Examination papers used at the examination of candidates for appointment to ...

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...
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Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ...

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...
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Euclid's Elements of geometry, books i. ii. iii. iv

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...
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The school Euclid: comprising the first four books, by A.K. Isbister

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....
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The elements of plane geometry; or, The first six books of Euclid, ed. by W ...

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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