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

Robert Potts - 1868 - 434 pages
...the remaining angle BA C. .. Therefore the angle at the center, &c. QED PROPOSITION XXI. THEOREM. The angles in the same segment of a circle are equal to one another. Let AB CD be a circle, , and BAD, BED angles in the same segment BAED. ' Then the angles BAD, BED shall...
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The Edinburgh university calendar

Edinburgh univ - 1868 - 336 pages
...contained by the whole, and one of the parts, may be equal to the square of the other part. 5. The angles in the same segment of a circle are equal to one another. 6. If a straight line touch a circle, and from the point of contact a straight line be drawn cutting...
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Elementary Geometry, Volume 2

James Maurice Wilson - Geometry - 1868 - 150 pages
...arc of a circle is half of the angle subtended by the same arc at the centre . . . . . . 11 COR. 1. Angles in the same segment of a circle are equal to one another . . . . . . . . . .12 COR. i. If a circle is divided into any two segments by a chord, the angles in...
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Examination Papers for Science Schools and Classes

Great Britain. Education Department. Department of Science and Art - 1869 - 98 pages
...and triangles upon the same base and between the same parallels are equal to one another. (10.) 23 5. Angles in the same segment of a circle are equal to one another. *6. Divide a" — SaV + 3aV — a6 by a3 — 3a?x + Sax* — ar>. (10.) 7. Solve the equations : —...
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A Treatise on the Principles and Practice of Levelling: Showing Its ...

Frederick Walter Simms - Leveling - 1870 - 220 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 e'qual to one another.* The method is as follows : — Place a theodolite at B and another at C, the two terminations of the...
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A TREATISE ON THE PRINCIPLES AND PRACTICE OF LEVELLING

FREDERICK W. SIMMS - 1870 - 174 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 0, the two ter* Euclid, Book III,...
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The Elements of Plane and Solid Geometry

Henry William Watson - Geometry - 1871 - 320 pages
...one, and only one, circumference can be drawn (Bk. II. Prop. 5, Cor.) ; let this be BPC. Because the angles in the same segment of a circle are equal to one another, if any point Q, different from P, be taken in the circumference BPC, the angle BQC will be equal to...
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Mathematical Instruments: Their Construction, Adjustment, Testing ..., Volume 1

John Fry Heather - Drawing instruments - 1871 - 236 pages
...may be accomplished without travelling beyond the limits of the drawing board. By Euclid iii. 36, the angles in the same segment of a circle are equal to one another, and the property demonstrated in this theorem has already been applied in the construction of the centrolinead,...
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The Elements of Plane and Solid Geometry

Henry William Watson - Geometry - 1872 - 326 pages
...the exterior angle is double of either of the interior non-adjacent angles. PROPOSITION u. The angks in the same segment of a circle are equal to one another. Let BAC and BDC be angles in the same segment of the Fig. 12. Fig. 13. A ^ -^ DA First let the segment...
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Elements of geometry, containing the first two (third and fourth ..., Part 2

Euclides - 1872 - 102 pages
...AOB is drawn a flat angle, and in fig. 2, AOB is drawn a reflex angle. PROPOSITION XXI. THEOREM. The angles in the same segment of a circle are equal to one another. Fig. 1. Let BAC, BDCb6 angles in the same segment BADC. Then must L BAG = L .BDC. First, when segment...
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