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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 ... - Side 81
av Euclid, Robert Simson - 1829 - 516 sider
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General Report on Public Instruction in the Bengal Presidency

1863
...alternate angles equal to one another. Trisect (1) a right angle, (2) one-fourth of a right angle. 2. The angles in the same segment of a circle are equal to one another. If two circles cut each other the line joining their centres bisects their common chord ; and the common...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - 1853
...the remaining angle BDC. Therefore the angle at the centre, etc. QE o. PROPOSITION XXI. THEOR. The angles in the same segment of a circle are equal to...the angles BAD, BED are equal to one another. Take (1. in.) F, the centre of the circle ABCD : and, first, let the segment BAED be greater than a semicircle,...
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - 1853 - 147 sider
...XXI. — THEOREM, The angles in tlie same segment of a circle are equal to one anotlier. LET abСd be a circle, and bad, bed angles in the same segment...equal to one another. Take f the centre of the circle ab С d : and, first, let the segment baed be greater than a semicircle, and join bf, fd : and because...
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The synoptical Euclid; being the first four books of Euclid's Elements of ...

Euclides - 1853
...Therefore, the angle at the centre, &c. . QE.D. ' . . ' - PROP. XXI. — THEOREM. The angles in the sapie segment of a circle are equal to one another. Let ABCD be a circle, and BAJ>, BED, angles in the same segment BAED: the angles BAD, BED, are equal to one another. A First,...
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The Elements of Euclid. Books I.-VI.; XI. 1-21 XII. 1-2. A New Text ..., Bok 1

Euclides - 1853
...PROP. XXI. THEOE. The angles in the same segment of a circle shall be equal to one another. Let ABC be a circle, and BAD, BED angles in the same segment BAED. Then the angles BAD, BED shall be equal. There are two cases according as the segment BAED is greater,...
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Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - 1855 - 318 sider
...reason, the angle BFD is double of the angle BED : therefore the angle BAD is equal to the angle BED. Let ABCD be a circle, and BAD, BED angles in the'...BAED : the angles BAD, BED are equal to one another. But, if the segment BAED be not greater than a semicircle, let BAD, BED be angles in it, these also...
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Minutes of the Committee of Council on Education

Great Britain. Committee on Education - 1855
...from a given point, either without or in the circumference, which shall touch a given circle. 9. The angles in the same segment of a circle are equal to one another. 10. If two straight lines cut one another within a circle, the rectangle contained by the segments...
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National Society's Monthly Paper

1855
...from a given point, either without or in the circumference, which shall touch a given circle. 9. The angles in the same segment of a circle are equal to one another; 10. If two straight lines cut one another within a circle, the rectangle contained by the segments...
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Liber Cantabrigiensis, an account of the aids afforded to poor students, the ...

Robert Potts - 1855
...intercepted between the perpendicular let fall upon it from the opposite angle, and the acute angle. 6. The angles in the same segment of a circle are equal to one another. AB and AC are given in position, and BCis of constant length; prove that if PS and PC be drawn making...
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The geometry of the three first books of Euclid, by direct proof from ...

Euclides - 1856
...may be) is double of BAG, the sum or difference of the angles BAT, FAG. LX.— EucLin III. 21. The angles in the same segment of a circle are equal to one another. Let ABCD (Fig. 48) be a circle; BAD, BED angles in the same segment BAE D. The angles BAD, BED are equal. Let...
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