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

John Playfair - Circle-squaring - 1819 - 350 pages
...double of the remaining angle BAC. Therefore the angle at the centre, &c. Q, ED PROP. XXI. 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 centre, and the angle BAD at the...
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Rational Amusement for Winter Evenings, Or, A Collection of Above 200 ...

John Jackson (Private teacher of the mathematics.) - Geographical recreations - 1821 - 140 pages
...make up the whole circle. The above construction evidently depends upon Euclid, III. 21 ; viz, ."The angles in the same segment of a circle are equal to one another.'' 33. See plate III. Jig. 24. Suppose A, B, and C, the three given points. With the centre A, aźd radius...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 1046 pages
...the remaining angle BDC. Therefore the angle at the centre, &c. QED Proposition XXI. Tlieorem. The angles in the same segment of a circle are equal to...The angles BAD, BED are equal to one another. Take Fj the centre of the circle ABCD : And first, let the segment BAED be greater than a semicircle, and...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 546 pages
...centre, 8tc. QED PROP. XXI. THEOR. The angles in the same segment of a circle are effual to See None another. Let ABCD be a circle, and BAD, BED angles in the same segmentBAED : the angles BAD, BED shall be equal to one another. First, let the segment BAED be greater...
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Elements of Geometry: With Notes

John Radford Young - Euclid's Elements - 1827 - 228 pages
...propositions, has rendered it necessary that he should, in the succeeding proposition, demonstrate that " The angles in the same segment of a circle are equal to one another," a proposition which presented two cases requiring separate consideration. It was absolutely necessary...
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - Geometry - 1829 - 210 pages
...B PROPOSITION XXL THEOREM. The angles at the circumference of a circle, standing on the same arch, are equal to one another. Let ABCD be a circle, and BAD, BED, angles at the circumference, standing on the same arch BC D ; the angles BAD, BED are equal to each other....
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - Geometry - 1830 - 584 pages
...conversely ; also, any angles at the circumference are as the arcs upon which they stand cor. 86 (g) Angles in the same segment of a circle are equal to one another 86 (A) The angle in a semicircle is л right angle ; the angle in a segment, which is greater than...
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A Collection of Cambridge Mathematical Examination Papers: Papers in the ...

John Martin Frederick Wright - Astronomy - 1831 - 282 pages
...a right angle. 9. One circumference of a circle cannot cut another in more than two points. 10. The angles in the same segment of a circle are equal to one another. 11. Inscribe a circle in a given triangle. 12. Ratios that are the same to the same ratio, are the...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Euclid's Elements - 1832 - 358 pages
...double of the remaining angle BAC. Therefore the angle at the centre, &c. QED PROP. XXI. THEOR. The angles in the same segment of a circle are equal to...ABCD be a circle, and BAD, BED angles in the same sejrment BAED: The angles BAD, BED are equal to one another. Take F the centre of the circle ABCD:...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 pages
...angles in the same segment of a circle are See N. equal to one another. Let ABCD be a circle, and BAD, A BED angles in the same segment BAED: The angles BAD,...: And, first, let the segment BAED be greater than a semicircle, .— and join BF, FD : And because the .O angle BFD is at the centre, and the angle BAD...
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