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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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Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

1835
...the circumference are as the arcs upon which they stand. (13. and II. 17.) I»EOP. 15. (EUC. Ш. 21.) Angles in the same segment of a circle are equal to one another. For they are halves of the same angle, viz. the angle at the centre which stands upon their common...
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The Element of Geometry

John Playfair - 1836 - 114 sider
...double of the remaining angle BDC. Therefore, the angle at the centre, &c. QED PROP. XIII. 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 cantre, and the angle BAD at the...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1836 - 311 sider
...the remaining ^cx C angle BAC. Therefore the angle at the centre, &c. Q. E, D PROP, XXI. THEOR. The angles in the same segment of a circle are ^ equal...are equal to one another. Take F the centre of the eircle ABCD: And, first, let the segment BAED be greater than a semicircle, and join BF, FD : And because...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

1836 - 472 sider
...the circumference, upon the same base, that is, upon the same point of the circumference. XXI. The angles in the same segment of a circle are equal to one another. XXII. The opposite angles of any quadrilateral figure described in a circle, are together equal to...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1837 - 318 sider
...other ; therefore the remaining angle BDC is double of the remaining angle BAC. PROP. XXI. THEOR. The angles in the same segment of a circle are equal to...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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Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - 240 sider
...therefore the remaining angle BDC is double of the remaining angle BAG. PROPOSITION XXI. TIIEOREM. 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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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1837 - 390 sider
...this case is not given in a separate form, its proof is contained in that of either of the others. ANGLES in the same segment of a circle are equal to...circle, and BAD, BED angles in the same segment BAED : these angles are equal. Take (111. 1.) F the centre of the circle ABCD ; and join BF, FD : draw also...
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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - 1837 - 88 sider
...similarly 2 Z GDB = Z GEB, 4. that :. remaining /_ BEC = 2 remaining Z BDC. PROPOSITION XXI. Theorem. The angles in the same segment of a circle are equal to one another. Steps of the Demonstration to Case ^st, In which the segment is > ^ © . 1. Prove that Z BFD = 2 Z...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Euclid, Robert Simson - 1838 - 416 sider
...double of the remaining angle BDC. Therefore the angle at the centre, &c. QED PROP. XXI. THEOR. THE angles in the same segment of a circle are equal to one another.* Let ABCD be a circle, and BAD, BED AE angles in the same segment BAED : the angles BAD, BED are equal to one another. Take F the centre...
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838
...circumference. PROP. XXI. THEOR. The angles in the same segment of a circle are ejual to one another. Let A BCD be a circle, and BAD, BED angles in the same segment BAED; these angles ahull be equal to one another. Take F the centre of the circle,* draw BF, FD, as also...
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