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" In the same circle, or in equal circles, equal arcs are subtended by equal chords ; and, conversely, equal chords subtend equal arcs. "
Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ... - Page 56
by Nathan Scholfield - 1845
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1819 - 208 pages
...a given point to the same straight line, which is impossible (54). -. ' THEOREM. Fig;. 50. 102. In the same circle, or in equal circles, equal arcs are subtended by equal c/wrds, and conversely, equal chords subtend equal arcs. Demonstration. The radius AC (Jig. 50) being...
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1822 - 367 pages
...straight lines drawn from the same point to the same straight line, which is impossible (Prop. 16. I.). PROPOSITION IV. THEOREM. In the same circle, or in...ENG ; then the chord AD will be equal to the chord EG. plied exactly to the semicircle ENGF, and the curve line AMDB will coincide entirely with the curve...
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Elements of Geometry

Adrien Marie Legendre - 1825 - 574 pages
...lines drawn from a given point to the same straight line. which is impossible (54). THEOREM. 102. In the same circle, or in equal circles, equal arcs are...chords, and conversely, equal chords subtend equal arcs. Fig. so. Demonstration. The radius AC (fig. 50) being equal to the radius EO, and the arc AMD equal...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1825 - 224 pages
...lines drawn from a given point to the same straight line, which is impossible (54). THEOREM. 7 102. In the same circle, or in equal circles, equal arcs are...chords, and conversely, equal chords subtend equal arcs. Fig. 50. Demonstration. The radius AC (fig. 50) being equal to the radius 0, and the arc AMD equal...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1825 - 224 pages
...lines drawn from a given point to the same straight lin which is impossible (54). THEOREM. 102. In the same circle, or in equal circles, equal arcs are...chords, and conversely, equal chords subtend equal arcs. .Fig. 50. Demonstration. The radius AC (Jig. 50) being equal to the radius 0, and the arc AMD equal...
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1828 - 316 pages
...drawn from the same point to the same straight line, which is impossible (54.). THEOREM. Ll 102. In the same circle, or in equal circles, equal arcs are...and, conversely, equal chords subtend equal arcs. v If the radii AC, EO, are equal, and the arcs AMD, ENG ; then the chord AD will be equal to the chord...
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Elements of Geometry Upon the Inductive Method: To which is Added an ...

James Hayward - Geometry - 1829 - 172 pages
...equal angks at the centre are measured by equal arcs ; and equal arcs subtend equal angles. (2). In the same circle, or in equal circles, equal arcs are subtended by equal chords ; and when, in the same circle, the chord. are equal, the arcs are equal. As the triangle would not be changed...
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1830 - 344 pages
...lines drawn from the same point to the same straight line, which is impossible (54.). THEOREM. 103. In the same circle, or in equal circles, equal arcs, are subtended by equal chorda ; and, conversely, equal chords subtend equal arcs. If the radii AC, EO, are equal, and the...
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - Geometry - 1830 - 584 pages
...another. And, in like manner, the converse. Therefore, &c. Cor. 1. (Eue. iii. 28 and 29.) In the same or in equal circles, equal arcs are subtended by equal chords ; and conversely (11. Cor.). Cor. 2. By a similar demonstration it may be shown that in the same or in equal circles,...
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Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

Mathematics - 1835
...another. And, in like manner, the converse. Therefore, &c. Cor. 1. (Eue. iii. 28 and 29.) In the same or in equal circles, equal arcs are subtended by equal chords ; and conversely (11. Cor.). Cor. 2. By a similar demonstration it may be shown that in the same or in equal circles,...
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