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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. "
SYLLABUS OF PLANE GEOMETRY - Side 28
1876
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Elements of Geometry

Adrien Marie Legendre - 1819 - 208 sider
...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 - 1822 - 367 sider
...same point to the same straight line, which is impossible (Prop. 16. I.). PROPOSITION IV. THEOREM. In the same circle, or in equal circles, equal arcs are subtended by equal chords ; and, conversely, equal chords subtend equal arcs. If the radii AC, EO are equal, and the arcs AMD, ENG ;...
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Elements of Geometry

Adrien Marie Legendre - 1825 - 224 sider
...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 subtended by equal chords, and conversely, equal chords subtend equal arcs. .Fig. 50. Demonstration. The radius AC (Jig. 50) being...
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Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - 1825 - 224 sider
...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 subtended by equal chords, and conversely, equal chords subtend equal arcs. Fig. 50. Demonstration. The radius AC (fig. 50) being...
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Elements of Geometry

Adrien Marie Legendre - 1825 - 224 sider
...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 subtended by equal chords, and conversely, equal chords subtend equal arcs. Fig. so. Demonstration. The radius AC (fig. 50) being...
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Elements of Geometry Upon the Inductive Method: To which is Added an ...

James Hayward - 1829 - 172 sider
...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 - 1830 - 316 sider
...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 - 1830 - 272 sider
...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...
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Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

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...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - 1836 - 359 sider
...the same straight line, which is impossible (Book I. Prop. XV. Cor. 2.). PROPOSITION IV. THEOREM. In the same circle, or in equal circles, equal arcs are subtended by equal chords ; and, conversely, equal chords subtend equal arcs. Kate. When reference is made from one proposition to another,...
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