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Books Books 1 - 10 of 85 on THEOREM. In the same circle, or in equal circles, equal arcs are subtended by equal....  
" THEOREM. In the same circle, or in equal circles, equal arcs are subtended by equal chords ; and, conversely, equal chords subtend equal arcs. "
Elements of Geometry and Trigonometry: With Notes - Page 24
by Adrien Marie Legendre - 1822 - 367 pages
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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...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - 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...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - 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

Adrien Marie Legendre - 1825 - 224 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 Upon the Inductive Method

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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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - Geometry - 1830 - 272 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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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 359 pages
...drawn from the same point to the same straight line, which is impossible (Book I. Prop. XV. Cor. 2.). PROPOSITION IV. THEOREM. In the same circle, or in...and, conversely, equal chords subtend equal arcs. Kate. When reference is made from one proposition to another, in th ! Book, the number of the proposition...
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Elements of geometry and trigonometry

Adrien Marie Legendre - Geometry - 1837 - 359 pages
...same straight line, winch is impossible (Book I. Prop. XV. Cr. 2.). PROPOSITION IV. THEOREM. In ihe same circle, or in equal circles, equal arcs are subtended...; and, conversely, equal chords subtend equal arcs Note. When reference is made from one proposition to another, in th Mine Book, the number of the...
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1837 - 159 pages
...obtuse angle ; for it has for its measure the half of an arc greater than a semicircumference. 111. Theorem. In the same circle, or in equal circles, equal arcs are subtended by equal chords. Demonstration. Let the arc AB (fig. 52) be equal to ihe arc BC. ' Join AC; and, in the triangle ABC,...
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