| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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,... | |
| Society for the diffusion of useful knowledge (Great Britain) - 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,... | |
| 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... | |
| Adrien Marie Legendre - Geometry - 1837 - 359 pages
...same straight line, winch is impossible (Book I. Prop. XV. C«r. 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... | |
| 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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