| Adrien Marie Legendre - Geometry - 1819 - 574 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 - Geometry - 1822 - 394 pages
...from the same point to the same straight line, which is impossible (Prop. 16. I.). PROPOSITION IV. **THEOREM. In the same circle, or in equal circles,...and, conversely, equal chords subtend equal arcs.** If the radii AC, EO are equal, and the arcs AMD, ENG ; then the chord AD will be equal to the chord... | |
| Adrien Marie Legendre - 1825 - 570 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... | |
| Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 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, John Farrar - Geometry - 1825 - 294 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 - Geometry - 1828 - 346 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... | |
| James Hayward - Geometry - 1829 - 218 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 - 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,... | |
| 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... | |
| Mathematics - 1835 - 684 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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