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 - Page 24by Adrien Marie Legendre - 1825 - 224 pagesFull view - About this book
| Adrien Marie Legendre - Geometry - 1819 - 574 pages
...drawn from 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
...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...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, John Farrar - Geometry - 1825 - 280 pages
...straight 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...The radius AC (fig. 50) being equal to the radius £0, and the arc AMD equal to the arc ENG ; the chord AD will be equal to the chord EG. For, the diameter... | |
| Adrien Marie Legendre - 1825 - 570 pages
...straight 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...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 to the... | |
| Adrien Marie Legendre - Geometry - 1828 - 346 pages
...straight lines 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...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,... | |
| Adrien Marie Legendre - Geometry - 1836 - 394 pages
...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...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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