| Adrien Marie Legendre - Geometry - 1828 - 346 pages
...same name, and is the difference between a hemisphere and the former triangle. THEOREM. The surface of **a lune is to the surface of the sphere, as the angle of** this lune, is to four right angles, or as the arc which measures that angle, is to the circumference.... | |
| Pierce Morton - Geometry - 1830 - 584 pages
...the proportion which its surface bears to the surface of the sphere. For, since the surface of any **lune is to the surface of the sphere, as the angle of the lune** to four right angles (V. 21.), or as twice its angle to eight right angles ; if the surface of the... | |
| Mathematics - 1835 - 684 pages
...the proportion which its surface bears to the surface of the sphere. For, since the surface of any **lune is to the surface of the sphere, as the angle of the lune** to four right angles (V. 21.), or as twice its angle to eight right angles ; if the surface of the... | |
| Adrien Marie Legendre - Geometry - 1836 - 394 pages
...difference between a hemisphere and the former triangle. PROPOSITION XVII. THEOREM. The surface of **a lune is to the surface of the sphere, as the angle of** this lune, is to four right angles, or as the arc which measures that angle, is to the cwcumferenee.... | |
| Nathan Scholfield - Geometry - 1845 - 506 pages
...the difference between a hemisphere and the former triangle. PROPOSITION XIX. THEOREM. The surface of **a lune is to the surface of the sphere, as the angle of** this lune, is to four right angles, or as the arc which measures that angle, is 'to the circumference.... | |
| Charles William Hackley - Geometry - 1847 - 248 pages
...surface of the sphere would be expressed by the number 8. PROP. xv. The surface of a lune is to the whole **surface of the sphere as the angle of the lune is to four right angles,** or as the arc which measures the angle of the lune is to a circumference. It is evident, from a mere... | |
| Elias Loomis - Conic sections - 1849 - 252 pages
...be expressed in whole numbers, it may be proved, as in Prop. XIV., B. III., that the lune is still **to the surface of the sphere, as the angle of the lune** to four right angles. Cor. 2. We have seen that the entire surface of the sphere is equal to eight... | |
| George Roberts Perkins - Geometry - 1850 - 332 pages
...hemisphere and the former triangle. PROPOSITION XXXII. THEOREM. The surface of a lune is to the entire **surface of the sphere, as the angle of the lune is to four** rightangles, or as the arc which measures the angle of the lune is to the circumference. Suppose, in... | |
| Adrien Marie Legendre - Geometry - 1852 - 436 pages
...make a hemisphere, and eight the entire surface of a sphere. PROPOSITION XV. THEOEEM. The surface of **a lune is to the surface of the sphere, as the angle of the lune,** to four right angles ; or, as the arc which measures that angle, to the circumference. Let AMBN be... | |
| Charles Davies - Geometry - 1854 - 436 pages
...make a hemisphere, and eight the entire surface of a sphere. PROPOSITION XV. THEOREM. The surface of **a lune is to the surface of the sphere, as the angle of the lune,** to four right angles ; or, as the arc which measures that angle, to the circumference. Let AMBN be... | |
| |