 | Adrien Marie Legendre - 1828 - 346 σελίδες
...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 - 1830 - 584 σελίδες
...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... | |
 | 1835 - 684 σελίδες
...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 - 1836 - 394 σελίδες
...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 - 1845 - 506 σελίδες
...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 - 1847 - 248 σελίδες
...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 - 1849 - 252 σελίδες
...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 - 1850 - 332 σελίδες
...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 - 1852 - 436 σελίδες
...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 - 1854 - 436 σελίδες
...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... | |
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A lune is to the, surface of the sphere as the angle of the lune is to four right angles. Let... 
