 | 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... | |
 | 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... | |
 | George Roberts Perkins - 1856 - 460 σελίδες
...difference between a hemisphere and the former triangle. THEOREM XvI. The surface of a lune is to the entire 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 the circumference. Suppose, in the first place,... | |
 | Elias Loomis - 1857 - 242 σελίδες
...angle ABC. Therefore, in a spherical triangle, &c. PROPOSITION XVIII. THEOREM. The area of a lune is to the surface of the sphere, as the angle of the lune is to four right angles. Let ADBB be a lune, upon a sphere whose center is C, and the diameter AB ; then will the area of the... | |
 | Elias Loomis - 1858 - 256 σελίδες
...angle ABC. Therefore, in a spherical triangle, &c. PROPOSITION XVIII. THEOREM. The area of a lune is to the surface of the sphere, as the angle of the lune is to four right angles. Let ADBE be a lune, upon a sphere whose center is C, and the diameter AB ; then will the area of the... | |
 | Horatio Nelson Robinson - 1860 - 470 σελίδες
...equivalent to the lune DCHAD, whose angle is ADC. PROPOSITION XV. TJu 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 that angle is to the circumference of a great circle. 'LetABFCA be... | |
 | Benjamin Greenleaf - 1862 - 532 σελίδες
...the demonstration would be the same. PROPOSITION XVIII. — THEOREM. 558. The area of a lunc is to the surface of the sphere as the angle of the lune is to four right angles, or as the arc which measures that, angle is to the circumference. Let А С В D be a lunc upon a sphere... | |
 | Benjamin Greenleaf - 1862 - 518 σελίδες
...the demonstration would be the same. PROPOSITION XVIII. — THEOREM. 558. The area of a lune is to the surface of the sphere as the angle of the lune is to four right angles, or as the arc which measures that angle is to the circumference. Let ACBD be a luno upon a sphere whose... | |
 | Benjamin Greenleaf - 1863 - 504 σελίδες
...the demonstration would be the same. PROPOSITION XVIII. — THEOREM. 558. The area of a lune is to the surface of the sphere as the angle of the lune is to four right angles, or as the arc which measures that angle is to the circumference. Let ACBD be a lune upon a sphere whose... | |
 | Adrien Marie Legendre - 1863 - 464 σελίδες
...analogous to that employed in Book IV., Proposition III. Hence, in all cases, the area of a lune is to the surface of the sphere, as the angle of the lune is to four right angles, or as the arc which measures that angle is to the circumference of a great circle ; which was to be... | |
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The area of a lune is to the area of the surface of the sphere as the angle of the lune is to four right angles. 
