 | 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... | |
 | 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... | |
 | George Roberts Perkins - Geometry - 1856 - 460 pages
...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 - Conic sections - 1857 - 242 pages
...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 - Conic sections - 1858 - 256 pages
...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 - Geometry - 1860 - 470 pages
...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 - Geometry - 1862 - 532 pages
...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 - Geometry - 1862 - 518 pages
...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... | |
 | Adrien Marie Legendre - Geometry - 1863 - 464 pages
...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... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...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... | |
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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. 
