 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.  Solid Geometry - Page 456by George C. Shutts - 1913Full view - About this book
 | Adrien Marie Legendre - Geometry - 1828 - 346 pages
...triangle which bears the 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
...the same name, and is the 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 - Conic sections - 1845 - 244 pages
...the same name, and is 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.... | |
 | Nathan Scholfield - 1845 - 894 pages
...the same name, and is the difference between a hemisphere and the former triangle. PROPOSITION XIX. THEOREM. The surface of a lune is to the surface of the sphere, at the an^le of this lune, is to four right angles, or as the arc which measures that angle, is to... | |
 | 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... | |
 | Charles Davies - Trigonometry - 1849 - 372 pages
...the same name, and is the 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 anglt of this lune, is to four right angles, or as the arc which measures that angle, is to the circumference.... | |
 | Elias Loomis - Conic sections - 1849 - 252 pages
...greater than the 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 angl e of the lune is to four right angles. Let ADBE be a lune, upon a sphere whose center is C, and... | |
 | 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... | |
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