 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.  The Elements of Geometry - Page 342by Webster Wells - 1894 - 378 pagesFull view - About this book
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...hemisphere, four 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
...hemisphere, four 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... | |
 | 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
...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 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... | |
 | Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
...hemisphere, four make a hemisphere, and eight the entire surface of a sphere. PROPOS1TION XV. THEOREM. The surface of a lune is to the surface of the sphere, as the angle of the lune, to foi\c right angles ; or, as the arc which measures that angle, to the circumference. Let AMBN be... | |
 | Elias Loomis - Conic sections - 1858 - 256 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. 1. On equal spheres, two lunes are to each other as the angles included... | |
 | 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 - 518 pages
...all other respects 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 - Geometry - 1861 - 638 pages
...other respects the demonstration would be the same. PROPOSITION XVIII. — THEOREM. 558. T/ie 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... | |
 | Benjamin Greenleaf - Geometry - 1862 - 532 pages
...respects 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... | |
| |
