 | George Roberts Perkins - Geometry - 1850 - 332 pages
...tri-rectangular spherical triangle, or the triangle whose angles are all right, and whose sides are quadrants. Scholium. The spherical ungula bounded by the planes...the whole solid sphere, as the angle A is to four right-angles ; for, the lunes being equal, the spherical ungulas will also be equal; hence two spherical... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...angle of the lune is of one right angle. Scholium. The spherical ungula, bounded by the planes A MB, ANB, is to the whole solid sphere, as the angle A...For, the lunes being equal, the spherical ungulas are also equal ; hence, two spherical ungulas are to each other, as the angles formed by the planes... | |
 | Charles Davies - Geometry - 1854 - 436 pages
...which expression, A represents such a part of unity, as the angle of the lune is of one right angle. Scholium. The spherical ungula, bounded by the planes...For, the lunes being equal, the spherical ungulas are also equal ; hence, two spherical ungulas are to each other, as the angles formed by the planes... | |
 | George Roberts Perkins - Geometry - 1856 - 460 pages
...triangle, or the triangle whose angles are all right, and whose sides are quadrants. ANB, is to the whole sphere, as the angle A is to four right angles ; for, the limes being equal, the spherical ungulas will also be equal ; hence two spherical ungulas are to each... | |
 | Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
...which expression, A represents such a part of unity, as ti.e angle of the lune is of one right angle. ,Scholium. The spherical ungula, bounded by the planes...For, the lunes being equal, the spherical ungulas are also equal ; hence, two spherical ungulas are to each other, as the angles formed by the planes... | |
 | Elias Loomis - Conic sections - 1858 - 256 pages
...The spherical ungula, comprehended by the planes ADB, AEB, is to the entire sphere, as the angle DCE is to four right angles. For the lunes being equal,...the spherical ungulas will also be equal ; hence, in equal spheres, two ungulas are to each other as the angles included between their planes. PROPOSITION... | |
 | George Roberts Perkins - Geometry - 1860 - 472 pages
...triangle whose angles are all right, and whos«ides are quadrants. GEOMETRY. ANT3, is to the whole sphere, as the angle A is to four right angles ; for,...each other as the angles formed, by the planes which bound them. THEOREM XVH. Two symmetrical spherical triangles are equal in surface. Let ABC, DEF be... | |
 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...3. The spherical ungula included by the planes ACB, ADB, is to the whole sphere as the angle D 0 C is to four right angles. For, the lunes being equal,...will also be equal ; hence, two spherical ungulas on the same sphere, or on equal spheres, are to each other as the angles included between their planes.... | |
 | Benjamin Greenleaf - Geometry - 1861 - 638 pages
...3. The spherical ungula included by the planes ACB, ADB, is to the wtelc sphere as the angle D 0 C is to four right angles. For, the lunes being equal,...will also be equal ; hence, two spherical ungulas on the same sphere, or on equal spheres, are to each other as the angles included between their planes.... | |
 | Benjamin Greenleaf - Geometry - 1862 - 532 pages
...spherical úngula included by the planes А С В, ADB, is to the whole sphere as the angle D О С is to four right angles. For, the lunes being equal, the spherical úngulas will also be equal ; hence, two spherical ungidas on the same sphere, or ou equal spheres,... | |
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Scholium. The spherical ungula, bounded by the planes AMB, ANB, is to the whole solid sphere, as the angle A is to four right angles. For, the lunes being equal, the spherical ungulas will also be equal ; hence two spherical ungulas are to each other,... 
