 | Adrien Marie Legendre - Geometry - 1819 - 574 pages
...plane AE and in the plane AD (354) ; therefore it is their common intersection AP. I THEOREM. 356. If a solid angle is formed by three plane angles, the sum of either two of these ang'es will be greater than the third. Demonstration. We need consider only the... | |
 | Adrien Marie Legendre - Geometry - 1822 - 394 pages
...plane AD (19. V. Cor.) ; therefore it is their common intersection AP. PROPOSITION XXI. THEOREM. If a solid angle is formed by three plane angles, the sum of any two of these angles -wul be greater than the third. The proposition requires demonstration only when the plane... | |
 | Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...plane AB and in the plane AD (354) ; therefore it is their common intersection AP, THEOREM. 356. If a solid angle is formed by three plane angles, the sum of either two of these angles will be greater than the third. Demonstration. We need consider only the... | |
 | Adrien Marie Legendre - Geometry - 1825 - 276 pages
...plane AB and in the plane AD (354) ; therefore it is their common intersection AP. • THEOREM. 356. If a solid angle is formed by three plane angles, the sum of either two of these angles will be greater than the third. Demonstration. We need consider only the... | |
 | Adrien Marie Legendre - Geometry - 1836 - 394 pages
...AD (Prop. XVII. Cor.) ; therefore it is theii common intersection AP. PROPOSITION XIX. THEOREM. If a solid angle is formed by three plane angles, the sum of any two of these angles will be greater than the third. The proposition requires demonstration only when the plane... | |
 | Adrien Marie Legendre - Geometry - 1837 - 376 pages
...AD (Prop. XVII. Cor.) ; therefore it »s theii common intersection AP. PROPOSITION XIX. THEOREM. Jfa solid angle is formed by three plane angles, the sum of any two of these angles will be greater than the third. The proposition requires demonstration only when the plane... | |
 | Benjamin Peirce - Geometry - 1837 - 216 pages
...the planes, is called the vertex of the angle. Solid Angle formed by three Planes. 337. Theorem. If a solid angle is formed by three plane angles, the sum of either two of these angles is greater than the third. Demonstration. Let S (fig. 159) be a solid angle... | |
 | Adrien Marie Legendre - Geometry - 1841 - 288 pages
...plane AB and in the plane AD (354) ; therefore it is their common intersection AP. THEOREM. 356. If a solid angle is formed by three plane angles, the sum of either two of these angles will be greater than the third. Demonstration. We need consider only the... | |
 | Cambridge univ, exam. papers - 1843 - 50 pages
...limitation is there to the alternation of a geometrical proportion ? 2. If a solid angle be contained by three plane angles, the sum of any two of them is greater than the third. 3. If an integer be prime to two other integers, it is prime to their product. Shew that an integer... | |
 | James Bates Thomson - Geometry - 1844 - 268 pages
...plane, their common intersection is perpendicular to that third plane. PROPOSITION XIX. THEOREM. If a solid angle is formed by three plane angles, the sum of any two of these angles will be greater than the third. Suppose the solid angle S to be formed by three plane... | |
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But when a solid angle is formed by three plane angles, the sum of any two of them is greater than the third (Prop. 
