 | Benjamin Peirce - 1837 - 216 pages
...spherical sector. The base of the sector is the zone generated by the arc DF, or FH. 438. Theorem. Either side of a spherical triangle is less than the sum of the other two. Demonstration. From the centre O (fig. 179) of the sphere draw the radii OA, OB, OC to the vertices... | |
 | Adrien Marie Legendre - 1852 - 436 pages
...forming a polyedral angle is less than the sum of the two other angles (B. vi., P. 19); hence, any side of a spherical triangle is less than the sum of the two other sides. PROPOSITION II. THEOREM. The sum of all the sides of any spherical polygon is less... | |
 | Charles Davies - 1854 - 436 pages
...which bound a polyedral angle is less than the sum of the two other angles (B. vi., p. 19); hence, any side of a spherical triangle is less than the sum of the two other sides. PKOPOSITION II. THEOEEM. The sum of all the sides of any spherical polygon is less... | |
 | Benjamin Peirce - 1855 - 184 pages
...spherical sector. The base of the sector is the zone generated by the arc DF¡ or FIL 438. Theorem. Either side of a spherical triangle is less than the sum of the other two. Proof. From the centre O (fig. 179) of the sphere draw the radii OA, OB, OC to the vertices^,... | |
 | Benjamin Peirce - 1855 - 190 pages
...spherical sector. The base of the sector is the zone generated by the arc DF, or FIf. 438. Theorem. Either side of a spherical triangle is less than the sum of the other two. Proof. From the centre O (fig. 179) of the sphere draw the radii Od, OB, OC to the vertices A,... | |
 | Elias Loomis - 1858 - 256 pages
...the angle A to the angle D. Therefore, if two triangles, &c. PROPOSITION VIII. THEOREM. Any side of a triangle is less than the sum of the other two Let ABC be a triangle; any one of its aides is less than the sum of the other two, viz.: the side AB is less than... | |
 | Charles Davies, Adrien Marie Legendre - 1858 - 454 pages
...which bound a polyedral angle is less than the sum of the two other angles (B. VI., p. 19) ; hence, any side of a spherical triangle is less than the sum of the two other sides. PKOPOSITION II. THEOKEM. The sum of all the sides of any spherical polygon is less... | |
 | Elias Loomis - 1860 - 246 pages
...angle A to the angle D. Therefore, if two triangles, &c. PROPOSITION VIII. THEOREM. v Any side of a triangle is less than the sum of the other -two Let ABC be a triangle; any one of its aides is less than the sum of the other two, viz.: the side AB is less than... | |
 | Elias Loomis - 1861 - 254 pages
...the angle A to the angle D. Therefore, if two triangles, &c. PROPOSITION VIII. THEOREM. Any side of a triangle is less than the sum of the other two Let ABC be a triangle; any one of its sides is less than the sum of the other two, viz.: the side AB is less than... | |
 | Elias Loomis - 1861 - 244 pages
...the angle A to the angle D. Therefore, if two triangles, &c. PROPOSITION VIII. THEOREM. Any side of a triangle is less than the sum of the other two Let ABC be a triangle; any one of its sides is less than the sum of the other two, viz.: the side AB is less than... | |
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Any one side of a spherical triangle is less than the sum of the other two. Let ABC be any spherical triangle, and O the centre of the sphere; 
