 | Webster Wells - Trigonometry - 1896 - 236 pages
...opposite the greater side. 3. The sum of the sides of a spherical triangle is less than 360°. 80 4. The sum of the angles of a spherical triangle is greater than 180°, and less than 540°. 5. If A'B'C' is the polar triangle of ABC, that is, if A, B, and С are... | |
 | George Albert Wentworth - Mathematics - 1896 - 68 pages
...two polar triangles each angle of the one is the supplement of the opposite side in the other. 737. The sum of the angles of a spherical triangle is greater than 180° and less than 540°. 741. In a bi-rectangular spherical triangle the sides opposite the right... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 574 pages
...AB and AC. In a similar manner the remaining relations are proved. QED PROPOSITION XXX. THEOREM 8Y8. The sum of the angles of a spherical triangle is greater than two, and less than six, right angles. GIVEN the spherical triangle ABC. Denote its angles by A, B, C, and the sides opposite in the polar... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1897 - 374 pages
...a similar manner the remaining relations are proved. QED PROPOSITION XVIII. THEOREM 7 89* The s1nn of the angles of a spherical triangle is greater than two, and less than six, right angles. GIVEN the spherical triangle ABC. Denote its angles by A, B, C, and the sides opposite in the polar... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1897 - 376 pages
...In a similar manner the remaining relations are proved. QED PROPOSITION XVIII. THEOREM 780. The sion of the angles of a spherical triangle is greater than two, and less than six, right angles. GIVEN the spherical triangle ABC. Denote its angles by A,B, C, and the sides opposite in the polar... | |
 | Yale University - 1898 - 212 pages
...perpendicular to a third plane, their line of intersection is also perpendicular to that third plane. 3. The sum of the angles of a spherical triangle is greater than two, and less than six, right angles. 4. Calculate the surface and volume of a sphere whose radius is one foot, to four decimal places. 5.... | |
 | Mathematics - 1898 - 228 pages
...perpendicular to a third plane, their line of intersection is also perpendicular to that third plane. 3. The sum of the angles of a spherical triangle is greater than two, and less than six, right angles. 4. Calculate the surface and volume of a sphere whose radius is one foot, to four decimal places. 5.... | |
 | James Howard Gore - Geometry - 1898 - 232 pages
...mutually equilateral, their polar triangles are mutually equiangular. PROPOSITION V. THEOREM. 516. The sum of the angles of a spherical triangle is greater than two, and less than six, right angles. Let ABC be any spherical triangle. To prove that vl + JB+C'>180°<540 0 . Let A'B'C ' be the polar... | |
 | James William Nicholson - Trigonometry - 1898 - 204 pages
...lies opposite the greater side. 3. The sum of the sides of a spherical triangle is less than 360°. 4. The sum of the angles of a spherical triangle is greater than 180°, and less than 540°. 5. If A'B'C' is the polar triangle of ABC, that is, if A, B, and С are... | |
 | Arthur A. Dodd, B. Thomas Chace - Geometry - 1898 - 490 pages
...is the limit of a' + b' + c' ? [Prop. XV.] Can you now demonstrate that the sum of the angles of any spherical triangle is greater than two and less than six right angles. 659. Cor. How many right ,angles may a spherical triangle have? how many obtuse angles? 660. A bireclangular... | |
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The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC... 
