| Mathematics - 1898 - 208 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... | |
| 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... | |
| 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... | |
| James William Nicholson - Trigonometry - 1898 - 196 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... | |
| Mansfield Merriman - Geodesy - 1899 - 261 pages
...triangle is one included by three arcs of great circles. It is a well-known geometrical theorem that **the sum of the angles of a spherical triangle is greater than two right angles,** and that the excess above two right angles bears the same ratio to a sight angle as the area of the... | |
| William James Milne - Geometry - 1899 - 404 pages
...of the given triangle or any spherical triangle? Express your conclusions in terms of right angles. **Theorem. The sum of the angles of a spherical triangle is greater than two** and less than six right angles. Data: Any spherical triangle, as ABC, ^ whose angles are A, B, and... | |
| Harvard University - Geometry - 1899 - 39 pages
...sides of a convex spherical polygon is less than the circumference of a great circle. THEOREM XVI. **The sum of the angles of a spherical triangle is greater than two,** and less than six, right angles. 28 THEOREM XVIII, If two arcs of great circles intersect on the surface... | |
| Webster Wells - Geometry - 1899 - 178 pages
...+ CD + DA < 360°. (By § 458, sum of AAOE, BOC, COD, and DOA is < 360°.) PROP. XX. THEOREM. 596. **The sum of the angles of a spherical triangle is greater than two,** and less than six, right angles. 341 o' Given A, B, and C the A, expressed in degrees, of spherical... | |
| William James Milne - Geometry - 1899 - 396 pages
...of the given triangle or any spherical triangle? Express your conclusions in terms of right angles. **Theorem. The sum of the angles of a spherical triangle is greater** tlian two and less tlian six right angles. Data : Any spherical triangle, as ABC, whose angles are... | |
| George Albert Wentworth - Geometry, Solid - 1899 - 248 pages
...way all the other relations are proved. QED BOOK VIII. SOLID GEOMETRY. PROPOSITION XV. THEOREM. 795. **The sum of the angles of a spherical triangle is greater than** 180° and less than 540°. Let ABC be a spherical triangle, and let A, B, C denote the values of its... | |
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