| 1873 - 164 pages
...triangular pyramid is a third part of a triangular prism of the same base and altitude. 5. Prove that **the sum of the angles of a spherical triangle is greater than two right angles.** 6. Given the radius of a sphere = 2 inches. Compute the volume and convex surface. III. 1. If two planes... | |
| Harvard University - 1876 - 554 pages
...opposite to it in the other. 8. Any side of a spherical triangle is less than the sum of the other two. 9. **The sum of the angles of a spherical triangle is greater than two** and less than six right angles. 10. The volume of a spherical pyramid is equal to the area of its base... | |
| Elias Loomis - Geometry - 1877 - 458 pages
...angle BAC is greater than the angle ABC. Therefore, in a spherical triangle, etc. PROPOSITION XVII. **THEOREM. The sum of the angles of a spherical triangle is greater than two,** and less than six right angles. Let A, B, and C be the angles of a spherical triangle. The arcs which... | |
| George Albert Wentworth - Geometry - 1877 - 442 pages
...relations polar triangles are often called supplemental triangles. PROPOSITION XVIII. ТНЕOДЕМ. 732. **The sum of the angles of a spherical triangle is greater than two,** and less than six, right angles. Let ABC be a spherical triangle. We are to prove ZA + ZB + ZC greater... | |
| William Frothingham Bradbury - Geometry - 1877 - 262 pages
...theorem AC <^ AB, which is also contrary to the hypothesis. Hence the angle ABC>C. THEOREM XV. 37 1 **The sum of the angles of a spherical triangle is greater than two,** and less than six, right angles. The sum of the arcs which measure the angles of a spherical triangle... | |
| John Charles Snowball - Trigonometry - 1880 - 256 pages
...В) < \тг. .... COR. 4. a', V, c', being the sides of the polar triangle, . + BC; o?,A + BC<v. 21. **The sum of the angles of a spherical triangle is greater than two right angles,** and less than six, Let А, Б, О be the, angles, and а, Ъ, с the sides, of a triangle; А', В',... | |
| William Frothingham Bradbury - Geometry - 1880 - 260 pages
...theorem AC <^ AB, which is also contrary to the hypothesis. Hence the angle ABC>C. THEOREM XV. 37i **The sum of the angles of a spherical triangle is greater than two,** and less than six, right angles. The sum of the arcs which measure the angles of a spherical triangle... | |
| Elias Loomis - Geometry - 1880 - 452 pages
...is greater than the angle ABC. Therefore, in a spherical triangle, etc. PROPOSITION XVII. THEOEEJI. **The sum of the angles of a spherical triangle is greater than two,** and less than six right angles. Let A, B, and C be the angles of a spherical triangle. The arcs which... | |
| Isaac Sharpless - Geometry - 1882 - 292 pages
...spherical polygon of any number of sides, is less than the circumference of a great circle. Proposition 16. **Theorem. — The sum of the angles of a spherical triangle is greater than two,** and less than six right angles. For an angle of a triangle, together with the opposite side of the... | |
| Webster Wells - Trigonometry - 1883 - 234 pages
...spherical triangle is less than the circumference of a great circle ; that is, less than 360°. (/). **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... | |
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