| Education - 1862 - 752 pages
...following enunciations: "A dihedral angle is measured by the plane angle included between its sides;" **"The surface of a spherical triangle is measured by the excess of the sum of its three** angles above two right angles," etc.; enunciations which have no meaning in themselves, and from which... | |
| Henry Barnard - Military education - 1862 - 412 pages
...following enunciations: " A dihedral angle is measured by the plane angle included between its sides;" **"The surface of a spherical triangle is measured by the excess of the sum of its three** angles above two right angles," etc.; enunciations which have no meaning in themselves, and from which... | |
| Harvard University - 1873 - 732 pages
...to the base, what is the ratio of the volume above to that below the cutting plane ? 9. Prove that **the surface of a spherical triangle is measured by the excess of the sum of its** angles over 180°. 10. The slant height of a right cone is 3 ; the radius of the base is j. Show that... | |
| William Mitchell Gillespie - Surveying - 1875 - 204 pages
...correct sum and correction should be. (244.) The true spherical excess is found by this principle : " **The surface of a spherical triangle is measured by the excess • of** its angles above two right angles multiplied by the trirectangular triangle." ' Hence the surfaces... | |
| Harvard University - 1876 - 554 pages
...are equiangular with respect to each other, they are also equilateral with respect to each other. 6. **The surface of a spherical triangle is measured by the excess of the sum of its three** angles over two right angles. Prove. 7. Given that the area of the surface, generated by a straight... | |
| Elias Loomis - Conic sections - 1877 - 458 pages
...the lune whose angle is CBE. Therefore, if two great circles, etc. PROPOSITION XX. THEOREM. The area **of a spherical triangle is measured by the excess of the sum of its** angles above two right angles multiplied by the tri-vectangular triangle. Let ABC be any spherical... | |
| William Chauvenet - Trigonometry - 1879 - 266 pages
...spherical triangle, to compute the area. This problem is solved in geometry, where it is proved that **the surface of a spherical triangle is measured by the excess of the sum of** jts three angles over two right angles, by which is meant, that the area is as many times the area... | |
| Robert Fowler Leighton - 1880 - 428 pages
...have altitudes of six and eight feet. Give the ratio of their surfaces, and also of their volumes. 5. **The surface of a spherical triangle is measured by the excess of the sum of its three** angles over two right angles. ANALYTIC GEOMETKY. 1. PEOVE the formula for the tangent of the angle... | |
| Charles Scott Venable - 1881 - 380 pages
...... , . — 4T, and conCOR. 1. Making T = 1, we have ABC =A + B + C— 2. Hence we sometimes say the **spherical triangle is measured by the excess of the sum of its** angles abtwi two right angles. As many right angles as there are in this measure, just so many tri-rectangular... | |
| William Chauvenet - Geometry - 1896 - 274 pages
...spherical triangle, to eomput' the area. This problem is solved in geometry, -where it is proved that **the surface of a spherical triangle is measured by the excess of the sum of its three** angles over two right angles, by which is meant, that the area is as many times the area of the tri-rectangular... | |
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