| 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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