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THEOREM. The surface of a spherical triangle is measured by the excess of the sum of its three angles above two right angles, multiplied by the tri-rectangular triangle.
First Part of an Elementary Treatise on Spherical Trigonometry - Page 69
by Benjamin Peirce - 1836 - 71 pages

## The American Journal of Education, Volume 12

Education - 1862
...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...

## Military Schools and Courses of Instruction in the Science and Art ..., Part 1

...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...

## Catalogue - Harvard University

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...

## Treatise on Levelling, Topography and Higher Surveying

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...

## Catalogue - Harvard University

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...

## Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Geometry - 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...

## A Treatise on Plane and Spherical Trigonometry

William Chauvenet - Trigonometry - 1879 - 256 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...

## Harvard Examination Papers

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...