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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
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Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

Nathan Scholfield - 1845 - 896 pages
...sum of the triangles AOC, BOD is equivalent to the lune OBNDO, whose angle is BOD. PROPOSITION XXII. 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. Let ABC be the proposed...
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Elements of Geometry: With Practical Applications ...

George Roberts Perkins - Geometry - 1847 - 308 pages
...BOD is equal to the lune OBNDO whose angle is BOD. Y PROPOSITION XXXV. THEOREM. The surface of any spherical triangle is measured by the excess of the sum of its three angles above two right angles. Let ABC be the proposed triangle : produce its sides till they meet...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1849 - 252 pages
...is equivalent to the lune whose angle is CBE. Therefore, if two great circles, &c. PROPOSITION XX. THEOREM. The surface of a spherical triangle is measured by the excess of the sum of its angles above two right angles, multiplied by the quadrantal triangle. Let ABC be any spherical triangle...
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Elements of Geometry: With, Practical Applications

George Roberts Perkins - Geometry - 1850 - 332 pages
...AOC, BOD is equal to the lune OBNDO whose angle is BOD. PROPOSITION XXXV. THEOREM. The surface of any spherical triangle is measured by the excess of the sum of its three angles above two right-angles. Let ABC be the proposed triangle : produce its sides till they meet...
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A Treatise on Plane and Spherical Trigonometry

William Chauvenet - 1852 - 268 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 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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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1856 - 460 pages
...triangles AOC, BOD is equal to the lune OBKDO. whose angle is BOD. THEOREM XIX. The surface of any spherical triangle is measured by the excess of the sum of its three angles above two right angles. Let ABC be the proposed triangle : produce its sides till they meet...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1858 - 234 pages
...is equivalen-t to the lune whose angle is CBE. Therefore, if two great circles, &c. PROPOSITION XX. THEOREM. The surface of a spherical triangle is measured by the excess of the sum of its angles above two right angles, multiplied by the quadrantal triangle. Let ABC be any spherical triangle...
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Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous ...

Horatio Nelson Robinson - Geometry - 1860 - 453 pages
...equal spheres, are to each other as the angles of their rear ective lunes. PROPOSITION XVI. The area of a spherical triangle is measured by the excess of the sum of its angles over two right angles, multiplied by the tri-rectangular .triangle. SPHERICAL GEOMETRY. hence...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1861 - 244 pages
...equivalent to the lune whose angle is CBE. Therefore, if two great circles, &c. PROPOSITION XX , THEOEEM. The surface of a spherical triangle is measured by the excess of the sum of its angles above two right angles, multiplied by the quadrantal triangle. Let ABC be any spherical triangle...
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Military Schools and Courses of Instruction in the Science and Art of War ...

Henry Barnard - Military education - 1862 - 399 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...
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