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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 Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1822 - 367 pages
...equivalent to the spherical ungula whose angle is BOD. PROPOSITION XXIII. 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 Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1828 - 346 pages
...AOC, BOD for bases, are together equivalent to the spherical ungula whose angle is BOD. THEOREM. 501. The surface of a 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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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - Geometry - 1830 - 584 pages
...be represented by half 2 A+ 2B + 2C-4R, that is, byA+B + C2 R. And hence, it is commonly said, that the surface of a spherical triangle is measured by the excess of the sum of ils angles above two right angles ; it being understood that the surface of the sphere is measured...
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Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

Mathematics - 1835
...represented by half 2 + 2B+2C-4R, that is, by A + B + C2 R. And hence, it is commonly said, that the surface of a spherical triangle is measured by the excess of the sum of its angles above two right angles ; it being understood that the surface of the sphere is measured by eight...
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First Part of an Elementary Treatise on Spherical Trigonometry

Benjamin Peirce - Spherical trigonometry - 1836 - 92 pages
...and ABC compose the lunary surface ABC A' which is measured by 2 A. Therefore the (890) sum of ABC and DEF is also measured by 2 A. 87. Theorem. The...Let ABC (fig. 10.) be the given triangle. Produce А С to form the circum(892) ference ACA'C', also produce AB and B С to form the semicircumferences...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 359 pages
...BOD, for bases, are together equivalent to the spherical ungula whose angle is BOD. PROPOSITION XX. 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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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1837 - 216 pages
...surface ABCA' which is measured by 2 A. Therefore the sum of ABC and DEF is also measured by 2 A. 468. Theorem. The surface of a spherical triangle is measured by the excess of the sum of its three angles over two right angles, or 180. Demonstration. Let ABC (fig. 190) be the given triangle. Produce...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1837 - 359 pages
...equivalent to the spherical ungula whose angle is BOD. PROPOSITION XX. THEOREM. The surface of a splierical 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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A Series on Elementary and Higher Geometry, Trigonometry, and Mensuration ...

Nathan Scholfield - Conic sections - 1845
...BOD for bases, are together equivalent to the spherical ungula whose angle is BOD. PROPOSITION XXH. 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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Higher Geometry and Trigonometry: Being the Third Part of a Series on ...

Nathan Scholfield - Geometry - 1845 - 506 pages
...sum of the triangles AOC, BOD is equivalent to the lune OBNDO, whose angle is BOD. PBOPOSITION 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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