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" Scholium. The spherical ungula, bounded by the planes AMB, ANB, is to the whole solid sphere, as the angle A is to four right angles. For, the lunes being equal, the spherical ungulas will also be equal ; hence two spherical ungulas are to each other,... "
Elements of Geometry, After Legendre, with a Selection of Geometrical ... - Page 276
by Charles Scott Venable - 1881
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1819 - 208 pages
...quadrants. 496. Sdiolivm. The spherical wedge comprehended by the planes AMB, jJJVB, is to the entire sphere, as the angle A is to four right angles. For the lunary surfaces being equal, the spherical wedges will also be equal ; therefore two spherical wedges...
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1822 - 367 pages
...spherical triangle, or the triangle whose angles are all right, and whose sides are quadrants. Scltolium. The spherical ungula, bounded by the planes AMB, ANB,...the whole solid sphere, as the angle A is to four rifht angles. For, the lunes being equal, the spherical ungulas will also be equal ; hence two spherical...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1825 - 224 pages
...lunary surfaces being equal, the spherical wedges will also be equal ; therefore two spherical wedges are to each other as the angles formed by the planes which comprehend them. THEOREM. 497. Two symmetrical spherical triangles are equal in surface. Demonstration....
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Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...quadrants. 496. Scholium. The spherical wedge comprehended by the planes AMB, ANB, is to the entire sphere, as the angle A is to four right angles. For the lunary surfaces being equal, the spherical wedges will also be equal ; therefore two spherical wedges...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1825 - 280 pages
...quadrants. 496. Scholium. The spherical wedge comprehended by the planes AMB, ANB, is to the entire sphere, as the angle A is to four right angles. For the lunary surfaces being equal, the spherical wedges will also be equal ; therefore two spherical wedges...
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1828 - 346 pages
...spherical triangle, or the triangle whose angles are all right, and whose sides are quadrants. 496. Scholium. The spherical ungula, bounded by the planes...each other, as the angles formed by the planes which bound them. THEOREM. 497. Two symmetrical spherical triangles are equal in surface. Let ABC, DEF be...
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1830 - 344 pages
...right, and whose sides are quadrants. 496. Scholium. The spherical ungula, bounded by the planes AMI3, ANB, is to the whole solid sphere, as the angle A...each other, as the angles formed by the planes which bound them. THEOREM. \ 497. Two symmetrical spherical triangles are equal in surface. Let ABC, DEF...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 359 pages
...which expression, A represents such a.part of unity, as the angle of the lune is of one right angle. Scholium. The spherical ungula, bounded by the planes...as the angle A is to. four right angles. For, the limes being equal, the spherical ungulas will also be equal ; hence two spherical ungulas are to each...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1837 - 372 pages
...which expression, A represents such a part of unity, as the angle of the lune is of one right angle. Scholium. The spherical ungula, bounded by the planes...each other, as the angles formed by the planes which bound them. PROPOSITION XVIII. THEOREM. Two symmetrical spherical triangles are equivalent. Let ABC,...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1838 - 384 pages
...>vhich expression, A represents such a part of unity, as the angle of the lune is of one right angle. Scholium. The spherical ungula, bounded by the planes...being equal, the spherical ungulas will also be equal ; henpe two spherical ungulas are to each other, as the angles formed by the planes which bound them....
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