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" THEOREM. If two triangles on the same sphere, or on equal spheres, are mutually equiangular, they will also be mutually equilateral. Let A and B be the two given triangles; P and Q their polar triangles. Since the angles are equal in the triangles A and... "
An Elementary Treatise on Plane and Solid Geometry - Page 142
by Benjamin Peirce - 1837 - 159 pages
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1822 - 367 pages
...side BC of the first triangle be greater than the third side EF of tlie second. PROPOSITION XVIII. THEOREM. If two triangles on the same sphere, or on equal spheres, are mutually equiangular, they will also be mutually equilateral. Let A and B be the two given triangles...
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1828 - 316 pages
...placed on the other, as is done in the corresponding case of rectilineal triangles (38.). THEOREM. 482. If two triangles on the same sphere, or on equal spheres, have all their sides respectively equal, their angles will likewise be all respectively equal, the equal...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 359 pages
...BC<AC. Both these conclusions are false : hence the angle BAC is greater than ABC. PROPOSITION XV. THEOREM. If two triangles on the same sphere, or on equal spheres, are mutually equiangular, they will also be mutually equilateral. Let A and B be the two given triangles...
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Higher Geometry and Trigonometry: Being the Third Part of a Series on ...

Nathan Scholfield - Conic sections - 1845 - 244 pages
...done in the corresponding case of rectilineal triangles, (Prop. IX. B. II. El. Geom.) PROPOSITION XIV. THEOREM. If two triangles on the same sphere, or on equal spheres have all their sides respectively equal, their angles will likewise be all respectively equal, the equal...
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Higher Geometry and Trigonometry: Being the Third Part of a Series on ...

Nathan Scholfield - Geometry - 1845 - 506 pages
...BC<AC. Both these conclusions are false : hence the angle BAG is greater than ABC. PROPOSITION XVII. THEOREM. If two triangles on the same sphere, or on equal spheres, are mutually equiangular, they will also be mutually equilateral. Let A and B be the two given triangles...
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A Series on Elementary and Higher Geometry, Trigonometry, and Mensuration ...

Nathan Scholfield - Conic sections - 1845
...BC<AC. Both these conclusions are false : hence the angle BAG is greater than ABC. PROPOSITION XVII. THEOREM. If two triangles on the same sphere, or on equal spheres, are mutually equiangular, they will also be mutually equilateral. Let A and B be the two given triangles...
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Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

Nathan Scholfield - 1845
...BC<AC. Both these conclusions are false : hence the angle BAG is greater than ABC. PROPOSITION XVII. THEOREM. If two triangles on the same sphere, or on equal spheres, art mutually equiangular, they will also be mutually equilateral, Let A and B be the two given triangles...
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1847 - 150 pages
...equiangular with respect to each other, but cannot be applied to each other,' as. ABC, ABC (fig. 183). 451. Theorem. If two triangles on the same sphere, or on equal spheres, have a side, and the two adjacent angles of the one respectively equal to a side and the two adjacent angles...
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Elements of Geometry: With Practical Applications ...

George Roberts Perkins - Geometry - 1847 - 308 pages
...< AC. Both these conclusions are false ; hence the angle BAC is greater than ABC. PROPOSITION xxx. THEOREM. If two triangles on the same sphere, or on equal spheres, are mutually equiangular, they will also be mutually equilateral. Let A and B be the two given triangles...
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An Elementary Treatise of Spherical Geometry and Trigonometry

Anthony Dumond Stanley - Geometry - 1848 - 134 pages
...remaining angles of one triangle are equal to the corresponding angles of the other. PBOP. XXXIII. If two triangles on the same sphere or on equal spheres have two angles and the intermediate side of one, severally equal to two angles and the intermediate side of...
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