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 142by Benjamin Peirce - 1837 - 159 pagesFull view - About this book
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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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