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 B, the... Solid Geometry - Page 479by William Betz, Harrison Emmett Webb - 1916 - 178 pagesFull view - About this book
| Adrien Marie Legendre - Geometry - 1822 - 394 pages
...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 ; P and Q their polar triangles.... | |
| Adrien Marie Legendre - Geometry - 1836 - 394 pages
...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 ; P and Q their polar triangles.... | |
| Adrien Marie Legendre - Geometry - 1837 - 376 pages
...these conclusions are false : hence the angle BAC is greater than ABC. PROPOSITION XV. THEOREM/ Jf 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.... | |
| Nathan Scholfield - Geometry - 1845 - 506 pages
...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 ; P and Q, their polar triangles.... | |
| Nathan Scholfield - Conic sections - 1845 - 542 pages
...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 ; P and Q their polar triangles.... | |
| Nathan Scholfield - Conic sections - 1845 - 244 pages
...these conclusions are false : hence the angle BAC is greater than ABC. PROPOSITION XVII. THEOREM. Jf 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.... | |
| George Roberts Perkins - Geometry - 1847 - 326 pages
...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 ; P and Q their polar triangles.... | |
| Charles Davies - Trigonometry - 1849 - 372 pages
...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; P and Q their polar triangles.... | |
| George Roberts Perkins - Geometry - 1850 - 332 pages
...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. polar triangles. Since the angles are equal in the triangles A and... | |
| Adrien Marie Legendre - Geometry - 1852 - 436 pages
...contrary to the supposition : hence, the angle BAC is greater than ABC. PROPOSITION XIII. THEOEEM. If two triangles on the same sphere, or on equal spheres, are mutually equiangular, they are also mutually equilateral. Let A and B be the two given triangles ; P and Q their polar triangles.... | |
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