 | Adrien Marie Legendre - 1822 - 394 σελίδες
...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 - 1828 - 346 σελίδες
...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 - 1836 - 394 σελίδες
...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 - 1845 - 244 σελίδες
...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 - 1845 - 506 σελίδες
...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 - 542 σελίδες
...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 - 894 σελίδες
...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 - 1847 - 204 σελίδες
...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 - 1847 - 326 σελίδες
...< 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 - 1848 - 134 σελίδες
...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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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... 
