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
| Charles Davies - Trigonometry - 1849 - 384 pages
...find 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;... | |
| George Roberts Perkins - Geometry - 1850 - 332 pages
...BC<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. polar triangles. Since the angles... | |
| Adrien Marie Legendre - Geometry - 1852 - 436 pages
...the other, as is done in the corresponding case of rectilineal triangles (B. L; p. 6). PROPOSITION X. **THEOREM. If two triangles on the same sphere, or 'on equal spheres, have** all their sides equal, each to each, their angles ivill likewise be equal, each to each, the equal... | |
| Charles Davies - Geometry - 1854 - 436 pages
...conditions is contrary to the supposition : hence, the angle BAC is greater than ABC. PROPOSITION XIII. **THEOREM. 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... | |
| George Roberts Perkins - Geometry - 1856 - 235 pages
...the included side of the one are equal to two angles and the included side of the other. THEOREM XI. **If two triangles on the same sphere, or on equal spheres, have** all their sides respectively equal, their angles will likewise l)e all respectively equal, ike equal... | |
| George Roberts Perkins - Geometry - 1860 - 443 pages
...the included side of the one are equal to two angles and the included side of the other. THEOREM XI. **If two triangles on the same sphere, or on equal spheres, have** all their sides respectively equal, their angles will likewiss bo all respectively equal, the equal... | |
| Benjamin Greenleaf - Geometry - 1862 - 520 pages
...are equivalent. For in that case the triangles will be mutually equilateral. 556. Cb^2. Hence, also, **if two triangles on the same sphere, or on equal spheres, have two sides and the included angle,** or have two angles and the included side, in the one equal to those in the other, the two triangles... | |
| Benjamin Greenleaf - Geometry - 1862 - 514 pages
...mutually equiangular, are at the samo time mutually equilateral. PROPOSITION XIV. — THEOREM. 549. **If two triangles on the same sphere, or on equal spheres, have two sides and the included angle** in the one equal to two sides and the included angle in the other, each to each, the two triangles... | |
| Benjamin Greenleaf - Geometry - 1863 - 320 pages
...equivalent. For in that case the triangles will be mutually equilateral. 556. Cor. 2. Hence, also, **if two triangles on the same sphere, or on equal spheres, have two sides and the included angle,** or have two angles and the included side, in the one equal to those in the other, the two triangles... | |
| Benjamin Peirce - Geometry - 1865 - 186 pages
...symmetrical. Proof. If the two triangles ABC, I>EF (fig. 183) have the side JIB = DE, the angle BAC=EDF, **and the angle ABC = DEF; the side DE can be placed upon AB, and the sides DF, FE will fall upon AC,** EC, or upon the sides AC', BC' of the triangle ABC1, symmetrical to ABC. 452. Theorem. If two triangles... | |
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