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
| Benjamin Greenleaf - 1868 - 338 pages
...mutually equiangular, are at the same 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 Peirce - Geometry - 1869 - 150 pages
...symmetrical. Proof. If the two triangles ABC, DEF (fig. 183) have the side AB = DE, the angle BAC = EOF, **and the angle ABC = DEF; the side DE can be placed...symmetrical to ABC. 452. Theorem. If two triangles** ori the same sphere, or on equal spheres, have two sides, and the included angle of the one respectively... | |
| Aaron Schuyler - Geometry - 1876 - 384 pages
...to the two curves at their point of intersection and the center of the sphere. 8. If two spherical **triangle~s on the same sphere or on equal spheres have two sides** of the one respectively equal to two sides of the other, and the included angles unequal, the third... | |
| Sophia Foster Richardson - Geometry, Solid - 1914 - 234 pages
...corresponding parts equal and placed in reverse order. (§ 393) 146 407. THEOREM. If two spherical **triangles on the same sphere or on equal spheres have two sides and the included angle of** one equal respectively to two sides and the included angle of the other, they are congruent or symmetrical... | |
| Fletcher Durell, Elmer Ellsworth Arnold - Geometry, Solid - 1917 - 220 pages
...spheres situated with reference to each other? SOLID GEOMETRY. BOOK IX PROPOSITION XII. THEOREM 686. **If two triangles, on the same sphere or on equal spheres, have** the three sides of one equal, respectively, to the three sides of the other, the triangles are either... | |
| David Eugene Smith - Geometry, Solid - 1924 - 238 pages
...with respect to AA'R'X (Ax. 5). §§ 252, 253 185 Proposition 10. Mutually Equilateral Triangles 253. **Theorem. If two triangles on the same sphere or on equal spheres** are mutually equilateral, they are mutually equiangular and are either congruent or symmetric. Given... | |
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