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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... "
An Elementary Treatise on Plane and Solid Geometry - Page 142
by Benjamin Peirce - 1837 - 159 pages
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Elements of Geometry: With Practical Applications to Mensuration

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...
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An Elementary Treatise on Plane and Solid Geometry

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...
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Elements of Geometry with Exercises for Students: An an Introduction to ...

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...
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Solid Geometry

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...
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Solid Geometry

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...
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Essentials of Solid Geometry

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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