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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 and Trigonometry Translated from the French of A.M ...

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;...
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Elements of Geometry: With, Practical Applications

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...
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Elements of Geometry and Trigonometry

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...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

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...
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

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...
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

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...
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Elements of Geometry and Trigonometry: With Practical Applications

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...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

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...
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Elements of Geometry: With Practical Applications to Mensuration

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...
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An Elementary Treatise on Plane and Solid Geometry

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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