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" 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 B, the... "
Solid Geometry - Page 479
by William Betz, Harrison Emmett Webb - 1916 - 178 pages
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1822 - 394 pages
...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 ; P and Q their polar triangles....
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 394 pages
...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 ; P and Q their polar triangles....
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1837 - 376 pages
...these conclusions are false : hence the angle BAC is greater than ABC. PROPOSITION XV. THEOREM/ Jf 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....
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Higher Geometry and Trigonometry: Being the Third Part of a Series on ...

Nathan Scholfield - Geometry - 1845 - 506 pages
...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 ; P and Q, their polar triangles....
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A Series on Elementary and Higher Geometry, Trigonometry, and Mensuration ...

Nathan Scholfield - Conic sections - 1845 - 542 pages
...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 ; P and Q their polar triangles....
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Higher Geometry and Trigonometry: Being the Third Part of a Series on ...

Nathan Scholfield - Conic sections - 1845 - 244 pages
...these conclusions are false : hence the angle BAC is greater than ABC. PROPOSITION XVII. THEOREM. Jf 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....
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Elements of Geometry: With Practical Applications ...

George Roberts Perkins - Geometry - 1847 - 326 pages
...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 ; P and Q their polar triangles....
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Elements of Geometry and Trigonometry Translated from the French of A.M ...

Charles Davies - Trigonometry - 1849 - 372 pages
...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; P and Q their polar triangles....
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Elements of Geometry: With, Practical Applications

George Roberts Perkins - Geometry - 1850 - 332 pages
...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 are equal in the triangles A and...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1852 - 436 pages
...contrary to the supposition : hence, the angle BAC is greater than ABC. PROPOSITION XIII. THEOEEM. 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 ; P and Q their polar triangles....
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