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" Theorem. If two spherical triangles on the same sphere, or on equal spheres, are equilateral with respect to each other, they are also equiangular with respect to each other. "
A Treatise on Spherics: Comprising the Elements of Spherical Geometry, and ... - Page 43
by Daniel Cresswell - 1816 - 294 pages
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Catalogue - Harvard University

Harvard University - 1873 - 732 pages
...angles of its polar triangle if the sides and angles of both are expressed in degrees, minutes, etc. 6. If two spherical triangles on the same sphere, or on equal spheres, are equilateral with respect to each other, they are also equiangular with respect to each other. 7....
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Elements of Geometry with Exercises for Students: An an Introduction to ...

Aaron Schuyler - Geometry - 1876 - 384 pages
...embracing the tangents 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,...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - Geometry - 1878 - 398 pages
...sides which subttnd them are also equal. (Bucl. I. 6.) SE PROPOSITION C. THEOREM. If two triangles have the three sides of the one equal to the three sides of the otlwr, each to each, the triangles must be equal in all respeett. Let the three sides of the A s ABC,...
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Elementary Geometry, Plane and Solid: For Use in High Schools and Academies

Thomas Franklin Holgate - Geometry - 1901 - 462 pages
...second are symmetrical. Proposition IX can then be stated as follows: // two spherical triangles lying on the same sphere, or on equal spheres, have the three sides of one equal, respectively, to the three sides of the other, they are either identically equal or symmetrical,...
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Elementary Geometry, Plane and Solid: For Use in High Schools and Academies

Thomas Franklin Holgate - Geometry - 1901 - 460 pages
...spherical triangle is equiangular, its polar triangle is equilateral, and conversely. § 635. (13) If two spherical triangles on the same sphere, or on equal spheres, are mutually equiangular, their polar triangles are mutually equilateral, and conversely. § 636. (14)...
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Plane and Solid Geometry

Edward Rutledge Robbins - Geometry - 1907 - 428 pages
...equiangular (?) (746, III). Hence, the A can he made to coincide. SOLID GEOMETRY 765. THEOREM. Provided two spherical triangles on the same sphere (or on equal spheres) have their parts arranged in reverse order, they are symmetrical: I. If two sides and the included angle...
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Solid Geometry

Sophia Foster Richardson - Geometry, Solid - 1914 - 236 pages
...spheres have their parts respectively equal and similarly placed, they are congruent. 409. COROLLARY 2. If two spherical triangles on the same sphere or on equal spheres are both symmetrical with the same third triangle, they are congruent. EXERCISE 217. To find the radius...
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Plane and Solid Geometry

Webster Wells, Walter Wilson Hart - Geometry - 1916 - 490 pages
...of A'B'C' and DEF of D'E'F'. § 655 5. .-. A ABC and A DEF are mutually equilateral. Why ? 710. Cor. If two spherical triangles on the same sphere or on equal spheres are mutually equiangular, I. They are congruent if the equal parts are arranged in the same order....
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Solid Geometry

John Charles Stone, James Franklin Millis - Geometry, Solid - 1916 - 196 pages
...triangles such that to each side of one there corresponds an equal side of the other. 473. Corollary 2. — If two spherical triangles on the same sphere, or on equal spheres, are mutually equiangular, their polar triangles are mutually equilateral ; and conversely. The proof...
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Solid Geometry

Fletcher Durell, Elmer Ellsworth Arnold - Geometry, Solid - 1917 - 220 pages
...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 equal or symmetrical....
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