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" The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180 and less than 540. (gr). If A'B'C' is the polar triangle of ABC... "
An Elementary Treatise on Plane and Solid Geometry - Page 138
by Benjamin Peirce - 1871 - 150 pages
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Plane Geometry

Walter Burton Ford, Charles Ammermann - Geometry, Modern - 1923 - 406 pages
...70, 90, and 80, respectively, find the sides of the polar triangle (in degrees). 367. Theorem IX. The sum of the angles of a spherical triangle is greater than 180 and less than 540. FIG. 264 Given the spherical A ABC having the sides a, b, and c. To prove...
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Essentials of Solid Geometry

David Eugene Smith - Geometry, Solid - 1924 - 256 pages
...respectively supplementary. SPHERICAL POLYGONS BOOK VIII Proposition 14. Sum of the Angles of a Triangle 201. Theorem. The sum of the angles of a spherical triangle is greater than 180 and less than 540. Given the spherical A ABC. Prove that 180 < ZA + Z 5 + ZC < 540. Proof....
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Journal of the Elisha Mitchell Scientific Society, Volumes 40-41

Elisha Mitchell Scientific Society (Chapel Hill, N.C.) - Natural history - 1924 - 738 pages
...There is nothing startling in this statement because, since the time of Euclid, it has been known that the sum of the angles of a spherical triangle is greater than 180. Whether the sum of the angles of a triangle is equal to, greater than, or even less than, 180,...
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Questions Set at the Examinations ...

College Entrance Examination Board - Universities and colleges - 1924 - 124 pages
...lines at their point of intersection, it is perpendicular to the plane of the two lines. 6. Prove: The sum of the angles of a spherical triangle is greater than 180 and less than 540. 7. Four balls have equal diameters of 2 inches, and fit into a cylindrical...
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Mathematics: Course of Study for Senior and Junior High Schools

Baltimore (Md.). Department of Education - Mathematics - 1924 - 182 pages
...equiangular. 3 . Each side of a spherical triangle is less than the sum of the other two sides. 5 . The sum of the angles of a spherical triangle is greater than 180 and less than 540. 6 . A plane tangent to a sphere is perpendicular to the radius drawn to...
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The Reorganization of Mathematics in Secondary Education (part I): A ..., Part 1

National Committee on Mathematical Requirements - Mathematics - 1927 - 208 pages
...other two sides. [74] 48. The sum of the sides of a spherical polygon is less than 360. [75] 49. The sum of the angles of a spherical triangle is greater than 180 and less than 540. [78*] 50. There cannot be more than five regular convex polyhedrons. [35]...
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The Harvard University Catalogue

Harvard University - 1876
...opposite to it in the other. 8. Any side of a spherical triangle is less than the sum of the other two. 9. The sum of the angles of a spherical triangle is greater than two and less than six right angles. 10. The volume of a spherical pyramid is equal to the area of its base...
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Empiricism, Logic and Mathematics: Philosophical Papers

Hans Hahn - Science - 1980 - 167 pages
...whose sides are arcs of great circles, and it is a well-known proposition of elementary geometry that the sum of the angles of a spherical triangle is greater than 1 80 degrees, and that the excess over 180 degrees is greater the larger the surface area of the triangle....
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Basic Concepts of Geometry

Walter Prenowitz, Meyer Jordan - Mathematics - 1986 - 380 pages
...the only possible definition. It is interesting to note that in Euclidean three-dimensional geometry, the sum of the angles of a spherical triangle is greater than 180, and the area of a spherical triangle is denned to be its "excess," that is, the sum of the degree...
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Cosmogenesis: The Growth of Order in the Universe

David Layzer - Science - 1991 - 336 pages
...triangles in a plane. For example, the sum of the angles of any plane triangle is exactly 180; but the sum of the angles of a spherical triangle is greater than 180 and increases with the area of the triangle. However, the geometry of a patch the size of Kansas...
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