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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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Geometry

Roger Fenn - Mathematics - 2007 - 330 pages
...calculus to be 1 T ..• -. . It follows that the area of the unit sphere is 47c. We have mentioned that the sum of the angles of a spherical triangle is greater than -. It turns out that this "excess" is equal to the area of the triangle. We first find the area of...
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Mathematics and Art: Mathematical Visualization in Art and Education

Claude Bruter - Mathematics - 2002 - 360 pages
...machines comes out essentially from the inequality 1 1 1 — H --- h .. > 1, pqr implied by the fact that the sum of the angles of a spherical triangle is greater than TT. A very natural extension of this would be to have "machines for building symmetry" in hyperbolic...
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Science and Polity in France: The End of the Old Regime

Charles Coulston Gillispie - Science - 2009 - 615 pages
...trigonometry, in effect treating their data as if the earth were flat and neglecting the inconvenience that the sum of the angles of a spherical triangle is greater than 180. Less easily satisfied was Legendre, the mathematical member of the French team, whose analysis...
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Parliamentary Papers, Volume 30

Great Britain. Parliament. House of Commons - Bills, Legislative - 1853 - 520 pages
...circumstances? What point in Reaumur's and in Centigrade scale correspond to 44 Fahrenheit. (8.) The sum of the angles of a spherical triangle is greater than two right angles, and less than six. Show that the angles at the base of an isosceles triangle are equal. (9.) Express...
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higher course geometry

284 pages
...the third side, and the sum of the three sides is less than the circumference of a great circle. 95. The sum of the angles of a spherical triangle is greater than two right angles, but less than six right angles. 96. The planes of the small circles of equal radii, on a sphere, envelop...
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Technical Manual

United States. War Department - 194 pages
...degrees of the central angle subtended at the center of the sphere in the plane of the circle.) (6) The sum of the angles of a spherical triangle is greater than ,0 180 and less than 540. Any angle of a spherical triangle must be less than 180. (c) The sum...
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Texas School Journal, Volume 21

Education - 1903 - 780 pages
...regular polyhedron? (b) How many regular convex polyhedrons are possible? (c) Name them. 3. Prove: The sum of the angles of a spherical triangle is greater than one, and less than three straight angles. 4. The angles of a spherical triangle are 120, 270, and...
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The Course of Study: A Monthly Publication for Teachers and Parents, Volume 1

Education, Elementary - 1900 - 1022 pages
...greater side, and conversely. 5. The sum of the sides of a spherical triangle is less than 360. 6. The sum of the angles of a spherical triangle is greater than 180 and less than 540. 7. I (the first of two spherical triangles is polar to the second, then...
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