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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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Yale University Entrance Examinations in Mathematics: 1884 to 1898

Mathematics - 1898 - 208 pages
...perpendicular to a third plane, their line of intersection is also perpendicular to that third plane. 3. The sum of the angles of a spherical triangle is greater than two, and less than six, right angles. 4. Calculate the surface and volume of a sphere whose radius is one...
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Entrance Examinations in Mathematics, 1884 to 1898 [with Supplements to 1900]

Yale University - 1898 - 212 pages
...perpendicular to a third plane, their line of intersection is also perpendicular to that third plane. 3. The sum of the angles of a spherical triangle is greater than two, and less than six, right angles. 4. Calculate the surface and volume of a sphere whose radius is one...
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Plane and Solid Geometry

James Howard Gore - Geometry - 1898 - 232 pages
...mutually equilateral, their polar triangles are mutually equiangular. PROPOSITION V. THEOREM. 516. The sum of the angles of a spherical triangle is greater than two, and less than six, right angles. Let ABC be any spherical triangle. To prove that vl + JB+C'>180<540...
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Elements of Plane and Spherical Trigonometry

James William Nicholson - Trigonometry - 1898 - 196 pages
...lies opposite the greater side. 3. The sum of the sides of a spherical triangle is less than 360. 4. The sum of the angles of a spherical triangle is greater than 180, and less than 540. 5. If A'B'C' is the polar triangle of ABC, that is, if A, B, and С are...
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Elements of Precise Surveying and Geodesy

Mansfield Merriman - Geodesy - 1899 - 261 pages
...triangle is one included by three arcs of great circles. It is a well-known geometrical theorem that the sum of the angles of a spherical triangle is greater than two right angles, and that the excess above two right angles bears the same ratio to a sight angle as the area of the...
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Plane and Solid Geometry

William James Milne - Geometry - 1899 - 404 pages
...of the given triangle or any spherical triangle? Express your conclusions in terms of right angles. Theorem. The sum of the angles of a spherical triangle is greater than two and less than six right angles. Data: Any spherical triangle, as ABC, ^ whose angles are A, B, and...
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Syllabus of Propositions in Geometry: Intended for Use in Preparing Students ...

Harvard University - Geometry - 1899 - 39 pages
...sides of a convex spherical polygon is less than the circumference of a great circle. THEOREM XVI. The sum of the angles of a spherical triangle is greater than two, and less than six, right angles. 28 THEOREM XVIII, If two arcs of great circles intersect on the surface...
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The Essentials of Geometry

Webster Wells - Geometry - 1899 - 178 pages
...+ CD + DA < 360. (By 458, sum of AAOE, BOC, COD, and DOA is < 360.) PROP. XX. THEOREM. 596. The sum of the angles of a spherical triangle is greater than two, and less than six, right angles. 341 o' Given A, B, and C the A, expressed in degrees, of spherical...
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Plane and Solid Geometry

William James Milne - Geometry - 1899 - 396 pages
...of the given triangle or any spherical triangle? Express your conclusions in terms of right angles. Theorem. The sum of the angles of a spherical triangle is greater tlian two and less tlian six right angles. Data : Any spherical triangle, as ABC, whose angles are...
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Solid Geometry, Volumes 6-9

George Albert Wentworth - Geometry, Solid - 1899 - 248 pages
...way all the other relations are proved. QED BOOK VIII. SOLID GEOMETRY. PROPOSITION XV. THEOREM. 795. The sum of the angles of a spherical triangle is greater than 180 and less than 540. Let ABC be a spherical triangle, and let A, B, C denote the values of its...
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