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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

Yale University Entrance Examinations in Mathematics: 1884 to 1898

Mathematics - 1898 - 224 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...

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...

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...

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...

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...

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...

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...

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...

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...

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...