 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...  Plane and Solid Geometry - Page 295by Wooster Woodruff Beman, David Eugene Smith - 1895 - 320 pagesFull view - About this book
 | American Mathematical Society - Mathematics - 1905 - 1032 pages
...the triangle can be read off as L. e., p. 595. pure spherics. The proof of the theorem (§ 567) — the sum of the angles of a spherical triangle is greater than two and less than six right angles — assumes that a spherical triangle is always positive. The theorem... | |
 | Charles Ambrose Van Velzer, George Clinton Shutts - Geometry - 1894 - 416 pages
...sides of a convex spherical polygon is less than the circumference of a great circle. PROPOSITION XXVI. The sum of the angles of a spherical triangle is greater than two and less than six right angles. PROPOSITION XXVII. Two symmetrical spherical triangles are equal... | |
 | George Cunningham Edwards - Geometry - 1895 - 330 pages
...the area of any spherical polygon, the angles of which are given. NOTE. — It has been shown that the sum of the angles of a spherical triangle is greater than 180°: The amount, in degrees, by which the sum of the angles exceeds 180°, is called the spherical... | |
 | John Macnie - Geometry - 1895 - 386 pages
...the side of A'B'C' that is opposite ZA, etc., we have the relations : PROPOSITION XV. THEOREM. 633. The sum, of the angles of a spherical triangle* is greater than two, and less than six, right angles. Given: A, B, C, the angles of a spherical triangle ABC; To Prove... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 346 pages
...polars are mutually equilateral; if mutually equilateral, their polars are mutually equiangular. 2. The sum of the angles of a spherical triangle is greater than one and less than three straight angles. For by th. 11, /', 0 < a' + b' + c' <360°. .'. by subtracting... | |
 | Henry Dallas Thompson - Geometry, Solid - 1896 - 226 pages
...with the measure of the opposite angle of the polar equals two quadrants. 241. THEOREM. The measure of the sum of the angles of a spherical triangle is greater than two and less than six quadrants. For the measures of the three angles together with the three si'des... | |
 | Webster Wells - Trigonometry - 1896 - 236 pages
...opposite the greater side. 3. The sum of the sides of a spherical triangle is less than 360°. 80 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... | |
 | George Albert Wentworth - Mathematics - 1896 - 68 pages
...two polar triangles each angle of the one is the supplement of the opposite side in the other. 737. The sum of the angles of a spherical triangle is greater than 180° and less than 540°. 741. In a bi-rectangular spherical triangle the sides opposite the right... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 554 pages
...AB and AC. In a similar manner the remaining relations are proved. QED PROPOSITION XXX. THEOREM 878. The sum of the angles of a spherical triangle is greater than two, and less than six', right angles. GIVEN the spherical triangle ABC. Denote its angles by A, B,... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 574 pages
...AB and AC. In a similar manner the remaining relations are proved. QED PROPOSITION XXX. THEOREM 8Y8. The sum of the angles of a spherical triangle is greater than two, and less than six, right angles. GIVEN the spherical triangle ABC. Denote its angles by A, B,... | |
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