 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...  Solid Geometry - Page 376by George Albert Wentworth - 1899 - 218 pagesFull view - About this book
 | William Chauvenet - 1893 - 340 pages
...of a convex spherical polygon is less than the circumference of a great circle. PROPOSITION XVIII. The sum of the angles of a spherical triangle is greater than two, and less than six, right angles. PROPOSITION XIX. Two symmetrical spherical triangles are equivalent.... | |
 | Ephraim Miller - Plane trigonometry - 1894 - 222 pages
...90°. REMARK II. The functions of £a, $b, and $c, in [57] and [59], are real quantities. For since the sum of the angles of a spherical triangle is greater than 180°, and less than six right angles, then S, or $(A + В + C)- in [57] and [59], is greater than 90°, and less than three... | |
 | 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... | |
 | 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... | |
 | George Albert Wentworth - Geometry - 1895 - 458 pages
...SCHOLIUM. Two polar triangles are sometimes called supplemental triangles. PROPOSITION XVI. THEOREM. 737. The sum, of the angles of a spherical triangle is...triangle, and let A, B, C denote the values of its angles, and a', b', c', respectively, the values of the opposite sides in the polar triangle A'B'C'.... | |
 | 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 excess... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 344 pages
...Geometry. EXERCISES. 736. Show that a trirectangular triangle is its own polar. 737. From step 7 show that the sum of the angles of a spherical triangle is greater than a straight angle*. 738. A spherical triangle is to the surface of the sphere as the spherical excess... | |
 | 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
...Geometry. EXERCISES. 736. Show that a trirectangular triangle is its own polar. 737. From step 7 show that the sum of the angles of a spherical triangle is greater than a straight angle. 738. A spherical triangle is to the surface of the sphere as the spherical excess... | |
 | 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 the poles of the sides B'C',... | |
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