 | 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 can be proved in the usual way... | |
 | 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 in area. PROPOSITION XXVIII. PROPOSITION... | |
 | 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... | |
 | 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 : Z A+^ B+Z C> 180° and < 540°.... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | 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, C, and the sides opposite in the polar... | |
 | Henry Dallas Thompson - Geometry, Solid - 1896 - 226 pages
...less than six right angles. (This is a restatement of § 241). 243. DEFINITION. The angle by which the sum of the angles of a spherical triangle is greater than two right angles is called the angle of the spherical excess or the spherical excess of the triangle. The... | |
 | 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... | |
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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... 
