 | Ephraim Miller - 1894 - 222 sider
...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 - 1895 - 386 sider
...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 - 1895 - 344 sider
...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 - 1895 - 330 sider
...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... | |
 | Wooster Woodruff Beman, David Eugene Smith - 1895 - 346 sider
...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... | |
 | Andrew Wheeler Phillips, Irving Fisher - 1896 - 554 sider
...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 - 1896 - 226 sider
...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 - 1896 - 68 sider
...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... | |
 | Webster Wells - 1896 - 236 sider
...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... | |
 | Andrew Wheeler Phillips, Irving Fisher - 1896 - 574 sider
...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, C, and the sides opposite in the polar... | |
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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... 
