 | Edward Albert Bowser - Geometry - 1890 - 418 pages
...717. Sen. Two polar triangles are also called supple* mental triangles. Proposition 14. Theorem. 718. The sum of the angles of a. spherical triangle is greater than two, and less than six, right angles. Hyp. Let A, B, C denote the three Z s of the spherical A ABC. To prove A + B + C > 180° and < 540°.... | |
 | Edward Albert Bowser - Geometry - 1890 - 420 pages
...SCH. Two polar triangles are also called supplemental triangles. Proposition 14. Theorem. 718. TJie sum of the angles of a spherical triangle is greater than two, and less than six, right angles. Hyp. Let A, B, C denote the three Z s of the spherical A ABC. To prove A + B + C > 180° and < 540°.... | |
 | Robert Baldwin Hayward - Geometry, Solid - 1890 - 160 pages
...may in fact be regarded as the polar triangle of A'BC. V.— Spherical Excess. We can now prove that the sum of the angles of a spherical triangle is greater than two right angles. For the sum of the angles of the triangle and the sides of the polar triangle is equal... | |
 | Mansfield Merriman - Geodesy - 1903 - 274 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 right angle as the... | |
 | William Chauvenet - Geometry - 1891 - 344 pages
...the sphere is less than four right angles (VI., Proposition XXI.). PROPOSITION XVIII.— THEOREM. 63. The sum of the angles of a spherical triangle is greater...denoting the angles of' a spherical triangle by A, JB, C, and the sides respectively opposite to them in its polar triangle by a', b', cf, we have (Proposition... | |
 | Seth Thayer Stewart - Geometry - 1891 - 426 pages
...spherical polygon is at a quadrant's distance from every point in the side. PROPOSITION XI. 57O. Theorem : The sum of the angles of a spherical triangle is greater than two, and less than six right angles. Statement : Let ABC be any spherical triangle. The sum of its angles is less than six, and greater... | |
 | Seth Thayer Stewart - Geometry - 1891 - 428 pages
...two points of the arc of a great circle, it is the pole of that circle. PROPOSITION XI. 57O. Theorem: The sum of the angles of a spherical triangle is greater than two, and less than sijc right a ngles. Statement : Let ABC be any spherical triangle. The sum of its angles is less than... | |
 | Dascom Greene - Astronomia esferica y practica - 1892 - 176 pages
...middle meridian. SPHEKICAL EXCESS or TRIANGLES ON THE EARTH'S SURFACE. 159. It is shown in geometry that the sum of the angles of a spherical triangle is greater than two right angles, and that the excess of this sum over two right angles is to eight right angles as the... | |
 | 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. PROPOSITION XX. If two arcs of... | |
 | Arthur Latham Baker - Geometry, Solid - 1893 - 150 pages
...Scholium. Polar triangles are sometimes called supplementary triangles. PROPOSITION XII. THEOREM. 280. The sum of the angles of a spherical triangle is greater than two, and less than six, right angles. Notation. Same as in § 278. To prove A + B+O 180° < 540°. Proof. A = 180° — >i', B = 180° —... | |
| |
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... 
