| 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... | |
| Seth Thayer Stewart - Geometry - 1891 - 438 pages
...a 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... | |
| Mining schools and education - 1891 - 862 pages
...triangles, each angle of one is measured by the supplement of the side lying opposite to it in the other. 6. **The sum of the angles of a spherical triangle is greater than two** and less than six right angles. ?. The area of a spherical triangle, expressed in spherical degrees,... | |
| 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 area of the triangle... | |
| William C. Bartol - Geometry, Solid - 1893 - 106 pages
...right angles. Use the diagram of (209), and complete the demonstration by (45). PROPOSITION XXXIV. 211. **THEOREM. The sum of the angles of a spherical triangle is greater than** 180° and less than 5J THE ELEMENTS OF SOLID GEOMETRY. Now, A = 180° - B'C' . . . (205) and B = 180°... | |
| Arthur Latham Baker - Geometry, Solid - 1893 - 148 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.... | |
| 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.... | |
| George Clinton Shutts - Geometry - 1894 - 412 pages
...sides of a convex spherical polygon is less than 360°, or four right angles. PROPOSITION XXVII. 688. **Theorem. The sum of the angles of a spherical triangle is greater than two** and less than six right angles. Let ABC represent a spherical triangle. To prove that the sum 0} the... | |
| 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... | |
| American Mathematical Society - Mathematics - 1905 - 1030 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... | |
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