 | Trinity College (Hartford, Conn.) - 1888 - 978 pages
...dimensions. 3. A triangular pyramid is one third of a triangular prism of the same base and altitude. 4. The sum of the angles of a spherical triangle is greater than two right angles and less than six right angles. 5. The volume of a sphere is equal to the area of its surface multiplied... | |
 | 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 to six right... | |
 | 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 area of the... | |
 | 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... | |
 | 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 - 426 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... | |
 | 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 - 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.... | |
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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... 
