 | American Mathematical Society - Mathematics - 1902 - 738 pages
...shortest path between two points is on a straightest line or great circle. It is rigorously proved that two sides of a spherical triangle are together greater than the third. Thus is eliminated the objectionable assumption analogous to "the straight line is the shortest distance... | |
 | George Bruce Halsted - Geometry - 1904 - 324 pages
...impossible. 544. Convention. In general a sum of sects is a number of quadrants plus a sect. 545. Theorem. Any two sides of a spherical triangle are together greater than the third. Proof. Since each side is less than two quadrants, we have only to prove AB + BC>AC when AB<q, andBC<AC.... | |
 | George Bruce Halsted - Geometry - 1904 - 313 pages
...216. 544. Convention. In general a sum of sects is a number of quadrants plus a sect. 545. Theorem. Any two sides of a spherical triangle are together greater than the third. Proof. Since each side is less than two quadrants, we have only to prove AB + BC>AC when AB<q , andBC<AC.... | |
 | Charles Davison - Geometry, Solid - 1905 - 140 pages
...its sides are all equal to one another, and isosceles when two of its sides are equal. 100. PROP. 66. Any two sides of a spherical triangle are together greater than the third. Let BC, CA, AB (see figure of last article) be the sides of the spherical triangle ABC ; to prove that... | |
 | Henry Raper - Nautical astronomy - 1908 - 1018 pages
...angles are opposite equal sides, and equal sides are opposite equal angles. SrilKRICAL TRIGONOMETRY. B7A Any two sides of a spherical triangle are together greater than the third side. Each side of a spherical triangle is less than a semicircle or 180". In every spherical triangle... | |
 | Association of Ontario Land Surveyors - Surveying - 1909 - 254 pages
...side of a triangle is half another and the included angle is 60 degrees. Find the other angles. 7. Any two sides of a spherical triangle are together greater than the third side ; and the sum of the three sides is less than the circumference of the circle. 8. State Napier's... | |
 | John William Norie, J. W. Saul - Nautical astronomy - 1917 - 642 pages
...points. A SPHERICAL ANGLE is the inclination of two great circles of the sphere meeting one another. Any two sides of a spherical triangle are together greater than the third side ; and the three sides of a spherical triangle are together less than the circumference of a great... | |
 | William Norman Thomas - Surveying - 1920 - 552 pages
...latitude is not along the parallel, but along a great circle through A and B (see Example, p. 433). (2) Any two sides of a spherical triangle are together greater than the third, because any two of the plane angles which form the solid angle at 0 are together greater than the third... | |
 | 288 pages
...B, C. Fig. 95 94. The sum of any two sides of a spherical triangle is greater than the third side, and the sum of the three sides is less than the circumference of a great circle. 95. The sum of the angles of a spherical triangle is greater than two right angles, but less than six... | |
 | Great Britain. Parliament. House of Commons - Great Britain - 1872 - 912 pages
...scholarships of the second yenr will substitute for 10, 11, 12 of above the following. 10.* Prove that two sides of a spherical triangle are together greater than the third. On what proposition in Euclid does this depend 1 11.* Express the cosine of half the angle of a spherical... | |
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Any two sides of a spherical triangle are together greater than the third, and the sum of the three sides is less than the circumference of a great circle. 
