 | Isaac Todhunter - 1879 - 176 sider
...the corresponding angles. We shall see several examples of this principle in the next Chapter. 29. Any two sides of a spherical triangle are together greater than the third side. (See the figure of Art. 18.) For any two of the three plane angles which form the solid angle... | |
 | John Charles Snowball - 1880 - 256 sider
...Cos a = - - ' > ш which tie cosine of a side of a triangle is expressed in terms of the angles. 20. 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. For, Eucl. xi. 20,... | |
 | Isaac Sharpless - 1882 - 286 sider
...spherical angle is the inclination of the planes that form the angle. Proposition 5. Xlieorem. — Any two sides of a spherical triangle are together greater than the third. Let ABC be a spherical triangle ; any two sides are together greater than the third. Take D, the centre... | |
 | Canada. Department of the Interior - 1888 - 756 sider
...con2 A— 1. sin 4+sin B = 2 sin cos 29 20 18 SPHERICAL TRIGONOMETRY. Time, 3 hours. 1. Prove that any two sides of a spherical triangle are together greater than the third side, and that the sum of three sides is less than the circumference of a great circle. 2. Prove that... | |
 | Nathaniel Bowditch - 1888 - 704 sider
...primary at right angles. A great circle may be drawn through any two points on the surface of a sphere. The .shortest distance between any two points measured on the surface of a sphere is the arc of the great circle joining them. THEOREMS OF GEOMETRY. ffone Uni, AB, fall any... | |
 | John Casey - 1889 - 199 sider
...A'B'C', whose corresponding vertices are diametrically opposite, are called ANTIPODAL TKI ANGLES. 12. Any two sides of a spherical triangle are together greater than the third, and the sum of the three sides is less than a great circle. DEM. — ~LetABC be - the spherical triangle... | |
 | George Bruce Halsted - 1896 - 208 sider
...will be the third vertices of two symmetrical triangles with the three given sides. 371. Corollary I. Any two sides of a spherical triangle are together greater than the third. For if two be each less than a quadrant, and together equal to the third, the construction circles... | |
 | American Mathematical Society - 1902 - 738 sider
...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 - 1904 - 324 sider
...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 - 1904 - 313 sider
...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.... | |
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Any Two Sides of a Spherical Triangle are together Greater than the Third. 
