 | Benjamin Peirce - Geometry - 1837 - 216 pages
...-j- b -fc < 360ri. 441. Theorem. The angle formed by two arcs of great circles is measured by the arc described from its vertex as a pole, and included between its sides. Demonstration. The arc AM (fig. 177) measures the angle ACM, which, by art. 314, measures the angle... | |
 | Benjamin Peirce - Geometry - 1847 - 204 pages
...+ b -fc < 360°. 441. Theorem. The angle formed by two arcs of great circles is measured by the arc described from its vertex as a pole, and included between its sides. Proof. The arc AM (fig. 177) measures the angle •ACM, which, by 5) 315, measures the angle of the... | |
 | Elias Loomis - Conic sections - 1849 - 252 pages
...circles, is equal to the angle formed by the tangents of those arcs at the point of their intersection ; and is measured by the arc of a great circle described...vertex as a pole, and included between its sides. gents of these arcs at the point A, and it is measured by the arc DB described from the vertex A as... | |
 | Elias Loomis - Conic sections - 1857 - 242 pages
...circles, is equal to the angle formed by the tangents of those arcs at the point of their intersection ; and is measured by the arc of a great circle described...from its vertex as a pole, and included between its fides. Let BAD be an angle formed by two arcs of great circles; then will it be equal to the angle... | |
 | Elias Loomis - Conic sections - 1858 - 256 pages
...circles, is equal to the angle formed by the tangents of those arcs at the point of their intersection ; and is measured by the arc of a great circle described...vertex as a pole, and included between its sides. Let BAD be an angle formed by two arcs of great circles; then will it be equal to the angle EAF formed... | |
 | Benjamin Greenleaf - Geometry - 1862 - 532 pages
...circles is equal to the angle formed by the tangents of those arcs at the point of their intersection, and is measured by the arc of a great circle described from its vertex as a pole, and intercepted between its sides, produced if necessary. Let ВАС be an angle formed Ъу the two arcs... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...circles is equal to the angle formed by the tangents of those arcs at the point of their intersection, and is measured by the arc of a great circle described from its vertex as a pole, and intercepted between its sides, produced if necessary. Let BAC be an angle formed by the two arcs AB,... | |
 | Benjamin Greenleaf - 1869 - 516 pages
...circles is equal to the angle formed by the tangents of those arcs at the point of their intersection, and is measured by the arc of a great circle described from its vertex as a pole, and intercepted between its sides, produced if necessary. BOOK IX. Let BAC be an angle formed by the two... | |
 | Elias Loomis - Geometry - 1871 - 302 pages
...tangents of those arcs at the point of their intersection; and is measured by the arc of a great cir cle described from its vertex as a pole, and included between its sides. HOOK IX. gents of these arcs at the point A and it is measured by the arc DB described from the vertex... | |
 | William Chauvenet - Geometry - 1872 - 382 pages
...OA T, OA T', passed through the radius OA and each of the tangents. PROPOSITION XVI— THEOREM. 57. The angle of two arcs of great circles is equal to...Let AB and AB' be two arcs of great circles, .AT and AT' the tangents to these arcs at A, 0 the centre of the sphere. The planes passing through the centre... | |
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A spherical angle is measured by the arc of a great circle described from its vertex as a pole and included between its sides (produced if necessary). Let AB, AC be arcs of great circles intersecting at A; AB... 
