 | 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... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...XVI.— THEOREM. 57. The angle of two arcs of great circles is equal to the angle of their planes, and is measured by the arc of a great circle described...included between its sides (produced if necessary). Let AB and AB' be two arcs of great circles, AT and A T' the tangents to these arcs at A, O the centre... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...angle of two arcs of great circles is equal to the angle of their planes, and is measured by the are of a great circle described from its vertex as a pole...included between its sides (produced if necessary). Let AB and AB' be two arcs of great circles, A Tand AT' the tangents to these arcs at A, O the centre... | |
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The angle of two arcs of great circles is equal to the angle of their planes, and 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 and AB... 
