 | Adrien Marie Legendre - Geometry - 1822 - 394 pages
...VIII. THEOREM. The angle ~BAC,jbrrtied by AB, AC two arcs of great circles, is equal to the angle FAG formed by the tangents of these arcs at the point A ; and is therefore measured by the arc DE described from the point A as a pole, between the sides AB, AC,... | |
 | 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...then will it be equal to the angle EAF formed by the tanD gents of these arcs at the point A , and it is measured by the arc DB described from the vertex... | |
 | Elias Loomis - Conic sections - 1860 - 246 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...the tangents of these arcs at the point A, and it is measured by the arc DB describe 1 from the vertex A as a pole. For the tangent AE, drawn in the... | |
 | 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 - 1861 - 638 pages
...VII. — THEOREM. <• /*•• . ' arcs O BOOK IX. Let BAC be an angle formed by the two arcs AB, AC; then will it be equal to the angle EAF, formed by the tangents AE, AF, and it is measured by BC, the arc of a great circle described from the vertex A as a pole.... | |
 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...formed by the tangents of those arcs at BOOK IX. Let BAC be an angle formed by the two arcs AB, AC ; then will it be equal to the angle EAF, formed by the tangents AE, AF, and it is measured by BC, the arc of a great circle described from the vertex A as a pole.... | |
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... and is measured by the arc of a great circle described from its vertex as a pole, and included between its sides. 
