 A spherical angle is measured by the arc of the 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...  Solid Geometry - Page 370by George Albert Wentworth - 1899 - 218 pagesFull view - About this book
 | 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
...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 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
...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
...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 sides. Let BAD be an angle formed by two arcs of great circles; then will it be equal to the angle EAF formed... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...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 and...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 of the... | |
 | 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
...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...between its sides (produced if necessary). Let AB and AB' be two arcs of great circles, .AT and AT' the tangents to these arcs at A, 0 the centre of... | |
 | Cornell University - 1875 - 1012 pages
...equal to the angle of their planes, and is measured by the arc of a great circle described from the vertex as a pole and included between its sides (produced if necessary). 4. The diameter of a sphere is 20 inches. Find its convex surface, its volume, and the area of a zone... | |
 | Harvard University - 1876 - 554 pages
...of two ores 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). 7. In two polar triangles, each angle of one is measured by the supplement of the side lying opposite... | |
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