 | 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... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...through the centre of the sphere and the tangents to the two curves at their point of intersection. Let the curves, AB and AB', on the surface of a sphere...AB, AB', themselves; consequently the angle BAB', or TA T', is equal to the angle of these planes (56), the edge of this angle being the common diameter... | |
 | 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...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 sphere. The planes passing through... | |
 | 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... | |
 | 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
...a circle, every section made by a plane parallel to the base is a circle. 6. The angle of two ores of great circles is equal to the angle of their planes,...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... | |
 | William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...the angle of two arcs of great circles has the same measure as the dihedral of their planes, or as the arc of a great circle described from its vertex...included between its sides (produced, if necessary). COR. 2. If two arcs of great circles cut each other, their vertical angles arc equal. COR. 3. If A... | |
 | William Chauvenet - Geometry - 1887 - 364 pages
...space, whether drawn in the same plane or upon a surface of any kind. PROPOSITION IX.—THEOREM. 41. The angle of two arcs of great circles is equal to...circles, AT and AT' the tangents to these arcs at A, and O the centre of the sphere. TA and T'A lie in the planes of their arcs, and are perpendicular to... | |
 | William Chauvenet - Geometry - 1887 - 342 pages
...space, whether drawn in the same plane or upon a surface of any kind. PROPOSITION IX.— THEOREM. 41. The angle of two arcs of great circles is equal to...Let AB and AB' be two arcs of great circles, AT and A I" the tangents to these arcs at A, and O the centre of the sphere. TA and T'A lie in the planes... | |
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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... 
