 | Benjamin Greenleaf - Geometry - 1862 - 532 pages
...centres and the poiut of contact lie in the same straight line. PROPOSITION VII. — THEOREM. 534. The angle formed by two arcs of great 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... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...centers and the point of contact lie in the same straight line. PROPOSITION VII. — THEOREM. 534. The angle formed by two arcs of great 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... | |
 | Adrien Marie Legendre - Geometry - 1863 - 464 pages
...quadjant DFA round the point D, its extremity A will describe an arc of a great circle. PROPOSITION IV. THEOREM. The angle formed by two arcs of great circles, is equal t® that formed by the tangents to these arcs at their point of intersection, and is measured by the... | |
 | Gerardus Beekman Docharty - Geometry - 1867 - 474 pages
...without the sphere. Therefore the plane XYZ is a tangent to the sphere. PROPOSITION IV. The angles formed by two arcs of great circles is equal to the angle contained by the tangents drawn to these arcs at their point of intersection, and is measured by the... | |
 | Charles Davies, Adrien Marie Legendre - Geometry - 1869 - 470 pages
...quadrant DFA round the point D, its extremity A will describe an arc of a great circle. PROPOSITION IV. THEOREM. The angle formed by two arcs of great circles, is equal to that formed by the tangents to these arcs at their point of intersection, and is measured by the arc... | |
 | Elias Loomis - Geometry - 1871 - 302 pages
...radii ; in which case, the centers and the point of contact lie in on* straight line. PROPOSITION VII. THEOREM. The angle formed by two arcs of great 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 cir cle described... | |
 | Charles Davies - Geometry - 1872 - 464 pages
...quadrant DFA round the point D, its extremity A will describe an arc of a great circle. PROPOSITION IV. THEOREM. The angle formed by two arcs of great circles, is equal to that formed by the tangents to these arcs at their point of intersection, and is measured by the arc... | |
 | Adrien Marie Legendre - Geometry - 1874 - 500 pages
...quadrant DFA round the point D, its 'extremity A will describe an arc of a great circle. PROPOSITION IV. THEOREM. The angle formed by two arcs of great circles, is equal to that formed by the tangents to these arcs at their point of intersection, and is measured by the arc... | |
 | Elias Loomis - Conic sections - 1877 - 458 pages
...be out of the arc of a great circle ADB. Therefore the shortest path, etc. • ... PROPOSITION VII. THEOREM. The angle formed by two arcs of great circles is equal to the an~ gle formed by the tangents of those arcs at the point of their intersection, and is measured by... | |
 | Harvard University - Geometry - 1899 - 39 pages
...straight line joining the centres of the spheres, and the centre of which is in that line. THEOREM VII. The angle formed by two arcs of great circles is equal to the angle between the planes of the circles, and is measured by the arc of a great circle described from its... | |
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... this point of intersection, as a pole, and limited by the sides, produced if necessary. Let the angle BAC be formed by the two arcs AB, AC ; then it will be equal to the angle FAG formed by the tangents AF, AG, and be measured by the arc DE, described... 
