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General Theory of the Lambert Conformal Conic Projection: Cartography ...
U.S. Coast And Geodetic Survey
No preview available - 2014
angle arcs axis becomes called cent central meridian circle Coast and Geodetic complex variable computation conformal conic projection conjugate considered constant coordinates correct corresponding countries course curve denoting determined difference differentiation direction cosines distance e2 cos2 earth element of length ellipse equal equations expressed Fdudv follows formal formula functions Geodetic Survey given gives held hence identically isothermal orthogonal Lambert conformal conic Lambert projection latitude limited linear longitude mathematical method of projection necessary obtained parallel parametric perpendicular plane pole positions preserved problem radian radius ratio relation repre representation represented scale short similar sin2 Special Publication sphere spheroid square straight line sufficient surface tables taken tangent theory tion triangle u+iv United States Coast usual whole x+iy=f zero
Page 8 - A circular helix is given by the equations x = a cos t, y = a sin t, z = bt.
Page 5 - Those who preceded him in this work limited themselves to the development of a single method of projection, principally the perspective, but Lambert considered the problem of the representation of a sphere upon a plane from a higher standpoint and he stated certain general conditions that the representation was to fulfil, 5 the most important of these being the preservation of angles or conformality and equal surface or equivalence.
Page 6 - Lambert did not fully develop the theory of these two methods of projection, yet he was the first to express clearly the ideas regarding them. The former, conformality, has become of the greatest importance to pure mathematics, but both of them are of exceeding importance to the cartographer.