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The paper describes examples of applying elliptic integrals in mathematical cartography calculations, i.e. related with cartographic projections and reference surfaces. Selected equations and algorithms used in calculating the meridian arc length on an oblate spheroid, meridian arc length on a tri-axial ellipsoid, the equation and length of the geodesic, and coordinate transformation on an oblate spheroid, have been applied. Examples of elliptic integral application for the construction of cartographic projections...