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On the Construction of Geographical Maps

In: Mathematical Geography in the Eighteenth Century: Euler, Lagrange and Lambert

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  • Joseph-Louis Lagrange

Abstract

This is the translation of two memoirs of Lagrange that carry the same title. In these memoirs, Lagrange addresses the question of finding the general geographical maps in which the families of meridians and parallels are given as arbitrary families of lines. He then concentrates on the problem of finding the angle-preserving maps for which the meridians and the parallels are sent to circles. He introduces the definition of the local distorsion factor of an angle-preserving geographical map, which allows him to address in precise terms the question of finding maps of least distorsion. He gives a formula for this factor in special cases, in particular for maps which send meridians and parallels to circles or straight lines.

Suggested Citation

  • Joseph-Louis Lagrange, 2022. "On the Construction of Geographical Maps," Springer Books, in: Renzo Caddeo & Athanase Papadopoulos (ed.), Mathematical Geography in the Eighteenth Century: Euler, Lagrange and Lambert, chapter 0, pages 309-366, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-09570-2_15
    DOI: 10.1007/978-3-031-09570-2_15
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