On the Construction of Geographical Maps

Joseph-Louis Lagrange

Chapter Chapter 15 in Mathematical Geography in the Eighteenth Century: Euler, Lagrange and Lambert, 2022, pp 309-366 from Springer

Abstract: 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.

Date: 2022
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DOI: 10.1007/978-3-031-09570-2_15

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