  We consider the mathematical theory of geographical maps, with an emphasis on
the eighteenth century works of Euler, Lagrange and Delisle. This period is
characterized by the frequent use of maps that are no more obtained by the
stereographic projection or its variations, but by much more general maps from
the sphere to the plane. More especially, the characteristics of the desired
geographical maps were formulated in terms of an appropriate choice of the
images of the parallels and meridians, and the mathematical properties required
by the map concern the distortion of the maps restricted to these lines. The
paper also contains some notes on the general use of mathematical methods in
cartography in Greek Antiquity and in the modern period, and on the mutual
influence of the two fields, mathematics and geography. The final version of
this paper will appear in Ganita Bharati (Indian mathematics).
