Mathematics and map drawing in the eighteenth century

TL;DR

This paper explores 18th-century mathematical approaches to map drawing, focusing on the use of general sphere-to-plane maps and their properties, highlighting historical developments and the influence of mathematics on cartography.

Contribution

It analyzes the mathematical theories of map projection in the 18th century, emphasizing the shift from stereographic to more general mappings and their geometric properties.

Findings

Use of general sphere-to-plane maps in 18th-century cartography

Mathematical formulation of map characteristics via parallels and meridians

Historical influence of mathematics on geographical map design

Abstract

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).