On Delisle's geographical projection

TL;DR

This paper explores Joseph-Nicolas Delisle's geographical projection, analyzing Euler's mathematical study of it and its significance in 18th-century mathematical geography.

Contribution

It presents a detailed analysis of Delisle's projection and Euler's mathematical insights, highlighting historical and geometric aspects of 18th-century geography.

Findings

Euler's study clarified the mathematical properties of Delisle's projection.

The paper highlights the importance of metric geometry in understanding geographical projections.

Historical context of 18th-century scientific collaboration is discussed.

Abstract

Joseph-Nicolas Delisle was one of the most important scientists at the Saint Petersburg Academy of Sciences during the first period when Euler was working there. Euler was helping him in his work on astronomy and in geography. In this paper, Delisle's geographical projection is presented and Euler's study of this projection isexplained, highlighting some important mathematical points, in particular on the metric geometry of surfaces.The final version of this paper will appear in the book \emph{Mathematical Geography in the Eighteenth Century: Euler, Lagrange and Lambert}, ed. Renzo Caddeo and Athanase Papadopoulos, Springer International Publishing, 2022.