Elements of Spheroidal Trigonometry Drawn from the Method of Maxima and Minima

Leonhard Euler

Chapter Chapter 11 in Mathematical Geography in the Eighteenth Century: Euler, Lagrange and Lambert, 2022, pp 205-242 from Springer

Abstract: Abstract In this memoir, Euler’s aim is to develop the geometry and the trigonometry of the spheroid, which he considers as being the figure of the surface of the Earth. He starts by presenting the mathematical theory that is behind the measures of degrees of meridians that were conducted during the Peru and Lapland expeditions, the possible errors made during these measurements and their impact on the knowledge of the true figure of the Earth. The following are among the mathematical results contained in this memoir: Given the latitude of a point, to determine its distance to the centre of the Earth; given two points of which we know the latitudes and the difference of their longitudes, to find the shortest path between them; to determine the ratio of the diameter of the Equator to the axis of the Earth by a construction done in a small portion of the Earth. The methods are those of differential calculus and the calculus of variations.

Date: 2022
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DOI: 10.1007/978-3-031-09570-2_11

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