The science of **geodesy** is part of mathematical geography, of which the arts of surveying and cartography are applications.

The investigation of triangles and other figures drawn upon the surface of a sphere is all-important in the sciences of astronomy, **geodesy** and geography.

In "**geodesy**," and the cognate subject "figure of the earth," the matter of greatest moment with regard to the sphere is the determination of the area of triangles drawn on the surface of a sphere - the so-called "spherical triangles"; this is a branch of trigonometry, and is studied under the name of spherical trigonometry.

Legendre's theorem is a fundamental one in **geodesy**, and his contributions to the subject are of the greatest importance.

It will thus be seen that Legendre's works have placed him in the very foremost rank in the widely distinct subjects of elliptic functions, theory of numbers, attractions, and **geodesy**, and have given him a conspicuous position in connexion with the integral calculus and other branches of mathematics.

He remained at Dorpat, occupied with researches on double stars and **geodesy** till 1839, when he removed to superintend the construction of the new central observatory at Pulkowa near St Petersburg, afterwards becoming director.

Hence **geodesy** may be regarded as a branch of practical astronomy.