Commentatio mathematica... (original) (raw)
Commentatio mathematica...
By Bernhard Riemann
An essay of Bernhard Riemann
Commentatio mathematica, qua respondere tentatur quaestioni ab Illma Academia Parisiensi propositae:
> ``Trouver quel doit être l'état calorifique d'un corps solide homogène indéfeni pour qu'un système de courbes isothermes, à un instant donné, restent isothermes après un temps quelconque, de telle sorte que la température d'un point puisse s'exprimer en fonction du temps et de deux autres variables indépendantes.''
published inBernhard Riemann's Gesammelte Matheamtische Werke, edited by Heinrich Weber (2nd Edition, Teubner 1892, pp. 391-404), is available here in the following formats:
This essay was submitted to the Paris Academy in 1861, to compete for a prize relating to the conduction of heat. The second part of this essay contains some of the mathematical analysis underlying Riemann's inaugural lectureUeber die Hypothesen, welche der Geometrie zu Grunde liegenon the foundations of Geometry. A translation into English of an extract from this part of the essay is to be found in Volume II ofA Comprehensive Introduction to Differential Geometryby Michael Spivak (2nd Edition, Publish or Perish Inc, Berkeley, 1979, vol. II, pp. 179-182).
Links:
D.R. Wilkins
(dwilkins@maths.tcd.ie)
School of Mathematics
Trinity College, Dublin