A work on tidal theory... led me to Lagrange's Mécanique analytique and thereby I returned to those ideas of analysis. All the developments in that work were transformed through the principles of the new analysis in such a simple way that the calculations often came out more than ten times shorter than in Lagrange's work.

Note: the "ideas of analysis" to which he returned, are those quoted above. - Ausdehnungslehre (1844)