An Etymological Dictionary of the German Language/Annotated/desto

by Friedrich Kluge

desto, adverb, ‘so much the,’ from the equivalent Middle High German dëste, dëst, late Old High German dësde; in an earlier form two words, dës diu (dës, genitive, diu, instrumental of the article); the Gothic word was simply þê (instrumental of the article); thus, too, Anglo-Saxon þŷ before comparatives, English the (the more, desto mehr).