This may be a real stretch, but the passage may be a translation of a
line in chapter 10 of _Tom Sawyer_. "The boys (they) fixed their
eyes (Augen) on the goal of their hopes and bent their work to win it."
I wish my understanding of German were better, but I can see how a
translator might take the word "bent" which Twain used to mean "a fixed
course" and assume that he meant to "double something over on itself"
(verdoppelten). I don't know how the concept of "a lost goal" fits into
the translation, but maybe someone more familiar with German can work
out the rest of the puzzle.