Were there any successful flying machines that did not rely on Bernoulli's Principle? One of Leonardo da Vinci's flying machines appears to be a giant auger.  This design would not have exploited Bernoulli's Principle, but rather used the blade's rotation to push the air below it down to keep the craft airborne.



Image credit: Wikimedia

Were there any flying machines built like this that actually got off the ground?



EDIT: So maybe I have Bernoulli misunderstood, judging from the discussion.
How about all lighter-than-air vehicles:


Hot air balloons
Hydrogen- or helium-filled balloons
Airships


If you want to restrict the choice to heavier-than-air vehicles, rockets should still qualify.

You may also include VTOL aircraft which do not rely on their wings during hover, their internal turbo machinery would still use Bernoulli's principle, however, so for me they do not qualify.