Perverting beauty is also work of lust.

Again, the admiration of beauty is beauty itself. When twisted to lust, then it is not the same thing we are talking about.

The admiration comes first. Perversion is what infest and contaminates admiration to lust.

Also, will and desire have a different order in Aristotle.

The will of something comes first. The desire is when one is specific to accomplish the will.

If you mean Eros as synonym to desire, I would need to reword some of my previous sentences.

Again, cottage life is a topic of admiration to those contemplating beauty per se.