At the bottom VS At the back

Hi,

Can I interchangeably use “at the bottom” rather than “at the back” in the following cases?

  • We’ll put the table and chairs under the tree at the bottom of the garden.

  • We’ll put the table and chairs under the tree at the back of the garden.

  • Don’t let this book gather dust at the back of a shelf.

  • Don’t let this book gather dust at the bottom of a shelf.

… bottom of the garden.
… back of the shelf.

You might just about get awau with ‘back of the garden’, but the bottom of a shelf is not really possible. A shelf’s bottom would be underneath it.
This should not be confused with ‘the bottom shelf’ which means ‘the lowest shelf’.