Is it permissible to download a book in PDF format from the Internet after purchasing its original copy, knowing that I want to read it on the computer without needing an Internet connection, and that the purpose of this is not distribution?

There is no harm in downloading the book as long as the questioner has purchased it. The purpose of protecting rights is to preserve the material and intellectual value of the book and prevent its degradation, and this is achieved through purchase and commitment not to distribute it.