Here you'll find older versions of Calibre for installation with Homebrew.
brew install phaseone/calibre-cask-versions/<formula>
Replace <formula> with a major release of Calibre. e.g. brew install phaseone/calibre-cask-versions/calibre4 will install the 4.23.0 release of Calibre.
Or brew tap phaseone/calibre-cask-versions and then brew install <formula>.
brew help, man brew or check Homebrew's documentation.
For this tap repo, I've included the latest minor version of legacy versions of Calibre. If you'd like to see a version here other than those included, please submit a PR with the formula and rationale for its inclusion.