Need a way to "check out" the revision history of a single file

I’m looking for a way to checkout a single file’s revision history. For example, a utility that will pull out the last N times a single file has changed and committed , and populate them in the same directory as
the repo has .gitignore *~.

I think I could do it by using git log file and for each log entry git checkout followed by a mv (or even better, ln).

(Thanks to Andrew Francis for helping)

I have a shell script now that does most of what I wanted.
utility git-versions.sh which pulls old versions out of git history by masinter · Pull Request #333 · Interlisp/medley (github.com)

with some drawbacks (I don’t know awk or sed).