This is the 11447th most frequent French word.
reposez
"Reposez" means "rest" or "put down" in English.
Here, 'reposer' is used as a transitive verb, meaning 'to put back' or 'to rest an object,' and it indicates the action performed on the book.
Veuillez reposer le livre sur la table après l'avoir consulté.
Please put the book back on the table after reading it.
In this context, 'reposent' (from 'reposer') is used figuratively in the present tense to indicate that his arguments are supported or based on solid facts.
Ses arguments reposent sur des faits solides.
His arguments rest on solid facts.
In this usage, 'reposez' is used as a reflexive verb (se reposer) in the imperative mood, addressing the listener to advise them to take rest.