… The motto is "All the world's knowledge" I want to make sure my translation of Omnes scientam mundi is acceptable.
Sorry, your translation is not acceptable; with regard to the grammatical laws of Latin it should be: Omnis mundi scientia
(so-called closed arrangemnt of words), but stylistically you should perhaps prefer: Tota omnium hominum scientia,
i.e. word for word: The entire knowledge of all human beings.
all] The Latin adjective totus, a, um
denotes a thing in its entireness.
world] Horace uses the term mundus
denoting mankind as a whole; but you can also say ‚omnes homines
‘, genitive ‚omnium hominum
“ i.e. of the whole mankind (v.s.).
Also, what would be "The Great Imperial Library" in Latin?
The Vatican uses the term ‚Bibliotheca maxima pontificia‘; therefore we could say
‚Bibliotheca maxima imperatoria