The English version in use prior to the present one; so called because it was originally printed at Geneva (in 1560).
(The). The wine cup or beer pot. The pun is on Geneva, which is the synonym of gin. (Latin, bibo, I drink [gin].)
“Eh bien, Gudyil, lui dit le vieux major, quelle-diable de discipline? Vous avez déjà lu la Bible de Genève ce matin.” —Les Puritains d'Ecosse, part iii. chap. 2.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894