E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
Aimer mieux la manche que le bras. Cupboard love. Manche is a slang word; a gratuity given to a cicerone, cabman, or porter. It is the Italian buona mancia.
Jeter le manche apres la cognée. To throw the helve after the hatchet. To abandon what may be useful, out of caprice, because a part of what you expected has not been realised. A horse is stolen, and the man, in ill-temper, throws away saddle and bridle.