Rōmānōs ab Hannibale victōs esse cōnstat, it is well established that the Romans were defeated by Hannibal.
PECULIARITIES IN CONNECTION WITH THE USE OF THE DATIVE.
[358]. 1. The English for does not always correspond to a Dative notion in Latin, but is often the equivalent of prō with the Ablative, viz. in the senses—
a) In defense of; as,—
prō patriā morī, to die for one's country.
b) Instead of, in behalf of; as,—
ūnus prō omnibus dīxit, one spoke for all;
haec prō lēge dicta sunt, these things were said for the law.
c) In proportion to; as,—
prō multitūdine hominum eōrum fīnēs erant angustī, for the population, their territory was small.
2. Similarly, English to when it indicates motion is rendered in Latin by ad.