By dint of
By means of; as a result of - especially by the means of force.
Dint is now an archaic word and only exists, as it were, by dint of this particular phrase. Dint itself derives from the Old English 'dynt'. In current language the word has migrated to 'dent'. How do we get to the meaning 'as a result of' from the word 'dint'? That's simply via the earliest version of the phrase, 'by dint of sword', which was used when a result was obtained by the use of force. This is an ancient usage and dates from at least the 14th century, when it was recorded in The romances of Rouland and Vernagu, circa 1330:
"Alle the londes that were in Spayne, With dint Of swerd wan Charlmain."
It was some centuries before 'by dint of' came to be used without the specific mention of swordplay, although that citation is itself fairly old - Samuel Butler's narrative poem Hudibras, 1664:
"Chace evil spirits away by dint Of Cickle, Horse-shoe, Hollow-flint."