Stabbing and running, how are they related?

When you literally run through some where, e.g.

I have run through the streets of London

it is quite clear what is meant.

At a slightly more figurative level one might say,

I will run through our procedures with you.

This is also clear. One is teaching another something quickly, as if to make their mind run through the information.

But if I were a pirate and I found a dead body, I might say

He's been run through with a cutlass!

Now, I know that to run through means to stab all the way through the body, but how has run through come to mean that?

Solution 1:

Run through in that sense is first found used by John Lydgate in the fifteenth century, but run alone can also mean ‘stab’ and is found for the first time in the work of the same author. Given the sense of run as some kind of rapid movement, its use to describe the act of penetrating the flesh with a blade may be understandable. Running through seems to perform the operation more conclusively.