Footnote from 1640

[bristolloggerheads]

This is a footnote on a petition of 1640. I can see "for avoydance of" and reference to "a bond" and the odd word but don't have enough to make sense of this note.
All suggestions welcomed,

[horselydown86]

A couple of the easier fragments:

to relinquish his dwelling...........in ye [?]

to purchase a peace

[bristolloggerheads]

Thanks for this - it looks like a bond could be bought "in pieces" so I guess that is what is being referred to here.