a formal siege of fifteen days' open trenches,

[enkidu68]

Hi, folks this is coming from Colonel Jack by Daniel Defoe
I cannot comprehend this bold one compeletely, the country could have resisted to a siege which will last 15 more days and was made out of open trenches?
for he was master of no one place in the country that could have held out a formal siege of fifteen days' open trenches, and he knew all this very well; and therefore it seems, while the Duke of Vendôme resolved, if possible, to bring him to a battle, and to that end made dispositions to attack Luzara, we were surprised to find, the 15th of June 1702, the whole imperial army appeared in _battalia_, and in full march, to attack us.

 

[The Newt]

It sounds like the idea is "a formal siege carried out from open trenches, lasting 15 days."

 

[panjandrum]

he was master of no one place in the country that could have held out a formal siege of fifteen days' open trenches,

The relative clause in bold modifies "place in the country", not "country".

The quoted bit, above, means something like "None of the places in Italy that the Prince owned could have held out against a 15-day siege from open trenches."

It is written in the English of the time - published in 1722.

 

[Egmont]

It means that he did not control any well-defended, well-supplied cities. All the cities he controlled would have fallen to a simple, relatively weak siege (a siege from open trenches, that it, without defensive earthworks for the besieging army) after a short period of time (two weeks).