In which part of history is this true? When Napoleon invaded italy, the cost of taking over the country is the same regardless of how much land he actually had. It's the same piece of land, with the same amount of defences.
In the common sense part of history, though I understand it's not well known.
If you own a large area of land, it will cost more to get resources from one part of it to another. Sieges take a lot of resources, like, a really big lot of them. The more land you have, the more resources you need
Lets look at it like this. Your siege needs 100 food every day, and your army needs 10 food a day to deliver the food to the siege.
-If you have a small area of land, you can get the food to your siege in 1 day. You need only send 120 food. (100 for siege, 20 for delivery men.)
-If you have a large area of land, it takes a week to get the food to your siege. You need to send 840 food. (700 for siege, as it needs to last a week before the next delivery, and 140 for the delivery men)
The battles are trivial, that's the problem. It takes 10mins for a fully defended sector to be taken.
Ah, so if my maths is right, it only takes 1.25 minutes for a siege to be broken.
10 minutes to defeat 8 armies, 1/8th of that to defeat 1 army.