Without context, your question is too broad (there are many examples from the Ancient world, Ancient Rome/Greece, Medieval world, Renaissance, etc. that prove and disprove your assumption that armies ‘get stronger’ as the conquer)
Are you thinking about modern armies (ie post 1700AD onwards?) or medieval ones (600AD-1500AD) or something else?
You are also assuming that supply lines are a necessity (they are in modern wars, but ancient warfare didn’t require such a focus on logistics, they didn’t need a constant supply of gasoline for example) and that armies are not reinforced as they conquer, which isn’t the case (after conquering a foothold, many armies bring reinforcements and make up for any losses over time)
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