Final answer:
The trends in military personnel and state revenue are linked to the increasing centralization of state authority over local elites between 1450 and 1750, leading to stronger centralized states with better-funded armies at the cost of local elite power.
Step-by-step explanation:
The trends in military personnel and state revenue shown in the table are best understood in the context of the increasing centralization of authority by the state at the expense of local elites during the period of 1450–1750. This period saw significant changes in the relationship between states and local elites, such as states strengthening their military and diminishing the independent power of local nobles and elites. Countries with centralized governments and well-developed bureaucracies were able to effectively tax their populations, thus having the resources to pay for military developments and recruit soldiers more efficiently. They became more powerful as a result. As states centralized authority, the need for large tax revenues by local lords diminished, and many local potentates lost their tax privileges. Simultaneously, monarchs increasingly replaced local vassals with salaried bureaucrats, reducing the influence of local elites. Moreover, centralization sometimes occurred at the expense of local military forces, as mentioned regarding the 'castle lords' who eventually faced challenges from central governments.