Final answer:
Louis XIV of France and Frederick the Great of Prussia are noted as two of the greatest monarchs in Europe from 1648 through 1815 due to their enhancement of national power and influence.
Step-by-step explanation:
Among the greatest monarchs of Europe from 1648 through 1815 were Louis XIV of France, known as "the Sun King," who exemplified a divine-right monarch with centralized power, and Frederick the Great of Prussia, who expanded Prussian territories through military conquest during the Seven Years' War. Louis XIV successfully enhanced France's global influence, moving the royal court to Versailles and keeping a tight leash on the nobility, while modernizing Paris. Meanwhile, Frederick the Great played a pivotal role in maintaining the balance of power within Europe through his military strategies and foreign alliances.