Final answer:
Muslim thinkers al-Farabi and Ibn Sina engaged with European political thought by translating and developing ancient Greek philosophy, which influenced the Renaissance and Enlightenment in Europe.
Step-by-step explanation:
The Muslim thinkers al-Farabi and Ibn Sina, who were engaged with European traditions of political thought, did so primarily through their revival and innovative development of ancient Greek philosophy. These scholars, deeply influenced by figures like Aristotle and Plato, translated and preserved classical Greek texts in Arabic, which later became the bedrock for European intellectual movements, including the Italian Renaissance and Enlightenment. In doing so, they bridged a cultural and philosophical gap between the Islamic world and Europe, introducing complex systems of logic, medicine, and scientific thinking that had been at the risk of being lost with the decline of the Roman Empire. Additionally, their work in philosophy, science, law, and theology intersected with and influenced European theologians and philosophers, indicating a deep cross-cultural exchange of ideas.