Final answer:
The ideas introduced by Pythagoras, Plato, and Aristotle influenced Renaissance thinkers through their beliefs in the power of mathematics, the transcendence of the soul, and the importance of empirical observation.
Step-by-step explanation:
The ideas introduced by Pythagoras, Plato, and Aristotle greatly influenced Renaissance thinkers in several ways.
Pythagoras believed in the power of mathematics to explain the mysteries of the universe, including celestial movements and musical harmony. His Pythagorean theorem, a fundamental concept in geometry, continued to be taught in schools during the Renaissance.
Plato adopted the Pythagorean idea of transmigration of souls, which influenced his belief in the immortality of the soul and the idea of reincarnation. Plato also emphasized the superiority of mathematical thought over sensory observation as a means to attain ultimate knowledge.
Aristotle's philosophy, particularly his emphasis on the importance of empirical observation, influenced Renaissance thinkers in their approach to studying the world. This emphasis on direct observation and empirical knowledge had a significant impact on scientific advancements during the Renaissance.