On the basis of what was rationalism developed in Western European philosophy? a) analogies; b) induction; c) deductions; d) analysis; e) mathematical analysis.

The correct answer is e) mathematical analysis.<br /><br />Rationalism in Western European philosophy was developed on the basis of mathematical analysis. Rationalists believed that reason and logical deduction were the primary sources of knowledge, and they emphasized the importance of mathematical reasoning in understanding the natural world. They sought to establish a systematic and rigorous method of inquiry based on mathematical principles, which they believed could lead to a more accurate and comprehensive understanding of reality.