How did Leibniz distinguish truths of reason from truths of fact?

Gottfried Wilhelm Leibniz distinguished between truths of reason and truths of fact based on their necessity and the principles that govern them.1

• Truths of Reason: These are necessary propositions, such as those found in logic and mathematics, that hold true in all possible worlds. They are governed by the principle of contradiction, which states that a proposition and its negation cannot both be true; therefore, the nonexistence of a truth of reason would involve a logical contradiction.12
• Truths of Fact: These are contingent propositions that hold true only in some possible worlds, including the actual world. Their existence is not logically necessary but depends on God’s free choice. Consequently, they are governed by the principle of sufficient reason, which asserts that nothing is the case without an adequate reason to account for why it exists rather than not existing.12

In essence, while truths of reason are grounded in the internal consistency of ideas, truths of fact require an external explanation for their existence.21