How does the principle of contradiction apply to Leibniz’s truths of reason?

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Engraved portrait of Gottfried Wilhelm von Leibniz with long curly hair, wearing a buttoned coat and cravat, facing forward. — Gottfried Wilhelm Leibniz German philosopher and mathematician Gottfried Wilhelm Leibniz, engraving, c. 1701.

In the philosophy of Gottfried Wilhelm Leibniz, the principle of contradiction serves as the foundational governing rule for "truths of reason."1

Leibniz distinguished these truths from "truths of fact" by their necessity; while truths of fact are contingent and depend on God’s free choice, truths of reason are necessary propositions that hold true in all possible worlds. The principle of contradiction dictates that a proposition and its negation cannot both be true simultaneously. Consequently, for Leibniz, the nonexistence of a truth of reason would involve a logical contradiction. These truths, which include the principles of logic, numbers, and geometry, establish an indubitable connection of ideas that are essential to true reasoning.21