This work presents the principle of continuity in the natural philosophy of Josip Ruđer Bošković. We find continuity in the natural sciences, mathematics, theology, philosophy, history, and the question of continuity has been the subject of discussions since the very beginning of human thought. The concept of continuity was discussed by various philosophers such as Parmenides, Heraclitus, Plato, Aristotle, Leibniz. In Bošković, we find an a priori and inductive proof of the principle of continuity. Inductive proof confirms the principle of continuity as very reliable, but not completely certain, while metaphysical proof should confirm it as a completely certain and infallible, a priori proven principle. Bošković creates a metaphysical proof of the principle of continuity within the framework of the development of his theory of mutual forces. Evidence refers to a change in place over time and to a change in the intensity of a physical property. Bošković proves the continuity of these changes using the reductio ad absurdum method, reducing every assumption of a jump to an absurdity. Consequently, continuity remains as the only possibility, or necessity. There are several objections against the principle of continuity, and the main counterexample is the example of a jump that occurs when one body collides with another. In order to avoid an impact, and so a jump, Bošković introduces a repulsive force that stops the bodies moving closer to each other before they touch.