Whoever despises the high wisdom of mathematics nourishes himself on delusion and will never still the sophistic sciences whose only product is an eternal uproar.

Those who condemn the supreme certainty of mathematics feed on confusion, and can never silence the contradictions of the sophistical sciences which lead to eternal quackery.

Our present work sets forth mathematical principles of philosophy. For the basic problem of philosophy seems to be to discover the forces of nature from the phenomena of motions and then to demonstrate the other phenomena from these forces. It is to these ends that the general propositions in books 1 and 2 are directed, while in book 3 our explanation of the system of the world illustrates these propositions.

Mechanics is the paradise of the mathematical sciences, because by means of it one comes to the fruits of mathematics.

The merit of painting lies in the exactness of reproduction. Painting is a science and all sciences are based on mathematics. No human enquiry can be a science unless it pursues its path through mathematical exposition and demonstration.

No human investigation can be called real science if it cannot be demonstrated mathematically.