Reasoning draws a conclusion, but does not make the conclusion certain, unless the mind discovers it by the path of experience.

For if any man who never saw fire proved by satisfactory arguments that fire burns. His hearer's mind would never be satisfied, nor would he avoid the fire until he put his hand in it that he might learn by experiment what argument taught.

... mathematics is absolutely necessary and useful to the other sciences.

There are two modes of acquiring knowledge, namely by reasoning and experience. Reasoning draws a conclusion and makes us grant the conclusion, but does not make the conclusion certain, nor does it remove doubt so that the mind may rest on the intuition of truth, unless the mind discovers it by the path of experience.

Argument is conclusive, but it does not remove doubt, so that the mind may rest in the sure knowledge of the truth, unless it finds it by the method of experiment.

There are two modes of knowledge: through argument and through experience. Argument brings conclusions and compels us to concede them, but it does not cause certainty nor remove doubts that the mind may rest in truth, unless this is provided by experience.

First, by the figurations of art there be made instruments of navigation without men to row them, as great ships to brooke the sea, only with one man to steer them, and they shall sail far more swiftly than if they were full of men; also chariots that shall move with unspeakable force without any living creature to stir them. Likewise an instrument may be made to fly withall if one sits in the midst of the instrument, and do turn an engine, by which the wings, being artificially composed, may beat the air after the manner of a flying bird.