Mathematics is the gate and key to science.

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

[I]f in other sciences we should arrive at certainty without doubt and truth without error, it behooves us to place the foundations of knowledge in mathematics, in so far as disposed through it we are able to reach certainty in other sciences and truth by the exclusion of error.

But we must here state that we should not see anything if there were a vacuum. But this would not be due to some nature hindering species, and resisting it, but because of the lack of a nature suitable for the multiplication of species; for species is a natural thing, and therefore needs a natural medium; but in a vacuum nature does not exist.

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.

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.