There are four great sciences, without which the other sciences cannot be known nor a knowledge of things secured ... Of these sciences the gate and key is mathematics ... He who is ignorant of this [mathematics] cannot know the other sciences nor the affairs of this world.
Experimental science is the queen of knowledge.
All science requires mathematics.
As regards authority I so proceed. Boetius says in the second prologue to his Arithmetic, 'If an inquirer lacks the four parts of mathematics, he has very little ability to discover truth.' And again, 'Without this theory no one can have a correct insight into truth.' And he says also, 'I warn the man who spurns these paths of knowledge that he cannot philosophize correctly.' And Again, 'It is clear that whosoever passes these by, has lost the knowledge of all learning.'
All science requires mathematics. [Editors' summary of Bacon's idea, not Bacon's wording.]
... mathematics is absolutely necessary and useful to the other sciences.
No one really knew the sciences except the Lord Robert, Bishop of Lincoln, by reason of his length of life and experience, as well as of his studiousness and zeal. He knew mathematics and perspective, and there was nothing which he was unable to know; and at the same time he was sufficiently acquainted with languages to be able to understand the saints and the philosophers and the wise men of antiquity but his knowledge of languages was not such as to enable him to effect translations until the latter portion of his life.
Vacuum stands and remains a mathematical space. A cube placed in a vacuum would not displace anything, as it would displace air or water in a space already containing those fluids.
One man alone had really known the sciences, namely, Robert, Bishop of Lincoln.
In the mathematics I can report no deficience, except that it be that men do not sufficiently understand the excellent use of the pure mathematics, in that they do remedy and cure many defects in the wit and faculties intellectual. For if the wit be too dull, they sharpen it; if too wandering, they fix it; if too inherent in the sense, they abstract it.
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.
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.
The calendar is intolerable to all wisdom, the horror of all astronomy, and a laughing stock from a mathematician's point of view.
But concerning vision alone is a separate science formed among philosophers, namely, optics, and not concerning any other sense ... It is possible that some other science may be more useful, but no other science has so much sweetness and beauty of utility. Therefore it is the flower of the whole of philosophy and through it, and not without it, can the other sciences be known.
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