"Mathematics is the gate and key of the sciences. ... Neglect of mathematics works injury to all knowledge, since he who is ignorant of it cannot know the other sciences or the things of this world. And what is worse, men who are thus Ignorant are unable to perceive their own ignorance and so do not seek a remedy."

“Many secrets of art and nature are thought by the unlearned to be magical.”

“Argument is conclusive... but... it does not remove doubt, so that the mind may never rest in the sure knowledge of the truth, unless it finds it by the method of experiment. 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.”

“I shall draw... a figure (which all these matters are made clear as far as possible on a surface, but the full demonstration would require a body like the eye... The eye of a cow, pig, and other animals can be used for illustration, if anyone wishes to experiment.”

“One man I know, and one only, who can be praised for his achievements in this science. Of discourses and battles of words he takes no heed: he follows the works of wisdom, and in these finds rest. What others strive to see dimly and blindly, like bats in twilight, he gazes at in the full light of day, because he is a master of experiment. Through experiment he gains knowledge of natural things, medical, chemical, indeed of everything in the heavens or earth. He is ashamed that things should be known to laymen, old women, soldiers, ploughmen, of which he is ignorant. Therefore he has looked closely into the doings of those who work in metals and minerals of all kinds; he knows everything relating to the art of war, the making of weapons, and the chase; he has looked closely into agriculture, mensuration, and farming work; he has even taken note of the remedies, lot casting, and charms used by old women and by wizards and magicians, and of the deceptions and devices of conjurors, so that nothing which deserves inquiry should escape him, and that he may be able to expose the falsehoods of magicians. If philosophy is to be carried to its perfection and is to be handled with utility and certainty, his aid is indispensable. As for reward, he neither receives nor seeks it. If he frequented kings and princes, he would easily find those who would bestow on him honours and wealth. Or, if in Paris he would display the results of his researches, the whole world would follow him. But since either of these courses would hinder him from pursuing the great experiments in which he delights, he puts honour and wealth aside, knowing well that his wisdom would secure him wealth whenever he chose. For the last three years he has been working at the production of a mirror that shall produce combustion at a fixed distance; a problem which the Latins have neither solved nor attempted, though books have been written upon the subject.”

“I have labored much in sciences and languages, and I have up to now devoted forty years after I first learned the Alphabetum; and I was always studious. Apart from two of these forty years I was always in study , and I had many expenses just as others commonly have. Nevertheless, provided I had first composed a compendium, I am certain that within quarter or half a year I could directly teach a solicitous and confident person whatever I know of these sciences and languages. And it is known that no one worked in so many sciences and languages as I did, nor so much as I did. Indeed, when I was living in the other state of life , people marveled that I survived the abundance of my work. And still, I was just as involved in studies afterwards, as I had been before. But I did not work all that much, since in the pursuit of Wisdom this was not required.”

“Everything in nature completes its action through its own force and species alone... as, for example, fire by its own force dries and consumes and does many things. Therefore vision must perform the act of seeing by its own force. But the act of seeing is the perception of a visible object at a distance, and therefore vision perceives what is visible by its own force multiplied to the object. Moreover, the species of the things of world are not fitted by nature to effect the complete act of vision at once, because of its nobleness. Hence these must be aided by the species of the eye, which travels in the locality of the visual pyramid, and changes the medium and ennobles it, and renders it analogous to vision, and so prepares the passage of the species itself of the visible object... Concerning the multiplication of this species, moreover, we are to understand that it lies in the same place as the species of the thing seen, between the sight and the thing seen, and takes place along the pyramid whose vertex is in the eye and base in the thing seen. And as the species of an object in the same medium travels in a straight path and is refracted in different ways when it meets a medium of another transparency, and is reflected when it meets the obstacles of a dense body; so is it also true of the species of vision that it travels altogether along the path of the species itself of the visible object.”