All these foregoing sciences are, properly speaking, speculative. There is indeed in every science a practical side, as Avicenna teaches in the first book of his Art of Medicine. Nevertheless, of Moral Philosophy alone can it be said that it is in the special and autonomatic sense practical, dealing as it does with human conduct with reference to virtue and vice, beatitude and misery. All other sciences are called speculative: they are not concerned with the deeds of the present or future life affecting man's salvation or damnation. All procedures of art and of nature are directed to these moral actions, and exist on account of them. They are of no account except in that they help forward right action. Thus practical and operative sciences, as experimental alchemy and the rest, are regarded as speculative in reference to the operations with which moral or political science is concerned. This science is the mistress of every department of philosophy. It employs and controls them for the advantage of states and kingdoms. It directs the choice of men who are to study in sciences and arts for the common good. It orders all members of the state or kingdom so that none shall remain without his proper work.

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.

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Et hæc scientia certificat omnia naturalia et artificialia in particulari et in propria disciplina, per experientiam perfectam; non per argumenta, ut scientiæ pure speculativae, nec per debiles et imperfecta experientias ut scientiae operativæ. Et ideo hæc est domina omnium scientiarum præcedentium, et finis totius speculationis.

[H]aec vocatur scientia experimentalis, quae negligit argumenta, quoniam non certificant, quantumcunque sint fortia, nisi simul adsit experientia conclusionis. Et ideo haec docet experiri conclusiones nobiles omnium scientiarum, quae in aliis scientiis aut probantur per argumenta, aut investigantur per experientias naturales et imperfectas...

I have labored much in sciences and languages, and I have up to now devoted forty years [to them] after I first learned the Alphabetum; and I was always studious. Apart from two of these forty years I was always [engaged] in study [or at a place of 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 [as a Magister], 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.

I use the example of the rainbow and of the phenomena connected with it, of which sort are the circle around the sun and the stars, likewise the rod lying at the side of the sun or of a star which appears to the eye in a straight line... called the rod by Seneca, and the circle is called the corona, which often has the colors of the rainbow. But neither Aristotle nor Avicenna, in their Natural Histories, has given us knowledge of things of this sort, nor has Seneca, who composed a special book on them. But Experimental Science makes certain of them. [The experimenter] considers rowers and he finds the same colors in the falling drops dripping from the raised oars when the solar rays penetrate drops of this sort. It is the same with waters falling from the wheels of a mill; and when a man sees the drops of dew in summer of a morning lying on the grass in the meadow or the field, he will see the colors. And in the same way when it rains, if he stands in a shady place and if the rays beyond it pass through dripping moisture, then the colors will appear in the shadow nearby; and very frequently of a night colors appear around the wax candle. Moreover, if a man in summer, when he rises from sleep and while his eyes are yet only partly opened, looks suddenly toward an aperture through which a ray of the sun enters, he will see colors. And if, while seated beyond the sun, he extend his hat before his eyes, he will see colors; and in the same way if he closes his eye, the same thing happens under the shade of the eyebrow; and again, the same phenomenon occurs through a glass vessel filled with water, placed in the rays of the sun. Or similarly if any one holding water in his mouth sprinkles it vigorously into the rays and stands to the side of the rays; and if rays in the proper position pass through an oil lamp hanging in the air, so that the light falls on the surface of the oil, colors will be produced. And so in an infinite number of ways, as well natural as artificial, colors of this sort appear, as the careful experimenter is able to discover.

And because this Experimental Science is wholly ignored by the general run of students, for that reason I can not convince people of its utility unless I show at the same time its excellence and its property. This science alone, then, knows how to test perfectly by experience what can be done by nature, what by the industry of art, what by imposture; what the incantations, conjurations, invocations, deprecations, sacrifices (which are magical devices) seek and dream of; and what is done in them, so that all falsity may be removed and that only the truth of art and nature be retained. This science alone teaches one to consider all the insanities of magicians, not that they may be confirmed but that they may be avoided, just as logic considers sophistical argument.

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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.

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.

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.

For the things of this world cannot be made known without a knowledge of mathematics. For this is an assured fact in regard to celestial things, since two important sciences of mathematics treat of them, namely theoretical astrology and practical astrology. The first … gives us definite information as to the number of the heavens and of the stars, whose size can be comprehended by means of instruments, and the shapes of all and their magnitudes and distances from the earth, and the thicknesses and number, and greatness and smallness, … It likewise treats of the size and shape of the habitable earth … All this information is secured by means of instruments suitable for these purposes, and by tables and by canons .. For everything works through innate forces shown by lines, angles and figures.

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There are in fact four very significant stumbling blocks in the way of grasping the truth, which hinder every man however learned, and scarcely allow anyone to win a clear title to wisdom, namely, the example of weak and unworthy authority, longstanding custom, the feeling of the ignorant crowd, and the hiding of our own ignorance while making a display of our apparent knowledge.