And it is difficult to find any of these inventions that has done as much good as the discovery of those marvelous telescopes, which, being in use for only a short time, have already revealed more new stars in the sky, and numerous other objects above the Earth, than we had seen before: such that, projecting our vision much farther than the imagination of our ancestors was accustomed to go, they seem to have opened the path for us to come to a much greater and more perfect knowledge of nature than they had. But, to the shame of our sciences, this invention, so useful and so admirable, was first found only by experiment and good fortune. And it is only on this model that all the others that we have seen have been made, without anyone that I know of having sufficiently determined the shapes that the lenses 1 ought to have. And, inasmuch as the execution of the things of which I shall speak will depend upon the industry of artisans, who ordinarily have not done much studying, I shall attempt to make myself intelligible to everyone, without omitting anything or assuming anything known from other sciences. This is why I shall begin with the explanation of light and of its rays; then, having made a brief description of the parts of the eye, I will specifically say how vision operates, and then, having remarked on all the techniques that can make it more perfect, I will teach how the field of these techniques may be broadened by the inventions which I will describe. Now, having no other occasion to speak of light here, except to explain how its rays enter the eye, and how they can be deflected by the various bodies they encounter, there is no need for me to attempt to say what its true nature is, and I believe that it will suffice for me to make use of two or three comparisons which aid in conceiving it in the manner which seems to me the most correct to explain all of its properties that experience has made known to us, and then to deduce all the other properties which cannot so easily be noticed.
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The town of La Haye, which lies 47 kilometers south of Tours, has subsequently been renamed Descartes. When Descartes was thirteen and one-half months old, his mother, Jeanne Brochard, died in childbirth. He followed the usual course of studies, which included five or six years of grammar school, including Latin and Greek grammar, classical poets, and Cicero, followed by three years of philosophy curriculum.
By rule, the Jesuit philosophy curriculum followed Aristotle; it was divided into the then-standard topics of logic, morals, physics, and metaphysics. The Jesuits also included mathematics in the final three years of study. Aristotle himself frequently discussed the positions of his ancient predecessors. Within this framework, and taking into account the reading of Cicero, Descartes would have been exposed in school to the doctrines of the ancient atomists, Plato, and the Stoics, and he would have heard of the skeptics.
Hence, although scholastic Aristotelian philosophy was dominant in his school years, it was not the only type of philosophy that he knew.
His family wanted Descartes to be a lawyer, like his father and many other relatives. To this end, he went to Poitiers to study law, obtaining a degree in But he never practiced law or entered into the governmental service such practice would make possible Rodis-Lewis , 18— Instead, he became a gentleman soldier, moving in to Breda, to support the Protestant Prince Maurice against the Catholic parts of the Netherlands which parts later formed Belgium , which were controlled by Spain—a Catholic land, like France, but at this point an enemy.
Beeckman set various problems for Descartes, including questions about falling bodies, hydrostatics, and mathematical problems. Since antiquity, mathematics had been applied to various physical subject matters, in optics, astronomy, mechanics focusing on the lever , and hydrostatics. Beeckman and Descartes brought to this work a commitment to atoms as the basic constituents of matter; as had ancient atomists, they attributed not only size, shape, and motion but also weight to those atoms At this time, Descartes discovered and conveyed to Beeckman the fundamental insight that makes analytic geometry possible: the technique for describing lines of all sorts by using mathematical equations involving ratios between lengths.
Descartes himself did not foresee replacing geometrical constructions with algebraic formulas; rather, he viewed geometry as the basic mathematical science and he considered his algebraic techniques to provide a powerful alternative to actual compass-and-ruler constructions when the latter became too intricate.
Descartes attended the coronation and was returning to the army when winter caught him in the small town of Ulm or perhaps Neuburg , not far from Munich. On the night of November 10, , Descartes had three dreams that seemed to provide him with a mission in life. The dreams themselves are interesting and complex see Sebba Descartes took from them the message that he should set out to reform all knowledge.
He decided to begin with philosophy, since the principles of the other sciences must be derived from it —2. In , he recalled having read various works in philosophy around the year , written by well-known commentators on Aristotle: Francisco Toledo —96 , Antonio Rubio — , and the Coimbran commentators active ca.
He was in France part of the time, visiting Poitou to sell some inherited properties in and visiting Paris. He went to Italy — Upon his return he lived in Paris, where he was in touch with mathematicians and natural philosophers in the circle of his long-time friend and correspondent Marin Mersenne — While in Paris, he worked on some mathematical problems and derived the sine law of refraction, which facilitated his work on formulating mathematically the shapes of lenses later published in the Dioptrics.
His major philosophical effort during these years was on the Rules, a work to convey his new method. In the Rules, he sought to generalize the methods of mathematics so as to provide a route to clear knowledge of everything that human beings can know. His methodological advice included a suggestion that is familiar to every student of elementary geometry: break your work up into small steps that you can understand completely and about which you have utter certainty, and check your work often.
But he also had advice for the ambitious seeker of truth, concerning where to start and how to work up to greater things. These faculties allow the seeker of knowledge to combine simple truths in order to solve more complex problems, such as the solution to problems in optics , or the discovery of how a magnet works By the end of , Descartes had abandoned work on the Rules, having completed about half of the projected treatise.
In that year he moved to the Dutch Netherlands, and after that he returned to France infrequently, prior to moving to Sweden in In Summer, , an impressive set of parhelia, or false suns, were observed near Rome.
When Descartes heard of them, he set out to find an explanation. He ultimately hypothesized that a large, solid ice-ring in the sky acts as a lens to form multiple images of the sun . This work interrupted his investigations on another topic, which had engaged him for his first nine months in the Netherlands —the topic of metaphysics, that is, the theory of the first principles of everything that there is.
The metaphysical objects of investigation included the existence and nature of God and the soul , Subsequently, Descartes mentioned a little metaphysical treatise in Latin—presumably an early version of the Meditations—that he wrote upon first coming to the Netherlands , While working on the parhelia, Descartes conceived the idea for a very ambitious treatise.
This work eventually became The World, which was to have had three parts: on light a general treatise on visible, or material, nature , on man a treatise of physiology , and on the soul. Only the first two survive and perhaps only they were ever written , as the Treatise on Light and Treatise on Man. In these works, which Descartes decided to suppress upon learning of the condemnation of Galileo , , he offered a comprehensive vision of the universe as constituted from a bare form of matter having only length, breadth, and depth three-dimensional volume and carved up into particles with size and shape, which may be in motion or at rest, and which interact through laws of motion enforced by God —4.
These works contained a description of the visible universe as a single physical system in which all its operations, from the formation of planets and the transmission of light from the sun, to the physiological processes of human and nonhuman animal bodies, can be explained through the mechanism of matter arranged into shapes and structures and moving according to three laws of motion.
In fact, his explanations in the World and the subsequent Principles made little use of the three laws of motion in other than a qualitative manner. After suppressing his World, Descartes decided to put forward, anonymously, a limited sample of his new philosophy, in the Discourse with its attached essays.
It offered some initial results of his metaphysical investigations, including mind—body dualism. It did not, however, engage in the deep skepticism of the later Meditations, nor did it claim to establish, metaphysically, that the essence of matter is extension.
This last conclusion was presented merely as a hypothesis whose fruitfulness could be tested and proven by way of its results, as contained in the attached essays on Dioptrics and Meteorology.
In his Meteorology, Descartes described his general hypothesis about the nature of matter, before continuing on to provide accounts of vapors, salt, winds, clouds, snow, rain, hail, lightning, the rainbow, coronas, and parhelia. He presented a corpuscularian basis for his physics, which denied the atoms-and-void theory of ancient atomism and affirmed that all bodies are composed from one type of matter, which is infinitely divisible In the World, he had presented his non-atomistic corpuscularism, but without denying void space outright and without affirming infinite divisibility — Indeed, Descartes claimed that he could explain these qualities themselves through matter in motion , a claim that he repeated in the Meteorology —6.
The four Aristotelian elements, earth, air, fire, and water, had substantial forms that combined the basic qualities of hot, cold, wet, and dry: earth is cold and dry; air is hot and wet; fire is hot and dry; and water is cold and wet. For earth, that activity is to approach the center to the universe; water has the same tendency, but not as strongly. For this reason, Aristotelians explained, the planet earth has formed at the center, with water on its surface.
This form then organizes that matter into the shape of a rabbit, including organizing and directing the activity of its various organs and physiological processes.
Although in the World and Meteorology Descartes avoided outright denial of substantial forms and real qualities, it is clear that he intended to deny them ; ; , , Two considerations help explain his tentative language: first, when he wrote these works, he was not yet prepared to release his metaphysics, which would support his hypothesis about matter and so rule out substantial forms ; and, second, he was sensitive to the prudential value of not directly attacking the scholastic Aristotelian position , since it was the accepted position in university education and was strongly supported by orthodox theologians, both Catholic and Protestant —6; In , Descartes fathered a daughter named Francine.
This was the Meditations, and presumably he was revising or recasting the Latin treatise from In the end, he and Mersenne collected seven sets of objections to the Meditations, which Descartes published with the work, along with his replies , Some objections were from unnamed theologians, passed on by Mersenne; one set came from the Dutch priest Johannes Caterus; one set was from the Jesuit philosopher Pierre Bourdin; others were from Mersenne himself, from the philosophers Pierre Gassendi and Thomas Hobbes, and from the Catholic philosopher-theologian Antoine Arnauld.
As previously mentioned, Descartes considered the Meditations to contain the principles of his physics. Descartes and his followers included topics concerning the nature of the mind and mind—body interaction within physics or natural philosophy, on which, see Hatfield Once Descartes had presented his metaphysics, he felt free to proceed with the publication of his entire physics.
However, he needed first to teach it to speak Latin , the lingua franca of the seventeenth century. He hatched a scheme to publish a Latin version of his physics the Principles together with a scholastic Aristotelian work on physics, so that the comparative advantages would be manifest.
For this purpose, he chose the Summa philosophiae of Eustace of St. That part of his plan never came to fruition. Ultimately, his physics was taught in the Netherlands, France, England, and parts of Germany.
The Principles appeared in Latin in , with a French translation following in He also presented an image of the relations among the various parts of philosophy, in the form of a tree: Thus the whole of philosophy is like a tree. The roots are metaphysics, the trunk is physics, and the branches emerging from the trunk are all the other sciences, which may be reduced to three principal ones, namely medicine, mechanics and morals.
His intent had been also to explain in depth the origins of plants and animals, human physiology, mind—body union and interaction, and the function of the senses. In the end, he had to abandon the discussion of plants and animals Princ.
Nonetheless, he was drawn into theological controversy with Calvinist theologians in the Netherlands. Already by , Gisbert Voetius — , a theologian at Utrecht, expressed his displeasure over this to Mersenne Controversy brewed, at first between Regius and Voetius, with Descartes advising the former. The controversy simmered through the mids. Descartes replied with his Comments on a Certain Broadsheet In the mids, Descartes continued work on his physiological system, which he had pursued throughout the s.
He allowed his Treatise on Man to be copied —7 and he began a new work , Description of the Human Body, in which he sought to explain the embryonic development of animal bodies.
During this period he corresponded with Princess Elisabeth, at first on topics in metaphysics stemming from her reading of the Meditations and then on the passions and emotions. Eventually, he wrote the Passions of the Soul , which gave the most extensive account of his behavioral physiology to be published in his lifetime and which contained a comprehensive and original theory of the passions and emotions. In , Descartes accepted the invitation of Queen Christina of Sweden to join her court.
On the day he delivered them to her, he became ill. He never recovered. He died on 11 February Readers of the philosophical works of Immanuel Kant are aware of the basic distinction between his critical and precritical periods. Readers of the works of G. Leibniz are also aware of his philosophical development, although in his case there is less agreement on how to place his writings into a developmental scheme. In effect, he adopted a hypothetico-deductive scheme of confirmation, but with this difference: the range of hypotheses was limited by his metaphysical conclusions concerning the essence of mind and matter, their union, and the role of God in creating and conserving the universe.
Argumentative differences among the World, Discourse, and Meditations and Principles may then be seen as arising from the fact that in the s Descartes had not yet presented his metaphysics and so adopted an empirical mode of justification, whereas after he could appeal to his published metaphysics in seeking to secure the general framework of his physics.
Other scholars see things differently. John Schuster finds that the epistemology of the Rules lasted into the s and was superseded unhappily, in his view only by the metaphysical quest for certainty of the Meditations. Daniel Garber , 48 also holds that Descartes abandoned his early method after the Discourse. Machamer and McGuire believe that Descartes expected natural philosophy to meet the standard of absolute certainty through the time of the Meditations, and that he in effect admitted defeat on that score in the final articles of the Principles, adopting a lower standard of certainty for his particular hypotheses such as the explanation of magnetism by corkscrew-shaped particles.
Nikazahn Thus all the parts of the subtle matter which are touched by the side of the sun which faces us, tend in a straight line towards our eyes at the very moment that they are opened, without impeding each other and even without being impeded by the heavier parts of the transparent bodies which are between the two: Here you see balls A, B, C figs. And on this alone is founded the entire invention of the telescopes composed of two lenses placed in the two ends of a tube, which gave me occasion to write this Treatise. Finally, inasmuch as the action of light descartees in this respect the same laws as the movement of this ball, it must be said that, when its rays pass obliquely from one transparent body into another, which receives them more or less easily than the first, they are deflected in such a way that they always 7 Yes, Descartes really is creating the image of a tennis racket appearing out of nowhere to whack the ball downwards as it enters the water! The justification for this interpretation almost always involves citing one or another of a host descartees more or less obscure and often inconsistent references to ideas, their content, causes, resemblances or the lack of same to thoughts obscureimages, pictures, engravings, etc. It is the 7th discourse that Spinoza and Jelles are discussing. Discourse on Method, Optics, Geometry, and Meteorology.
In the first model, he compares light to a stick that allows a blind person to discern his environment through touch. Descartes says: You have only to consider that the differences which a blind man notes among trees, rocks, water, and similar things through the medium of his stick do not seem less to him than those among red, yellow, green, and all the other colors seem to us; and that nevertheless these differences are nothing other, in all these bodies, than the diverse ways of moving, or of resisting the movements of, this stick. He uses a metaphor of wine flowing through a vat of grapes, then exiting through a hole at the bottom of the vat. Now consider that, since there is no vacuum in Nature as almost all the Philosophers affirm, and since there are nevertheless many pores in all the bodies that we perceive around us, as experiment can show quite clearly, it is necessary that these pores be filled with some very subtle and very fluid material, extending without interruption from the stars and planets to us. Thus, this subtle material being compared with the wine in that vat, and the less fluid or heavier parts, of the air as well as of other transparent bodies, being compared with the bunches of grapes which are mixed in, you will easily understand the following: Just as the parts of this wine Descartes uses a tennis ball to create a proof for the laws of reflection and refraction in his third model.
DESCARTES DIOPTRICS PDF
The town of La Haye, which lies 47 kilometers south of Tours, has subsequently been renamed Descartes. When Descartes was thirteen and one-half months old, his mother, Jeanne Brochard, died in childbirth. He followed the usual course of studies, which included five or six years of grammar school, including Latin and Greek grammar, classical poets, and Cicero, followed by three years of philosophy curriculum. By rule, the Jesuit philosophy curriculum followed Aristotle; it was divided into the then-standard topics of logic, morals, physics, and metaphysics. The Jesuits also included mathematics in the final three years of study.