DESCARTES DIOPTRICS PDF

In natural philosophy, he can be credited with several specific achievements: co-framer of the sine law of refraction, developer of an important empirical account of the rainbow, and proposer of a naturalistic account of the formation of the earth and planets a precursor to the nebular hypothesis. More importantly, he offered a new vision of the natural world that continues to shape our thought today: a world of matter possessing a few fundamental properties and interacting according to a few universal laws. This natural world included an immaterial mind that, in human beings, was directly related to the brain; in this way, Descartes formulated the modern version of the mind—body problem. In metaphysics, he provided arguments for the existence of God, to show that the essence of matter is extension, and that the essence of mind is thought. Descartes claimed early on to possess a special method, which was variously exhibited in mathematics, natural philosophy, and metaphysics, and which, in the latter part of his life, included, or was supplemented by, a method of doubt.

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In natural philosophy, he can be credited with several specific achievements: co-framer of the sine law of refraction, developer of an important empirical account of the rainbow, and proposer of a naturalistic account of the formation of the earth and planets a precursor to the nebular hypothesis.

More importantly, he offered a new vision of the natural world that continues to shape our thought today: a world of matter possessing a few fundamental properties and interacting according to a few universal laws. This natural world included an immaterial mind that, in human beings, was directly related to the brain; in this way, Descartes formulated the modern version of the mind—body problem.

In metaphysics, he provided arguments for the existence of God, to show that the essence of matter is extension, and that the essence of mind is thought. Descartes claimed early on to possess a special method, which was variously exhibited in mathematics, natural philosophy, and metaphysics, and which, in the latter part of his life, included, or was supplemented by, a method of doubt.

Descartes presented his results in major works published during his lifetime: the Discourse on the Method in French, , with its essays, the Dioptrics , Meteorology , and Geometry ; the Meditations on First Philosophy i. Important works published posthumously included his Letters in Latin and French, —67 ; World, or Treatise on Light , containing the core of his natural philosophy in French, ; Treatise on Man in French, , containing his physiology and mechanistic psychology; and the Rules for the Direction of the Mind in Latin, , an early, unfinished work attempting to set out his method.

Descartes was known among the learned in his day as a top mathematician, as the developer of a new and comprehensive physics or theory of nature including living things , and as the proposer of a new metaphysics. In the years following his death, his natural philosophy was widely taught and discussed. In the eighteenth century aspects of his science remained influential, especially his physiology, as did his project of investigating the knower in assessing the possibility and extent of human knowledge; he was also remembered for his failed metaphysics and his use of skeptical arguments for doubting.

In the nineteenth century he was revered for his mechanistic physiology and theory that animal bodies are machines that is, are constituted by material mechanisms, governed by the laws of matter alone.

He has been seen, at various times, as a hero and as a villain; as a brilliant theorist who set new directions in thought, and as the harbinger of a cold, rationalistic, and calculative conception of human beings.

Those new to the study of Descartes should engage his own works in some detail prior to developing a view of his legacy. Descartes was born on 31 March in his maternal grandmother's house in La Haye, in the Touraine region of France. 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's philosophy was approached through textbook presentations and commentaries on Aristotle's works. Aristotle himself frequently discussed the positions of his ancient predecessors.

The most extensive commentaries also elaborated in some detail on positions other than Aristotle's. 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. Descartes was familiar with both mainstream philosophy and recent innovators those who, among other things, rejected aspects of Aristotle's philosophy , including reading that he did from on. 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.

In , he recalled having read Thomas Campanella's De Sensu Rerum about fifteen years before, and not being much impressed — Descartes' activities during the early s are not well-documented. 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 Upon arriving in the Netherlands, Descartes undertook work on two sorts of topics. 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. The Discourse recounted Descartes' own life journey, explaining how he had come to the position of doubting his previous knowledge and seeking to begin afresh.

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.

Unlike Descartes' purely extended matter, which can exist on its own having only size and shape, many scholastic Aristotelians held that prime matter cannot exist on its own. 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; Descartes' correspondence from the second half of the s repays close study, among other things for his discussions of hypothesis-confirmation in science, his replies to objections concerning his metaphysics, and his explanation that he had left the most radical skeptical arguments out of this work, since it was written in French for a wide audience , In , Descartes fathered a daughter named Francine.

Her mother was Descartes' housekeeper, Helena Jans. They lived with Descartes part of the time in the latter s, and Descartes was arranging for them to join him when he learned of Francine's untimely death in September Descartes subsequently contributed a dowry for Helena's marriage in Watson , 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. For the Catholic lands, the teaching of his philosophy was dampened when his works were placed on the Index of Prohibited Books in , although his followers in France, such as Jacques Rohault —72 and Pierre Regis — , continued to promote Descartes' natural philosophy.

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Dioptrique

In its place he attempted to establish a dualistic system that rested on a clear distinction between the mind, the origin of thought, and matter. He is, perhaps, most commonly remembered for his philosophical declaration, "Cogito, ergo sum" I think, therefore I am. However, in addition to his many philosophical reflections, Descartes made significant contributions to mathematics and the sciences, including optics. His father served in Parliament and his mother died when he was still an infant. Though his father remarried, Descartes and his siblings were reared by their maternal grandmother and a nurse. In his youth, Descartes was educated at a Jesuit school and displayed an exceptional mental capacity.

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René Descartes

In this essay Descartes uses various models to understand the properties of light. This essay is known as Descartes' greatest contribution to optics, as it is the first publication of the Law of Refraction. The first discourse captures Descartes' theories on the nature of light. In the first model, he compares light to a stick that allows a blind person to discern his environment through touch. Descartes says:.

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