Descarte laid the foundation for 17th-century continental rationalism, later advocated by Spinoza and Leibniz, and was later opposed by the empiricist school of thought consisting of Hobbes, Locke, Berkeley, and Hume.
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Descarte is credited as the father of analytic geometry—used in the discovery of infinitesimal calculus and analysis.
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Descarte concluded from these visions that the pursuit of science would prove to be, for him, the pursuit of true wisdom and a central part of his life's work.
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Descarte arrived in La Haye in 1623, selling all of his property to invest in bonds, which provided a comfortable income for the rest of his life.
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Descarte studied both mathematics with Jacobus Golius, who confronted him with Pappus's hexagon theorem, and astronomy with Martin Hortensius.
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Descarte's was baptized a Protestant and died of scarlet fever at the age of 5.
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Descarte met Dirck Rembrantsz van Nierop, a mathematician and surveyor.
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Descarte was so impressed by Van Nierop's knowledge that he even brought him to the attention of Constantijn Huygens and Frans van Schooten.
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Descarte identifies four ordinary sources to reach wisdom and finally says that there is a fifth, better and more secure, consisting in the search for first causes.
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Descarte was a guest at the house of Pierre Chanut, living on Vasterlanggatan, less than 500 meters from Tre Kronor in Stockholm.
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Descarte relates this to architecture: the top soil is taken away to create a new building or structure.
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Descarte gave reasons for thinking that waking thoughts are distinguishable from dreams, and that one's mind cannot have been "hijacked" by an evil demon placing an illusory external world before one's senses.
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Descarte argued that the great differences between body and mind make the two ontologically distinct.
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Descarte argued, for example, that fear is a passion that moves the soul to generate a response in the body.
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Descarte argued that these motions in the pineal gland are based on God's will and that humans are supposed to want and like things that are useful to them.
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Descarte argued that external motions, such as touch and sound, reach the endings of the nerves and affect the animal spirits.
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Descarte challenged the views of his contemporaries that the soul was divine, thus religious authorities regarded his books as dangerous.
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Descarte argues that sensory perceptions come to him involuntarily, and are not willed by him.
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Descarte argued that animals did not lack sensations or perceptions, but these could be explained mechanistically.
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Descarte "pioneered the standard notation" that uses superscripts to show the powers or exponents; for example, the 2 used in x to indicate x squared.
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Descarte was first to assign a fundamental place for algebra in the system of knowledge, using it as a method to automate or mechanize reasoning, particularly about abstract, unknown quantities.
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Descarte's rule of signs is a commonly used method to determine the number of positive and negative roots of a polynomial.
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Descarte outlined his views on the universe in his Principles of Philosophy, where he describes his three laws of motion.
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Descarte independently discovered the law of reflection, and his essay on optics was the first published mention of this law.
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