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Geometry - Wikipedia

Geometry is a branch of mathematics concerned with questions of shape, size, relative position By the early 17th century, geometry had been put on a solid analytic footing by mathematicians such .. Plimpton , Pythagorean triples, and the Babylonian triangle parameter equations", Historia Mathematica, 8, , pp. Greene County Indiana the van dvd release date duotec fastener clearing .. service kruibeke voetbalclub gent feriado images yahoo fotoalbum ryeo wook twitter .. Greene County Indiana frigidaire washer fwsghs0 libro historia 1 aku berterima kasih youtube geometria analytical steinbruch solnhofen biker. فيلهلم شيكارد. ویلهلم شیکارد (ریاضی‌دان آلمانی). ভিলহেল্ম শিকার্ড. ヴィルヘルム・ シッカート. Dates. Dates: Creation class. Creation class: Computer file .

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The problem includes a diagram indicating the dimensions of the truncated pyramid. Egyptian mathematics refers to mathematics written in the Egyptian language. From the Hellenistic periodGreek replaced Egyptian as the written language of Egyptian scholars. Mathematical study in Egypt later continued under the Arab Empire as part of Islamic mathematicswhen Arabic became the written language of Egyptian scholars.

The most extensive Egyptian mathematical text is the Rhind papyrus sometimes also called the Ahmes Papyrus after its authordated to c. In addition to giving area formulas and methods for multiplication, division and working with unit fractions, it also contains evidence of other mathematical knowledge, [27] including composite and prime numbers ; arithmeticgeometric and harmonic means ; and simplistic understandings of both the Sieve of Eratosthenes and perfect number theory namely, that of the number 6.

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One problem is considered to be of particular importance because it gives a method for finding the volume of a frustum truncated pyramid. Finally, the Berlin Papyrus c. Greek mathematics The Pythagorean theorem. The Pythagoreans are generally credited with the first proof of the theorem.

Greek mathematics of the period following Alexander the Great is sometimes called Hellenistic mathematics. All surviving records of pre-Greek mathematics show the use of inductive reasoning, that is, repeated observations used to establish rules of thumb. Greek mathematicians, by contrast, used deductive reasoning. The Greeks used logic to derive conclusions from definitions and axioms, and used mathematical rigor to prove them. Although the extent of the influence is disputed, they were probably inspired by Egyptian and Babylonian mathematics.

According to legend, Pythagoras traveled to Egypt to learn mathematics, geometry, and astronomy from Egyptian priests. Thales used geometry to solve problems such as calculating the height of pyramids and the distance of ships from the shore. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. As a result, he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed.

The Pythagoreans are credited with the first proof of the Pythagorean theorem[38] though the statement of the theorem has a long history, and with the proof of the existence of irrational numbers.

Though he made no specific technical mathematical discoveries, Aristotle —c. The diagram accompanies Book II, Proposition 5. Thinking is thus every activity of a person of which the person is immediately conscious.

In this manner, Descartes proceeds to construct a system of knowledge, discarding perception as unreliable and, instead, admitting only deduction as a method. Mind-body problem and Mind-body dualism L'homme Descartes, influenced by the automatons on display throughout the city of Paris, began to investigate the connection between the mind and body, and how the two interact.

Known as Cartesian dualism or Mind-Body Dualismhis theory on the separation between the mind and the body went on to influence subsequent Western philosophies.

In Meditations on First PhilosophyDescartes attempted to demonstrate the existence of God and the distinction between the human soul and the body. Humans are a union of mind and body; [71] thus Descartes' dualism embraced the idea that mind and body are distinct but closely joined. While many contemporary readers of Descartes found the distinction between mind and body difficult to grasp, he thought it was entirely straightforward.

Descartes employed the concept of modes, which are the ways in which substances exist. In Principles of PhilosophyDescartes explained, "we can clearly perceive a substance apart from the mode which we say differs from it, whereas we cannot, conversely, understand the mode apart from the substance".

To perceive a mode apart from its substance requires an intellectual abstraction, [72] which Descartes explained as follows: The intellectual abstraction consists in my turning my thought away from one part of the contents of this richer idea the better to apply it to the other part with greater attention. Thus, when I consider a shape without thinking of the substance or the extension whose shape it is, I make a mental abstraction. Thus Descartes reasoned that God is distinct from humans, and the body and mind of a human are also distinct from one another.

But that the mind was utterly indivisible: Everything that happened, be it the motion of the stars or the growth of a treewas supposedly explainable by a certain purpose, goal or end that worked its way out within nature. Aristotle called this the "final cause", and these final causes were indispensable for explaining the ways nature operated.

With his theory on dualism Descartes fired the opening shot for the battle between the traditional Aristotelian science and the new science of Kepler and Galileo which denied the final cause for explaining nature. Descartes' dualism provided the philosophical rationale for the latter and he expelled the final cause from the physical universe or res extensa. For Descartes the only place left for the final cause was the mind or res cogitans. Therefore, while Cartesian dualism paved the way for modern physicsit also held the door open for religious beliefs about the immortality of the soul.

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A human was according to Descartes a composite entity of mind and body. Descartes gave priority to the mind and argued that the mind could exist without the body, but the body could not exist without the mind.

In Meditations Descartes even argues that while the mind is a substance, the body is composed only of "accidents". If this were not so, I, who am nothing but a thinking thing, would not feel pain when the body was hurt, but would perceive the damage purely by the intellect, just as a sailor perceives by sight if anything in his ship is broken.

What exactly is the relationship of union between the mind and the body of a person? It was this theory of innate knowledge that later led philosopher John Locke — to combat the theory of empiricismwhich held that all knowledge is acquired through experience. These animal spirits were believed to be light and roaming fluids circulating rapidly around the nervous system between the brain and the muscles, and served as a metaphor for feelings, like being in high or bad spirit.

These animal spirits were believed to affect the human soul, or passions of the soul. Descartes distinguished six basic passions: All of these passions, he argued, represented different combinations of the original spirit, and influenced the soul to will or want certain actions.

He argued, for example, that fear is a passion that moves the soul to generate a response in the body. In line with his dualist teachings on the separation between the soul and the body, he hypothesized that some part of the brain served as a connector between the soul and the body and singled out the pineal gland as connector.

Thus different motions in the gland cause various animal spirits. He 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.

But he also argued that the animal spirits that moved around the body could distort the commands from the pineal gland, thus humans had to learn how to control their passions. He argued that external motions such as touch and sound reach the endings of the nerves and affect the animal spirits. Heat from fire affects a spot on the skin and sets in motion a chain of reactions, with the animal spirits reaching the brain through the central nervous system, and in turn animal spirits are sent back to the muscles to move the hand away from the fire.

He challenged the views of his contemporaries that the soul was divinethus religious authorities regarded his books as dangerous. Descartes' writings went on to form the basis for theories on emotions and how cognitive evaluations were translated into affective processes.

Descartes believed that the brain resembled a working machine and unlike many of his contemporaries believed that mathematics and mechanics could explain the most complicated processes of the mind.

  • René Descartes
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In the 20th century Alan Turing advanced computer science based on mathematical biology as inspired by Descartes. His theories on reflexes also served as the foundation for advanced physiological theories more than years after his death. The physiologist Ivan Pavlov was a great admirer of Descartes.

Like the rest of the sciences, ethics had its roots in metaphysics. However, as he was a convinced rationalist, Descartes clearly states that reason is sufficient in the search for the goods that we should seek, and virtue consists in the correct reasoning that should guide our actions.

Nevertheless, the quality of this reasoning depends on knowledge, because a well-informed mind will be more capable of making good choicesand it also depends on mental condition. For this reason, he said that a complete moral philosophy should include the study of the body.

He discussed this subject in the correspondence with Princess Elisabeth of Bohemiaand as a result wrote his work The Passions of the Soul, that contains a study of the psychosomatic processes and reactions in man, with an emphasis on emotions or passions.

For Epicurus the sovereign good was pleasure, and Descartes says that, in fact, this is not in contradiction with Zeno's teaching, because virtue produces a spiritual pleasure, that is better than bodily pleasure.