... "Discours de la method pour bien conduire sa raison et chercher la verite dans les sciences", "La Dioptrique", "Les Meteores," and most importantly "La Geometrie." In The Geometry, Descartes unites topics of Algebra and Geometry in a way that no other had done (no other had so specifically linked the two together). Descartes believed that Math was absolute just as he was absolute ... of mechanics in "Principia Philosophiae." His goal was to create a single all-encompassing study that was based on the principals of mathematics. Although he never accomplished this, his work in geometry an...

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• Grade Level: High School

... the hypotenuse of a right angle triangle you must add the squared result of each of the other two legs of the triangle (Violatti). This is still used in schools and geometry classes around the world to this day. It is arguably one of the most important mathematical theories. The Babylonians knew this thousands of years earlier, but Pythagoras was the first ... mathematical advancements. The ancient Greeks were greatly influenced by Egyptian and Babylonian studies, but they added their own findings to previous theories. They expanded upon the fundamentals of calculus and geometry and tau...

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... rhetoric included the presentation of all these aspects in comprehension thought. The second step of the system was the Quadrivium consisted of arithmetic, geometry, music, and astronomy. Arithmetic was simple math such as addition, subtraction, multiplication and division; Geometry involved the study of math in three dimensions, which was related to music due to the fact that music encompassed the study of ... ...

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• Grade Level: Undergraduate

... a definitive answer, which led him to "what is justice?" Socrates disagreed with others, like a member of the academy named Theaetetus. In Theaetetus, Plato's dialogue from 367 b.c., Theaetetus defined knowledge as "geometry, the craft of shoemaking, and carpentry." According to Socrates, such a definition would be unacceptable because it is a mere list and because the craft of shoemaking can be defined as "knowing ... this action just", or "why is that mountain beautiful". This does not necessarily show an advance, but a different approach to similar topics. Plato used mathematics to e...

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• Grade Level: High School

... his name). Often called the father of modern philosophy, he is regarded as the bridge between scholasticism and all philosophy that followed him. Primarily interested in mathematics, he founded Analytic Geometry and originated the Cartesian Coordinates and Cartesian curves. To algebra he contributed the treatment of negative roots and the convention of exponent notation. Descartes also contributed to optics, physiology, and ... : I wouldn't say that one was more important than the other. Although my philosophies and scientific discoveries were revolutionary in thought, my mathematics was...

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... that we learned everything in an earlier life, before we became people. So, we already have all of our knowledge. He demonstrates this theory by asking the slave boy various geometry questions which the slave boy answers correctly (even though they are pretty much just "yes or no" questions)- proving that he knows and understands ... geometry, although he has not learned it previously. Therefore the knowledge was "recollected." As Socrates says in the text, "And if there have been always true thoughts in him, both at ... ...

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... : "you know that a square figure is like this" (82b) "Do you agree?" (82e) " is it not?" (83c). In reality the language and persuasion Socrates uses teaches the attendant about the geometry of which attendant had no prior knowledge, even in his soul. It was through Socrates" lesson that he came to the appropriate reasoning. He gave answers such as: "yes" (85b ... of Socrates. Meno would often respond with "Definitely" (76c), "it does" (76e), and "certainly" (97b). This is the same sort of answers the attendant employs to answer Socrates" questions about geometry. This is significant beca...

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... the nature of science. Plato was a believer in the "quadrivium" which is about four math fields of study in the liberal arts, which begins with arithmetic, then to plane geometry, solid geometry, and lastly astronomy and harmonics. Plato believed that knowledge was "forgotten" at birth, and was able to be remembered. Plato also believed that all substances are composed of either air ... ...

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... structure our minds, beliefs, and actions. "In his dialogue entitled the Meno, Plato illustrates how Socrates is able to show that even a young uneducated slave boy knows some truths of geometry not because somebody taught him that subject but because be naturally knows the relationship of various ideas to each other." (Stumpf 260) This quote illustrates how Socrates thought that the ... uneducated boy knew geometry. He recollected it from his soul. In the Meno, Socrates states that the boy is "recovering by oneself knowledge within oneself." (Plato 85D) Knowledge in the Meno is perceiv...

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... generally credited with the theory of the functional significance of numbers in the objective world and in music. His followers are credited with the development of the Pythagorean theorem in geometry and the application of number relationships to music theory, acoustics, and astronomy. His Pythagorean brotherhood's beliefs and ideas were rediscovered during the Renaissance and contributed to the development of mathematics ... . The mathematikoi lived permanently with the Society, had no personal possessions and were vegetarians. They were taught by Pythagoras himself and obeyed strict r...

• Word Count: 389
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• Grade Level: Undergraduate

... . Right in line with his theory of Forms Plato uses mathematics as his example in the dialogue with the boy, trying to demonstrate that he has some concept of the geometry of a square. Plato had hoped that this philosophical inquiry could yield similar results as what were later displayed in the Republic with his concept of justice by examining what was ... not knowing what justice is, or what beauty and goodness is. The same is true with the boy in Meno, he is not able to completely grasp these concepts of geometry because he is just imitating the Forms from knowledge in a previous life...

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... therefore not entirely conceptually aware of the perfect ideas the Forms translate. In the dialogue Meno Socrates attempts to demonstrate this argument using a slave boy with no previous knowledge of geometry. "Plato reveals that there is a sense in which the inquirer both knows and doesn't know what he is seeking."6 This has become known as 'Meno's Paradox'. Plato ... ...

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... that structuring could be synthetic and you could know those principles A priori. There are many examples of what Kant considered to be synthetic a priori judgements, all judgements of mathematics and geometry. In natural science such judgements as "every event has a cause." In metaphysics, "There is a God," and "the soul is a simple substance, distinct from the body ... ...

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... 's influence of devotion to liberty in particular would carry on to Locke's philosophical beliefs. John Locke studied at Christ College Church,Oxford University where he studied rhetoric, grammar, moral philosophy, geometry, and the Greek language based on the Teachings of the ancient Greek philosopher Aristotle. In the mid 1660's John Locke focused on philosophy while he lived in Oxford, then he ... ...

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... . Plato's republic assigned individuals to careers by way of education. The first of the citizens who failed in the education were assigned to businessmen and traders. Those remaining would learn geometry and mathematics. The batch of failures in this group would comprise the military. The final, few elite would learn what he considered the most important: philosophy. They would also learn ... ...

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... serious effort to defeat skepticism. He was convinced that the discovery of the proper method was the key to scientific advancement. Descartes is also credited as being the founder of geometry and Cartesian coordinates. Cartesian coordinate system is used for graphing equations and geometric shapes. Modern maps use the grid system that can be traced back to Descartes. Again, he believed ... ...

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... window in our dream while sleeping in the bed, the image is different from reality but two plus two is still four even while we are asleep. Sciences as such geometry and mathematics are certain and indubitable for Descartes. In science classes, instructors stress the importance of determining causation. The modern scientific method allows for many ways to describe every imaginable ... ...

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... in his form. Each could be reformulated into a basic case and the conclusion came from within the question. Of the six logic works, only one, the Prior Analytics, expounds formal geometry, as Aristotle himself understood the subject. Only one of six works on logic, deal with formal logic as Aristotle understood the subject. The five others deal with types of reasoning ... ...

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... of number, which became for them the ultimate principle of all proportion, order, and harmony in the universe. Through these studies they established a scientific foundation for mathematics, for example in geometry the great discovery of the school was the hypotenuse theorem, or Pythagoras' theorem. (see below) PYTHAGORAS' THEOREM:- Pythagoras' Theorem is a formula stating that the square of the hypotenuse of a right ... ...

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... "studying the path of the moon", investigate "phenomena underground" and examine "the lower reaches of hell" (page 120, Penguin edition, The Clouds, Aristophanes). The idea that Socrates investigates astronomy, cosmology, geometry and rhetoric seem believable enough, but other suggestions, such as the sophists believing that too much air is bad for the brain, seems to merely be an invention for the ... ...

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... knowledge, Descartes considered ancient logic. It is apparent that he believes that logic can only be used to com municate those concepts that are already known and accepted. He rejects geometry and algebraic analysis because of the restrictions which limit these subjects to figures alone. Instead, he prefers mathematics since it is controlled and limited by rigid ru les. Just as ... ...

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... XIV to not attack German areas. In Paris Leibniz studied mathematics under Christian Huygens. Huygens seemed to motivate Leibniz's interest in mathematics. Leibniz's relationship with Huygens led him into studying geometry, which Leibniz described as "opening a whole new world to him". Leibniz's works and ideas contributed to mathematics tremendously. He built the first mechanical calculator capable of multiplication and division. He ... ...

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... untruth due to his disbelief in metaphysics. Nietzsche also argues that living without falseness is impossible. To function at all in life, we have to use logic, simple maths and geometry etc. regardless of them being true or not. The "falseness" of such judgements is "no objection to them." "Untruth is a condition of life." The distinctions between the True and the ... ...

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... is credited with devising the standard 365-day year and the building of the Great Pyramid at Giza. Thoth was believed to be the inventor of astronomy, astrology, engineering, botany, geometry, and land surveying. The ancient Egyptians regarded Thoth as the embodiment of the Universal Mind. The Egyptian account is held by scholars believe to be the most accurate. Hermes was ... ...

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... window in our dream while sleeping in the bed, the image is different from reality but two plus two is still four even while we are asleep. Sciences as such geometry and mathematics are certain and indubitable for Descartes. In science classes, instructors stress the importance of determining causation. The modern scientific method allows for many ways to describe every imaginable ... ...

• Word Count: 1525
• Approx Pages: 6
• Has Bibliography
• Grade Level: Undergraduate