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Click www.ondix.com to visit our student-to-student file sharing network. Major Greek contributions include astronomy, optics, and acoustics, along with major advances in mathematics. Science in ancient Greece was based on logical thinking and mathematics. The Greeks were very interested to know about the world, the heavens, and themselves. Greek geniuses were lucid thinkers and bold reasoners. The Greek philosophers were very much drawn to mathematics. They invented its generality, analyzed its premises, and made notable discoveries of theorems by a rigid adherence to deductive reasoning. Geometry became the basic instrument for measuring all things. Plato examined the difference between the changing world of the senses and that of the permanent truths that could only be found through rational thought. The unchanging elements of geometry were the measures of this ideal, permanent thoughtworld. This union of logic with geometry laid the foundations of the Western way of life. Euclid's "Elements," is a comprehensive treatise on geometry, proportions, and the theory of numbers and is the most long-lived of all mathematical works. It includes the Pythagorean Theorem, which states that the square on the hypotenuse of a right triangle is equal to the sum of the square on the other two sides. Pythagoras studied geometry, and discovered the general proof of the theorem about right-angled triangles. He insisted on generality in reasoning. He is said to have taught that the mathematical entities, such as numbers and shapes, were the ultimate stuff out of which the real entities that we perceive are constructed. He asked, "what is the status of mathematical entities, such as numbers for example, in the realm of things?" He discovered the importance of dealing with abstractions; and in particular directed the attention of number as characterizing the periodicity of notes of music. His followers made important contributions to medicine and astronomy and were among the first to teach that the earth was a spherical planet, revolving about a fixed point. Archimedes is famous for his works on buoyancy, or floating bodies. The famous 'Eureka' incident where water overflowed in his bath led him to discover the principle of displacement. His works showed how the behavior of objects in various media might be shown to follow rules of behavior, which could be measured using geometric means. Archimedes shifted the emphasis from mysterious "qualities" which objects were thought to possess to quantifiable matters such as weight, centers of gravity, balance, and so on. He invented ingenious machines of war, calculated the value of "fnof;à, and devised a mathematical exponential system to express extremely large numbers. His best known invention was a machine for raising water called Archimedes screw. Greek philosophers and scientists developed a number of important astronomical ideas. Thales is credited with introducing geometrical ideas into astronomy. Greek approach to astronomy was geometric and schematic, best suited for complete cosmological models. The early Greek astronomers knew many of the geometrical relationships of the heavenly bodies. There are well preserved accurately illustrated zodiacal signs, a major source of Greek astronomy. Thales taught that everything in nature is composed of one basic thing, which he believed to be water. He and two generations of followers are credited with the invention of philosophy. They asked questions about how the universe worked and looked to naturalistic explanations for the origin of the world and everything in it. He is believed to have proven that a circle is bisected by its diameter, that the base angles of an isosceles triangle are equal and that opposing angles of intersecting lines are equal. Hipparchus is the first systematic astronomer of whom there are records. He made his observations chiefly on the island of Rhodes. He founded trigonometry and scientific geography. He discovered precession of equinoxes and invented methods of fixing terrestrial positions by circles of latitude and longitude. He located 850 stars and divided the stars that he could see into classes of apparent brightness. Hipparchus estimated the size and distance of the moon, found a way to predict eclipses, as well as calculated the length of the year to within 6 and 1/2 minutes. Greek view of nature was dramatic. They believed there was an end to each thing. The center of the universe was the end of motion for those things that were heavy and the celestial spheres were the end of motion for those things whose nature lead them upwards. Each thing in nature had its own role. There was an order to everything. Pythagoras argued that the earth was round. He developed an early system of cosmology. He also tried to explain the nature and structure for the universe as a whole. Pythagoras imagined the universe as a series of concentric spheres in which each of the seven "wanderers" (the sun, the moon, and the five known planets) were embedded. Euxodus had developed a mechanical system to explain the motions of the planets. Euxodus developed the idea of rotating spheres by introducing extra spheres for each of the planets. He taught that the planets, sun, the moon, and the stars revolved around the earth. Aristotle incorporated this earth centered, or geocentric theory into his philosophic system. Aristotle developed a common-sense view of the universe. To an ordinary observer the sky seems to move. The stars, whose positions never change, wheel past every night. At the pole they never disappear, circling round the North Star. Among the fixed stars five wandering lights can be seen. These are planets. The moon circles the earth, as does the sun. Aristotle explained this system with eight crystalline spheres on which the sun, moon, planets and stars were each fixed. These spheres rolled eternally round the earth, which did not move. He believed that the sky was perfect and unchanging while the earth was not. Earthly things decayed and died. Eternal circular motion was heavenly. All motion on earth was straight-line motion. Aristotle also believed that creation had taken place before the beginning of time and once that act had taken place certain events inevitably followed. Ancient Greek philosophers were amazed with volcanoes and earthquakes. Aristotle speculated that earthquakes resulted from winds within the Earth caused by the Earth's own heat and heat from the sun. Volcanoes, he thought, marked the points at which these winds finally escaped from inside the Earth into the atmosphere. Ptolemy expanded upon Aristotle's and Hipparchus' theories. He published a book called the Almagest, in which he presented his ideas and summarized those of his predecessors. This work is our main source of knowledge of Greek astronomy. Aristotle studied under Plato. He placed great emphasis on direct observation of nature, and in science he taught that theory must follow fact. Logic for Aristotle was the necessary tool of any inquiry, and the syllogism was the sequence that all logical thought followed. Aristotle developed the use of syllogisms to draw conclusions. He advocated the use of logical empirical observation to investigate nature. Syllogisms were dialectical, structured in three parts: a major premise, a minor premise and a conclusion. The purpose of a syllogism was to use two known facts to produce a third previously unknown fact. This technique was of particular use in the investigation of the natural world because it produced conclusions, which were logically necessary even if not themselves directly observable. Greek biologists were interested in how living things began, how they developed, how they functioned, and where they were found. They observed, described, and categorized the various forms of plants and animals. They also discovered the system of natural selection. Hero, also known as Heron of Alexandria, was a Greek mathematician and inventor known for his study of mechanics and pneumatics. He invented many contrivances operated by water, steam, or compressed air; these include a fountain, a fire engine, siphons, and an engine in which the recoil of steam revolves a ball or a wheel. Anaximander believed that marine life was the first life on earth and that changes occurred when animals moved to dry land. Aristotle believed that there was a purpose behind the way nature works. Lucretius believed that evolution was based on chance combinations and heredity, and that sexual reproduction entered only after earth itself had developed. From 1130 until the end of the twelfth century Greek science and logic flooded into Europe. There were Greek texts about medicine, astronomy, astrology, pharmacology, psychology, zoology, biology, botany, mineralogy, optics, chemistry, physics, mathematics, algebra, geometry, trigonometry, music, meteorology, geography, mechanics, hydrostatics, navigation, and history. For hundreds of years European science was based on the early theories of the Greeks. Keywords: major greek contributions include astronomy optics acoustics along with major advances mathematics science ancient greece based logical thinking mathematics greeks were very interested know about world heavens themselves greek geniuses were lucid thinkers bold reasoners greek philosophers were very much drawn mathematics they invented generality analyzed premises made notable discoveries theorems rigid adherence deductive reasoning geometry became basic instrument measuring things plato examined difference between changing world senses that permanent truths that could only found through rational thought unchanging elements geometry measures this ideal permanent thought world this union logic with geometry laid foundations western life euclid elements comprehensive treatise proportions theory numbers most long lived mathematical works includes pythagorean theorem which states that square hypotenuse right triangle equal square other sides pythagoras studied discovered general proof theorem about right angled triangles insisted generality reasoning said have taught mathematical entities such numbers shapes ultimate stuff which real entities perceive constructed asked what status mathematical entities such numbers example realm things discovered importance dealing with abstractions particular directed attention number characterizing periodicity notes music followers made important contributions medicine astronomy among first teach earth spherical planet revolving about fixed point archimedes famous works buoyancy floating bodies famous eureka incident where water overflowed bath discover principle displacement works showed behavior objects various media might shown follow rules behavior which could measured using geometric means archimedes shifted emphasis from mysterious qualities objects thought possess quantifiable matters such weight centers gravity balance invented ingenious machines calculated value fnof devised exponential system express extremely large best known invention machine raising water called archimedes screw philosophers scientists developed number important astronomical ideas thales credited introducing geometrical ideas into astronomy approach geometric schematic best suited complete cosmological models early astronomers knew many geometrical relationships heavenly bodies there well preserved accurately illustrated zodiacal signs major source thales taught everything nature composed basic thing believed water generations followers credited invention philosophy they asked questions universe worked looked naturalistic explanations origin everything believed have proven circle bisected diameter base angles isosceles triangle equal opposing angles intersecting lines equal hipparchus first systematic astronomer whom there records made observations chiefly island rhodes founded trigonometry scientific geography discovered precession equinoxes invented methods fixing terrestrial positions circles latitude longitude located stars divided stars could into classes apparent brightness hipparchus estimated size distance moon found predict eclipses well calculated length year within minutes view nature dramatic they believed there each thing center universe motion those things heavy celestial spheres motion those whose nature lead them upwards each thing role order everything pythagoras argued earth round developed early system cosmology also tried explain structure universe whole pythagoras imagined series concentric spheres each seven wanderers moon five known planets embedded euxodus developed mechanical system explain motions planets euxodus idea rotating spheres introducing extra planets taught moon stars revolved around earth aristotle incorporated this centered geocentric theory into philosophic aristotle common sense view ordinary observer seems move whose positions never change wheel past every night pole never disappear circling round north star among fixed five wandering lights seen these circles does aristotle explained eight crystalline fixed these rolled eternally round move perfect unchanging while earthly decayed died eternal circular motion heavenly straight line also creation taken place before beginning time once taken place certain events inevitably followed ancient philosophers amazed volcanoes earthquakes speculated earthquakes resulted from winds within caused heat heat from volcanoes marked points these winds finally escaped inside atmosphere ptolemy expanded upon hipparchus theories published book called almagest presented ideas summarized those predecessors work main source knowledge studied under plato placed great emphasis direct observation science theory must follow fact logic necessary tool inquiry syllogism sequence logical followed syllogisms draw conclusions advocated logical empirical observation investigate syllogisms dialectical structured three parts premise minor premise conclusion purpose syllogism known facts produce third previously unknown fact technique particular investigation natural because produced conclusions logically necessary even themselves directly observable biologists interested living began functioned where found observed described categorized various forms plants animals also natural selection hero heron alexandria mathematician inventor study mechanics pneumatics many contrivances operated steam compressed include fountain fire engine siphons engine recoil steam revolves ball wheel anaximander marine life first life changes occurred when animals moved land purpose behind lucretius evolution based chance combinations heredity sexual reproduction entered only after itself until twelfth century science logic flooded europe texts medicine astrology pharmacology psychology zoology biology botany mineralogy optics chemistry physics algebra trigonometry music meteorology geography mechanics hydrostatics navigation history hundreds years european based early theories greeks Keywords General: Essay, essays, termpaper, 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