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In his book Theoricae Novae Planetarum (Theory of the planets), Peurbach introduces the Ptomely epicycle. He believed that the planets were solid crystalline spheres, and that they were controlled by the sun.
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Nicolaus Copernicus was born in Torun, Poland. He was a priest, astonomer, and he brought the first theory that showed that the Earth was not in the center of the Universe. He wrote a book called, On the Revolutions of Celestial Spheres (De Revolutionibus orbium coelestiam). In this book he explained how the Earth was not the center of the univerese and instead the sun was the center.
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The book Narratio Prima is published which introduced Copernicus' heliocentric theory in this book. This was the first publication of Copernicus' theory. This book was also just an intro to the work Copernicus later publishes.
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Gerolamo's book, Ars Magna (The Great Art), was published which was about Algebra. The book showed new ways to solve algebra equations and brought ways to solve cubic equations.
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Tycho Brahe was one of the few men doing the elaborate math to calculate the motion of the universe. Tycho was one of the men that argued about the Copernicus theory. He believed the earth was in the center of the universe. He took extensive mathematical observations and calculations. This just helped prove Copernicus' theory more.
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Francis predicted that the universe like a machine. He was a person very truthful with the public and often said that old ways should be abandoned. He said that knowledged should be earned from experience and not books.
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Galileo processd the Copernicus theory and took a deeper look into it. Galileo bought a Dutch inovation called the telescope that was around for a fw years before. He was the first to use the telescope to see into the heavens. He saw that there were mountains on the moon which could be a possibility of life on the moon. He presented his findings in the his book, The Starry Messager which was published in 1610.
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Johannes Kepler belived that the sun was a spiritual essence and a presence of God. This is why he also believed that the sun was in the middle of the universe. He made a model of the universe which he published in his book New Astronomy in 1609. Soon others used his model to make their own predictions.