Eudoxus of Cnidus Eudoxus is a Greek mathematician and astronomer who was born in 342-390 BCE, Cindus, Asia. He substantially exceeded in proportion theory also contributed to learning the constellations; in addition, to the development of observational astronomy in the Greek times and established the first geometrical model of celestial motion. Furthermore, he wrote about geography and contributed in philosophical discussions with Plato, who was Eudoxus teacher at that time. Eudoxus in the Greek language means “honored” or “ good repute”. His father Aeschines of Cnidus loved to watch the stars at night with him; therefore, becoming interested in learning about the constellations. Around 387 BC, Eudoxus at age 23 traveled with a physician named …show more content…
Theomedon. Some believed that Theomedon was Eudoxus lover according to Diogenes Laertius. During their travel to Athens, they traveled with some followers from Socrates and attend Plato’s lectures. Eudoxus brilliant work on proportions shows an insight into numbers, and allows rigorous treatment of constant quantities and not just whole numbers, but also rational numbers as well. He was considered by most people the greatest of classical Greek mathematicians, and second only to Archimedes. He rigorously insisted on developing Antiphon’s method of exhaustion, which was a precursor to the integral calculus, which was used in a masterly way by Archimedes in the next century. In applying the method, he proved his mathematical statements as: areas of circles to one another as squares to their radii, volumes of spheres are to one another as the cubes of their radii, the volume of a pyramid is approximately one-third as a prism with a similar base and altitude, and the volume of a cone is one-third that of a corresponding cylinder. In addition, Eudoxus also introduces the idea of not qualified magnitude to help explain how geometrical entities such as: lines, quadrants, areas and volumes, to avoid the use of irrational numbers. By doing so, he reversed a Pythagorean on numbers and arithmetic while focusing on geometrical concepts of rigorous mathematics. The Pythagoreans soon discovered that the diagonal of a quadrilateral does not have a common unit of measurement with the sides of the quadrilaterals; this is the well known discovery that the square root cannot be described as a ratio of two integers. This discover has the existence of infinite quantities beyond the integers and rational fractions; however, at the same time it threw a question the calculations in geometry as a whole. For example, Euclid gives a brief elaborate explanation about the Pythagorean theorem, by using the addition of areas much later as a simpler proof of similar triangles, which depends on the ratios of line segments. As an astronomer, Eudoxus, was a very vigilant to recognize the constellations, both during his visit to Egypt and his home Cnidus, where he had an observatory.
He published two books called “Mirror” and “ The Phaenomena”, which took him a year for both books to be completed and revised by other astronomers. The works were lightly criticized, in the light of strong knowledge, by the intellectual astronomer Hipparchus two centuries later; however, they were pioneering compendia and was proved useful. Several verbatim quotes were given by Hipparchus in his commentary on the phenomenal poem of Aratus, which drew on Eudoxus and was entitled phenomena. Another book called “Disappearances of the Sun”, may have been worried with the eclipses, and perhaps with increasing s and settings as well. He composed an astronomical poem that may result in confusion with Aratus although a genuine Astronomia in hexameters, in tradition, is a probability. Nowadays, the mathematical labor of Eudoxus is not particularly well known to the public due to the fact that he did not leave anything behind that could ensure that he had posthumous fame. He left no important theorem as the Pythagoras, nor mathematical assumptions like Euclid. Eudoxus main contribution was the theory of proportions that helped in the involvement of Pythagorean geometry, which did not contain any source of
asymmetric quantities.
For Gallus told us that the other kind of celestial globe, which was solid and contained no hollow space, was a very early invention, the first one of that kind having been constructed by Thales of Mileus, and later marked by Eudoxus with the constellations and stars which are fixed in the sky. Price 56 -. This description is helpful for understanding the basic form of Thales' sphere, and for pinpointing its creation at a specific point in time. However, it is clearly a simplification of events that occurred several hundred years before Cicero's lifetime. Why would Thales create a spherical representation of the heavens and neglect to indicate the stars?
Geometry, a cornerstone in modern civilization, also had its beginnings in Ancient Greece. Euclid, a mathematician, formed many geometric proofs and theories [Document 5]. He also came to one of the most significant discoveries of math, Pi. This number showed the ratio between the diameter and circumference of a circle.
He took his teaching duties very seriously, while he was preparing lectures for his charge on variety an of topics about science. The first scientific work dates were all from this period. It involves topics, which would continue to occupy him throughout his life. In 1571, he began publication of his track. It was intended to form a preliminary mathematical part of a major study on the Ptolemaic astronomical model. He continued to embrace the Ptolemaic (Parshall 1).
In 1543 Nicholas Copernicus, a Polish Canon, published “On the Revolution of the Celestial Orbs”. The popular view is that Copernicus discovered that the earth revolves around the sun. The notion is as old as the ancient Greeks however. This work was entrusted by Copernicus to Osiander, a staunch Protestant who though the book would most likely be condemned and, as a result, the book would be condemned. Osiander therefore wrote a preface to the book, in which heliocentrism was presented only as a theory which would account for the movements of the planets more simply than geocentrism did, one that was not meant to be a definitive description of the heavens--something Copernicus did not intend. The preface was unsigned, and everyone took it to be the author’s. That Copernicus believed the helioocentric theory to be a true description of reality went largely unnoticed. In addition to the preface, this was partly because he still made reassuring use of Ptolemy's cycles and epicycles; he also borrowed from Aristotle the notion that the planets must move in circles because that is the only perfect form of motion.
Hippocrates taught in Athens and worked on squaring the circle and also worked on duplicating the cube. He grew far in these areas and although his work is not lost, it must have contained much of what Euclid later included in Books One and Two of the Elements.
Aristarchus lived from about the year 310 B.C. to about 230 B.C. Aristarchus was the first Greek philosopher and mathematician to make sense of the solar system. Others before him thought that the Earth is a sphere and that it moves, but he was the first to understand the heliocentric theory, which states that the sun is in the middle. In 288 or 287 B.C. he followed Theophrastus as the head of the Peripatetic School established by Aristotle.
(Adair, 19). Hypatia is also credited for editing Archimedes’ dimensions of the Circle, as well as commenting and working on Diophantus’
This source provided a lot of background information on Euclid and his discoveries. This source gave details about the many geometrical theories of Euclid, as well as his practical geometrical uses. This source also explained how geometry helped Greece a long time ago, and how it is used by many people everyday.
Euclid and Archimedes are two of the most important scientists and mathematicians of all time. Their achievements and discoveries play a pivotal role in today’s mathematics and sciences. A lot of the very basic principles and core subjects of mathematics, physics, engineering, inventing, and astronomy came from the innovations, inventions, and discoveries that were made by both Euclid and Archimedes.
He also used evidence based on observation. If the earth were not spherical, lunar eclipses would not show segments with a curved outline. Furthermore, when one travels northward or southward, one does not see the same stars at night, nor do they occupy the same positions in the sky. (De Caelo, Book II, chapter 14) That the celestial bodies must also be spherical in shape, can be determined by observation. In the case of the stars, Aristotle argued that they would have to be spherical, as this shape, which is the most perfect, allows them to retain their positions. (De Caelo, Book II, chapter 11) By Aristotle's time, Empedocles' view that there are four basic elements - earth, air, fire and water - had been generally accepted. Aristotle, however, in addition to this, postulated a fifth element called aether, which he believed to be the main constituent of the celestial bodies.
Nicolaus Copernicus was a man of many interest. He was an astronomer, mathematician, translator, artist, and physicist. Nicolaus Copernicus is the latin version of his name. His Polish name was Mikolaj Kopernik or Nicolaus Koppqrnigk. He was born February 19, 1473 in Toruń, Poland and he died May 24, 1543 in Frombork, Poland.
The importance of mathematics to nature has been a topic of debate within the Western scientific tradition. From ancient times through the middle ages, an outbreak of mathematical creativeness was often followed by centuries of inactivity. As we all know, mathematics has always been the vital importance in astronomy, and many ancient astronomers were also mathematicians. This means that the growth of mathematics was applied and motivated by astronomical calculations. Though, not everyone studying ancient astronomy was capable to use applications of mathematics.
Physics began when man first started to study his surroundings. Early applications of physics include the invention of the wheel and of primitive weapons. The people who built Stone Henge had knowledge of physical mechanics in order to move the rocks and place them on top of each other. It was not until during the period of Greek culture that the first systematic treatment of physics started with the use of mechanics. Thales is often said to have been the first scientist, and the first Greek philosopher. He was an astronomer, merchant and mathematician, and after visiting Egypt he is said to have originated the science of deductive geometry. He also discovered theorems of elementary geometry and is said to have correctly predicted an eclipse of the sun. Many of his studies were in astronomy but he also observed static electricity. Phythogoras was a Greek philosopher. He discovered simple numerical ratios relating the musical tones of major consonances, to the length of the strings used in sounding them. The Pythagorean theorem was named after him, although this fundamental statements of deductive geometry was most likely first an idea from Egyptian methods of measurements. With the help of his followers he discovered that the earth was a sphere, but he did not believe it revolved around the sun.
Euclid, also known as Euclid of Alexandria, lived from 323-283 BC. He was a famous Greek mathematician, often referred to as the ‘Father of Geometry”. The dates of his existence were so long ago that the date and place of Euclid’s birth and the date and circumstances of his death are unknown, and only is roughly estimated in proximity to figures mentioned in references around the world. Alexandria was a broad teacher that taught lessons across the world. He taught at Alexandria in Egypt. Euclid’s most well-known work is his treatise on geometry: The Elements. His Elements is one of the most influential works in the history of mathematics, serving as the source textbook for teaching mathematics on different grade levels. His geometry work was used especially from the time of publication until the late 19th and early 20th century Euclid reasoned the principles of what is now called Euclidean geometry, which came from a small set of axioms on the Elements. Euclid was also famous for writing books using the topic on perspective, conic sections, spherical geometry, number theory, and rigor.