Greek mathematics began during the 6th century B.C.E. However, we do not know much about why people did mathematics during that time. There are no records of mathematicians’ thoughts about their work, their goals, or their methods (Hodgkin, 40). Regardless of the motivation for pursuing mathematical astronomy, we see some impressive mathematical books written by Hippocrates, Plato, Eudoxus, Euclid, Archimedes, Apollonius, Hipparchus, Heron and Ptolemy. I will argue that Ptolemy was the most integral part of the history of Greek astronomy.
Mathematics and astronomy are very closely related. It is the mathematical procedures which help define time and space. However, Greek culture plays a role too. With a Greek mindset one would be restricted to believing that the universe is composed of perfect circles. This idea is rooted in Plato and Aristotle’s work. Plato believed that the celestial bodies were godly because their motion was consistent, whereas the Earth is always changing. Plato believed that the Earth was at the centre of the universe and all the celestial bodies orbited around it on perfect uniform circular paths. He chose a circular path because circles have no corners or edges. They are continuous like the motion of the planets (Cassidy, 9).
Similarly, Aristotle believed that the circle was a symbol of continuity. He applied this idea of continuity to the notion of time, which has no beginning or end. (Aristotle, IV) He also said that the circle is “the perfect, first, most beautiful form.” (Wikipedia, Perfection)
Ptolemy lived from approximately 90 A.D. to 168 A.D (Wikipedia, Ptolemy) and grew up in Alexandria, Egypt. Throughout his life time he studied astronomy and worked a great deal on astrology, g...
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Lahanas, M.Astronomy of ptolemy. Retrieved March 1, 2011, from http://www.mlahanas.de/Greeks/PtolemyAstronomy.htm
Professor Craig Fraser. (February 14, 2011). HPS390 class
Retrograde motion. (2010). Retrieved March 1, 2011, from http://www.lasalle.edu/~smithsc/Astronomy/retrograd.html
Swerdlow, N., & Neugebaur, O. (1984). Mathematical astronomy in copernicus's de revolutionibus. New York: Springer-Verlag.
Wikipedia. (2011). Almagest. Retrieved March 1, 2011, from http://en.wikipedia.org/wiki/Almagest
Wikipedia. (2011). Inferior and superior planets. Retrieved March 1, 2011, from http://en.wikipedia.org/wiki/Inferior_and_superior_planets
Wikipedia. (2011). Perfection. Retrieved March 1, 2011, from http://en.wikipedia.org/wiki/Perfection
Wikipedia. (2011). Ptolemy. Retrieved March 1, 2011, from http://en.wikipedia.org/wiki/Ptolemy
Ptolemy of Alexandria, the Influential Astronomer Ptolemy of Alexandria was the most influential astronomer of the ancient world. The books and theories Ptolemy developed served as a major basis for future astronomers. It was during the Renaissance period that his work became thoroughly studied and revised. Ptolemy collected all ancient knowledge of astronomy and geography including it in his book Almagest around 140 A.D. It follows, he then wrote a four volume astrological study known as the Tretrabiblos.
Clarke, Leonard W.‘Greek Astronomy and Its Debt to the Babylonians' The British Journal for the History of Science, Vol. 1, No. (Cambridge University Press. 1962)
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.
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.
Plato was born in Athens, Greece around 427 B.C. He was always interested in politics, until he witnessed his mentor and teacher, Socrates, death. After learning of the callousness of politics, Plato changed his mind and eventually opened up The Academy, which is considered if not the first, one of the first Universities. Students at the Academy studied many different fields of science, including biological and astronomical. The students also studied many other fields, such as math. Plato developed many views that were mathematical in nature. He expressed these views through his writings. According to Dr. Calkins of Andrew University, "Timaeus is probably the most renowned of Plato's thirty-five dialogues. [In it] Plato expresses that he believes that the heavenly bodies are arranged in perfect geometric form. He said that because the heavens are perfect, the various heavenly bodies move in exact circles." (Calkins 1). Of course that is a much summarized view of what Plato discusses in Timaeus, but still a solid view on Plato's beliefs about cosmology. Cosmology can be loosely defined as everything being explained and in its place or beautiful. The cosmos is beautiful because everything is perfect. Plato understood that when he defined the most perfect geometric design as the circle. In a circle one line is always equidistance from one point. In Plato's universe there are two realms, eternity and time. The factor that creates "time" out of the chaos of "eternity" is the Demiurge. Plato's Demiurge can be defined as an architect creator theological entity. The importance of the Demiurge in this paper is to compare and contrast him with Boethius's God in The Consolation of Philosophy.
At this time, it was usual for all students at a university to attend courses on mathematics. These courses usually included the four mathematical sciences: arithmetic, geometry, astronomy and music. However, what w...
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.
Astronomy is a very important field in science. Ancient Greece, China, and India all contributed to our everyday ideas and uses of astronomy. Ancient Greece was the most influential because the Indian’s based most of their astronomy off of Greece. The Greeks created calendars that were based off of the eclipse cycle, which they called by two different names, Hellenic Calendars and Lunisolar Calendars. Because of Ancient Greece, we now have calendars to keep us on track every day. The Greeks observed a celestial object passing through the eastern and western morning sky. After a long time of observations, they came to a realization that it was a planet and now that is the planet is well known as Venus. (Sarton, 75) Plato and Aristotle’s theories were incredible contributions on us today. Both of their theories were all about the behavior and life of the planets, such as their theory that the earth is spherical. (Sarton, 421). Ancient Greece als...
Our understanding of Greek Astronomy before the 4th century (BCE) is very piecemeal. Among the small number of surviving writings we have, the majority of our knowledge is composed of references and comments from Aristotle (mostly opinions and criticisms). What is clear is that the earth was believed to be spherical, and that there was an increasing determination to comprehend nature without supernatural explanations. One of the biggest sources of information for the Greeks actually came from “records of thousands of heavenly occurrences” left by the Babylonians (Ionides, Stephen A. and Margaret L.). Part of the Babylonian records left to the Greeks contained records of eclipses and had calculated the periods of their occurrences, the most famous of these was known as the Saros, which predicted that eighteen years and eleven days after an eclipse, another very similar eclipse will occur.
Since the first Egyptian farmers discovered the annual reappearance of Sirius just before dawn a few days before the yearly rising of the Nile, ancient civilizations around the Mediterranean have sought to explain the movements of the heavens as a sort of calendar to help guide them conduct earthly activities. Counting phases of the moon or observing the annual variations of day length could, after many years' collection of observations, serve as vital indicators for planting and harvesting times, safe or stormy season for sailing, or time to bring the flocks from winter to summer pastures. With our millennia of such observation behind us, we sometimes forget that seeing and recording anything less obvious than the rough position of sun or nightly change of moon phase requires inventing both accurate observation tools (a stone circle, a gnomon used to indicate the sun's shadow, a means to measure the position of stars in the sky) and a system of recording that could be understood by others. The ancient Greeks struggled with these problems too, using both native technology and inquiry, and drawing upon the large body of observations and theories gradually gleaned from their older neighbors across the sea, Egypt and Babylonia. Gradually moving from a system of gods and divine powers ordering the world to a system of elements, mathematics, and physical laws, the Greeks slowly adapted old ideas to fit into a less supernatural, hyper-rational universe.
The Scientific Revolution was sparked through Nicolaus Copernicusí unique use of mathematics. His methods developed from Greek astr...
Pythagoras held that an accurate description of reality could only be expressed in mathematical formulae. “Pythagoras is the great-great-grandfather of the view that the totality of reality can be expressed in terms of mathematical laws” (Palmer 25). Based off of his discovery of a correspondence between harmonious sounds and mathematical ratios, Pythagoras deduced “the music of the spheres”. The music of the spheres was his belief that there was a mathematical harmony in the universe. This was based off of his serendipitous discovery of a correspondence between harmonious sounds and mathematical ratios. Pythagoras’ philosophical speculations follow two metaphysical ideals. First, the universe has an underlying mathematical structure. Secondly the force organizing the cosmos is harmony, not chaos or coincidence (Tubbs 2). The founder of a brotherhood of spiritual seekers Pythagoras was the mo...
The concept of impossible constructions in mathematics draws in a unique interest by Mathematicians wanting to find answers that none have found before them. For the Greeks, some impossible constructions weren’t actually proven at the time to be impossible, but merely so far unachieved. For them, there was excitement in the idea that they might be the first one to do so, excitement that lay in discovery. There are a few impossible constructions in Greek mathematics that will be examined in this chapter. They all share the same criteria for constructability: that they are to be made using solely a compass and straightedge, and were referred to as the three “classical problems of antiquity”. The requirements of using only a compass and straightedge were believed to have originated from Plato himself. 1
Democritus was the leader of a group called Atomists. Although they were unable to prove that matter was made up of small particles, they were the first to come up with the idea. Democritus believed that atoms differed in size, shape, and movement but were all made of the same substances. Aristotle was the most important scientific philosopher in Greece. He believed that all matter on earth consisted of four pure substances or elements, which were earth, air, fire, and water. He also believed that the earth was the centre of the universe, and that anything beyond the earth consisted of a fifth pure substance called quintessence. Archimedes was an inventor and mathematician, who discovered several basic scientific principles and developed a number of measuring techniques. Ptolemy was an Egyptian astronomer. He developed a model for predicting the positions of the sun, moon, stars, and planets. Like Aristotle, he believed that the earth was the center of the universe. Between 400 AD. and 1000 AD.
Nicholaus Copernicus is one of the most well known astronomers of all time. He is even labeled as the founder of modern astronomy for the proposition of his heliocentric theory (“Nicolaus Copernicus”, Scientists: Their Lives and Works). The heliocentric theory was revolutionary for Copernicus’ time. Copernicus lived during the Renaissance. “The era of the Renaissance (roughly 1400-1600) is usually known for the “rebirth” of an appreciation of ancient Greek and Roman art forms, along with other aspects of classical teachings that tended to diminish the virtually exclusive concentration on religious teachings during the preceding centuries of the “Dark Ages.” New thinking in science was also evident in this time…” This time period became known as the scientific revolution (“Copernicus: On The Revolutions Of Heavenly Bodies). In other words, old ideas were revived in the arts and other means and less emphasis was placed o...