Claudius Ptolemy Research Paper

Claudius Ptolemy was an ancient scholar, famous in the fields of astronomy, geography, and mathematics. When compared to many other famous scholars, Claudius Ptolemy’s personal life is very much a mystery. However, his works in the math and scientific community are very well documented and he had a profound impact in these areas of interest. The most famous of his works is called the Almagest, which is a series of thirteen books that are dedicated to his work in astronomy and mathematics. However, the main focus in our journey will be in learning about a specific theorem Ptolemy proposed through his work in the first book of the Almagest. In addition to gaining an understanding of the theorem we will also be discussing the significance his

This indicates that he was most definitely a descended from a Greek family that was living in Egypt but also that he was a Roman citizen. This would have had to been as a result of a previous Roman emperor giving the reward of citizenship to one of Ptolemy's ancestors at some point in time. Ptolemy was born in Alexandria, Egypt roughly at around 90 AD, and lived in Alexandria for all of his life. This location is where almost all of his work comes from. His astronomical observations come during the years 127-141 AD, the first of which we can date exactly and it was made on March 26th, 127 AD while the last was made on February 2nd, 141 AD. At the time he used his mathematics to prove a geocentric model, which is the belief that everything revolved around the Earth. This was the accepted belief for more than a thousand years until the likes of Galileo, Copernicus, and Kepler came to test these theories and ultimately disprove

Ptolemy’s Theorem which is in his Almagest, Book 1, Chapter 10, states that “In any cyclic quadrilateral abcd the sum of the products of the opposite sides is equal to the product of the diagonals.” This generates the equation;|a-┤ ├ b┤|×|c-┤ ├ d┤|+|a-┤ ├ d┤|×|c-┤ ├ b┤|=|a-┤ ├ c┤|×|b-┤ ├ d┤|. By using this theorem Ptolemy applied it to Astronomy and in doing so was able to compute his famous table of chords. If one of the sides is the diameter it is easy to derive the addition theorem which is sin⁡〖(α-β)〗 〖=sin〗⁡α cos⁡β 〖-cos〗⁡α sin⁡β. The way in which Ptolemy was able to prove this theorem was by using a geometric trick. He constructed a point e on the line ¯ac such that ∠abc=∠cbd. Now the triangles ∆abc and ∆bcd are similar and with a simple proof of this we can come to a conclusion proving he is