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Jason Bock

Mr. Valencia

Geometry P. 1

5 December 2017

Ptolemy

Claudius Ptolemaeus who was more commonly known as Ptolemy was born in c. 100 CE and died c. 170 CE. Ptolemy was famous for being a well-renowned astronomer, mathematician, and geographer. He lived in Alexandria, Egypt a city founded by Alexander the Great 400 years prior Ptolemy’s birth.

Ptolemy’s first work was the Almagest an astronomical manual written about ad 150. It was used as the basic guide for Islamic and European astronomers until the commencement of the 17th century (https://www.britannica.com/topic/Almagest). Its original name was the Mathematike Syntaxis which translates to “The Mathematical Arrangement.” It got the new name Almagest when an Arabic misrepresentation of the Greek word for the greatest ‘megiste.’

The Almagest consists of 13 books, the first of which provides arguments for a geocentric, spherical universe and introduces the necessary trigonometry, along with a trigonometry table, that allowed Ptolemy in subsequent books to explain and predict the motions of the Sun, Moon, planets, and stars. The second book uses spherical trigonometry to explain cartography and astronomical phenomena (such as the length of the longest day) characteristic of various positions. The third book deals with the Sun’s motion and how to predict its position in the zodiac at any given time. The fourth and fifth books discuss the more complex intricacies of the Moon’s motions. The fifth book also illustrates the construction of the instruments used for his findings. His theory is advanced to point of being applied to solar and lunar eclipses in the sixth book (https://www.britannica.com/topic/Almagest).

The seventh and eighth books are mainly about the concerns of the fixed stars, giving ecliptic coordinates and magnitudes for at least 1,022 stars. The star catalog depends heavily on that of Hipparchus, made in 129 BC, and Ptolemy mostly just converted Hipparchus’s description of the location of each star to ecliptic coordinates and then shifted these values by a constant to account for precession over the intervening centuries. They also discuss the construction of a star globe that adjusts for precision. The last five books set forth in detail geometric models for the motion of the five planets visible to the naked eye, together with tables for predicting their positions at any given time (https://www.britannica.com/topic/Almagest).

Ptolemy was also famous for being a prominent mathematician for his time. He became famous for his use of mathematics as applied to astronomical problems. His most well-known contributions are for Trigonometry, the branch of mathematics concerned with specific functions of angles and their application to calculations. An example is Ptolemy’s Ptolemy’s lengths of chords in a circle of the table is the eldest surviving table of a trigonometric function. Ptolemy also applied fundamental theorems in spherical trigonometry to the solution of many basic astronomical problems (www.britannica.com).

Ptolemy also studied visual perception in his book Opitca, later in his life. Ptolemy went above and beyond others on the use of visual perception to empirical analysis when compared to others writers of optics, such as the Hero of Alexandria who asserted, purely for philosophical reasons, that an object and its mirror image must make equal angles to a mirror. While in contrast, Ptolemy established this principle by measuring angles of incidence and reflection for planar and curved mirrors set upon a disk graduated in degrees. Ptolemy also measured how lines of sight are refracted at the boundary between materials of different density, such as air, water, and glass, although he failed to discover the exact law relating the angles of incidence and refraction known now as Snell’s law (https://www.britannica.com/biography/Ptolemy#toc253371).

Ptolemy was also a noted geographer who’s most important geographical innovation was to record longitudes and latitudes in degrees for roughly 8,000 locations on the world map at the time, which made it possible to make an exact duplicate of his new map. This has allowed us to have a very finely detailed map of the Roman Empire at the height of its power. A problem with Ptolemy’s map is that it is gravely distorted in size and orientation when compared to maps of the modern world. Ptolemy also devised 2 ways of drawing a grid of lines on a map to represent the circles of longitude and latitude on a globe. The grid gives a visual impression of the Earth’s spherical surface and somewhat shows the proportions of distances.

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