Ptolemy

=Ptolemy=
 * 87-170 A.D.**

"Ptolemy created a universe that lasted a thousand years. Copernicus created a universe that lasted four hundred years. Einstein has created a universe, and I can't tell you how long it will last." -George Bernard Shaw



**//EARLY and PERSONAL LIFE//**
Ptolemy, or Claudius Ptolemaeus, lived in Alexandria, Egypt from approximately 80 to 170 A.D. He may have been born in the Hellenistic city of Ptolemais Hermii in the northern part of Egypt, but this information cannot be confirmed (1). His name gives us a few clues about his descent. Claudius Ptolemy is a mixture of the Greek Egyptian ‘Ptolemy’ and the Roman ‘Claudius,’ which leads historians to believe that he descended from a Greek family living in Egypt and was also a Roman citizen (2). Although little in known of Ptolemy’s personal life, he is regarded today as an incredible astronomer, geographer, and mathematician. He managed to codify the Greek geocentric view of the universe, and rationalize the apparent motions of the planets around Earth, as they were believed to be in his time (3). He wrote numerous books including //The Almagest, Optics, The Planetary Hypothesis, The Optics,// and //On the Criterion.//

**//HIPPARCHUS’S CHORD//**
In the study of Ptolemy and his contributions to astronomy, one must also closely examine the man who laid the foundation for Ptolemy’s work. [|Hipparchus of Rhodes] lived from 190-120 B.C. and like Ptolemy, very little is known today with regards to his personal life. Most of the information describing his work comes from Ptolemy’s //The Almagest,// which was published over 300 years after Hipparchus’ death. Through study of this work, it has been established that Hipparchus made significant improvements in mathematics, particularly trigonometry, a field that some claim he actually invented. He produced a table of chords (an early trigonometric table); this gave him a method of solving triangles that allowed him to avoid solving each triangle from first principles (4). Hipparchus was also the first Greek to divide a circle into 360 degrees. By the time of his death in 120 B.C., Hipparchus had calculated the length of the year to within 6.5 minutes and discovered the procession of the equinoxes, a very slow conical motion around the orbital axis. It is estimated that his star catalog contained about 850 stars, which was extremely helpful to Ptolemy when collecting observations to establish his own catalog (5). It has been difficult for historians and scientists to determine (from //Commentary on Aratus and Eudoxus,// Hipparchus’s only work that remains to this day) what information came, at least in part, from the observations and solutions provided by Hipparchus but it seems as though the man acted as a wonderful teacher to Ptolemy through this work.

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Ptolemy believed that the motions of the heavenly bodies could be explained in mathematical terms (6). In //The Almagest//, he writes, "“And so, in general, we have to state that the heavens are spherical and move spherically; that the earth, in figure, is sensibly spherical also when taken as a whole; in position, lies right in the middle of the heavens, like a geometrical centre; in magnitude and distance, has the ratio of a point with respect to the sphere of the fixed stars, having itself no local motion at all (7).” Ptolemy used Hipparchus’s system of the universe as a major building block and extended upon his ideas when creating his own universe. Ptolemy, however, wanted to improve upon Hipparchus’s model as Toomer writes, “Although Ptolemy obviously had studied Hipparchus’s writings thoroughly and had a deep respect for his work, his main concern was not to transmit it to posterity but to use it and, where possible, improve upon it in constructing his own astronomical system (8).” And that’s just what Ptolemy did. In [|Ptolemy's universe], at least 80 epicycles existed to explain the motions of the Sun, the Moon, and the planets (though only five had been discovered in Ptolemy’s time). He “used a complex mechanism using eccentric circles and epicycles to describe accurately the planetary motion in a geocentric model. The eccentric is the true center of planet motion and not the Earth (as Aristotle believed).====== The planet moves uniformly in relation to the Aequant, or Equant (9).” Ptolemy believed that the planets and the Sun orbited Earth in the order Mercury, Venus, Sun, Mars, Jupiter, and Saturn (10). He also argued that the orbits of the planets, the Moon, and the Sun around Earth were perfect circles; it was not until the time of Kepler that the shape of orbits was proven to be elliptical rather than spherical (11). The Ptolemaic system, a system with many parameters used to describe astronomic phenomena, actually predicts the positions of the planets accurately enough for observations made without the aid of a telescope (12). Although a summary of Ptolemy’s theory was published in the //Canobic Inscription// in 147-148 A.D. the Ptolemaic system was truly put forth in the book //The Mathematical Syntaxis.// It is also widely referred to as //The Almagest,// and was published in 150 A.D. //The Almagest// is a “thirteen book mathematical treatment of the phenomena of astronomy. It contains a myriad of information ranging from earth conceptions to sun, moon and star movements as well as eclipses and a breakdown on the length of months (13).” The book also included a star catalog containing 48 constellations, including Andromeda, Aquarius, Orion, Gemini, and Cassiopia (14). Ptolemy also extended upon Hipparchus’s star catalog, expanding the number of stars to 1022. Each of the books “deals with certain astronomical concepts pertaining to stars and to objects in the solar system (15).” The encyclopedic nature of the volumes made them incredibly useful to later astronomers and made the views contained with in them so profound. //The Almagest// is a combination of all the results obtained by Greek astronomers and is the main source of knowledge about Hipparchus’s, as well as Ptolemy's work. Ptolemy’s research was so well done that his explanation of planetary motion was accepted until Copernicus’s heliocentric view came into being in 1543. It should also be noted that Ptolemy’s system is actually more accurate than Copernicus’s; his heliocentric theory did not improve upon Ptolemy’s until Kepler’s Laws are added to it (16).

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//**Ptolemy as a Mathematician, Geographer, and Astrologist**//
Ptolemy is most remembered for his work as an astronomer, but he was also a well-renown [|mathematician, geographer, and astrologist]. Ptolemy is a highly regarded mathematician, mostly for his work that pertained to astronomical problems. He made significant contributions to trigonometry; his table of the lengths of chords in a circle is the earliest known table of a trigonometric function. Ptolemy also applied fundamental theorems to spherical trigonometry in order to discover the solution to many astronomical problems (17). In the book, //Optics//, Ptolemy used mathematics to establish that an object and its mirror image must make equal angles to a mirror. He did this by, “measuring angles of incidence and reflection for both planar and curved mirrors set upon a disk graduated in degrees (18).”

Comparable to his work in astronomy were the contributions Ptolemy made in the field of geography and cartography. He knew that the world was a sphere and his is the first known [|projection of a sphere] onto a plane (19). Ptolemy’s most important achievement was the creation of longitudes and latitudes in degrees for about 8,00 locations on his world map (20). This allowed him to make exact duplicates of his map. The geographer also, “devised two ways of drawing grid lines on a flat map to represent the circles of latitude and longitude on the globe. His grid gives a visual impression of the Earth’s spherical surface and also, to a limited extent, preserves the proportionality of distances (21).” His maps were extremely accurate for the time, but they incorrectly indicated that Asia extended much farther east than it truly does. This actually may have been one of the factors that pushed Columbus to sail west for the Indies (22).

Ptolemy made an effort to place astrology on a sound basis. He argued that astrology is a legitimate, yet imperfect, science that describes the physical effects of the heavens of human and animal life. He, “accepted the basic validity of the traditional astrological doctrines, but he revised the details to reconcile the practice with an Aristotelian conception of nature, matter, and change (23).”

**//OVERALL SIGNIFICANCE//**
The significance of Ptolemy's work and observations cannot be underestimated. His Ptolemaic model of the universe was taught and upheld for over one thousand years. Although his geocentric view was ultimately proven to be incorrect by Copernicus and Kepler, his conception of pushing the bounds of mathematics in order to improve astronomical knowledge allowed later scientists to discover things most people never thought possible. Ptolemy was also excellent at recording his data. His concise and accurate collections of data made scientists fairly confident in Ptolemy's observations. Though he is most often recognized for his work in astronomy, the improvements he made in mathematics and geography are just as impressive. Ptolemy had an extremely rich love for knowledge and discovering the unknown, and this love coupled with hard work and perseverance aided him in every field of work he studied.

**REFERENCES**
(1) Lahanas, Michael. “Astronomy of Ptolemy.” __Hellenica__. 11 July 2010. []

(2) Greene, Nick. “Ptolemy Biography: Journey to the Center of the Universe- Earth- Astronomy & Geography.” __About.com: Space & Astronomy__. 14 July 2010. []

(3) __Bill Arnett’s Amateur Astro Web Sites__. Arnett, Bill. 15 July 2010. []

(4) Lahanas, Michael. “The Astronomer Hipparchus of Rhodes.” __Hellenica__. 12 July 2010. []

(5) Lahanas, Michael. “The Astronomer Hipparchus of Rhodes.” __Hellenica__. 12 July 2010. []

(6) Jones, Alexander Raymond. “Claudius Ptolemaeus.” __Encyclopedia Britannica Online__. 20 July 2010. []

(7) Ptolemy. __The Almagest I-V__, in //Great Books of the Western World//, vol. 15, //Encyclopedia Britannica,// 1952.
(8) Lahanas, Michael. “The Astronomer Hipparchus of Rhodes.” __Hellenica__. 12 July 2010. []

(9) Lahanas, Michael. “Astronomy of Ptolemy.” __Hellenica__. 11 July 2010. []

(10) __Bill Arnett’s Amateur Astro Web Sites__. Arnett, Bill. 15 July 2010. []

(11) Lahanas, Michael. “Astronomy of Ptolemy.” __Hellenica__. 11 July 2010. []

(12) Lahanas, Michael. “Astronomy of Ptolemy.” __Hellenica__. 11 July 2010. []

(13) __Bill Arnett’s Amateur Astro Web Sites__. Arnett, Bill. 15 July 2010. []

(14) __Bill Arnett’s Amateur Astro Web Sites__. Arnett, Bill. 15 July 2010. []

(15) Lahanas, Michael. “Astronomy of Ptolemy.” __Hellenica__. 11 July 2010. []

(16) Lahanas, Michael. “Astronomy of Ptolemy.” __Hellenica__. 11 July 2010. []

(17) Jones, Alexander Raymond. “Claudius Ptolemaeus.” __Encyclopedia Britannica Online__. 20 July 2010. []

(18) Jones, Alexander Raymond. “Claudius Ptolemaeus.” __Encyclopedia Britannica Online__. 20 July 2010. []

(19) Greene, Nick. “Ptolemy Biography: Journey to the Center of the Universe- Earth- Astronomy & Geography.” __About.com: Space & Astronomy__. 14 July 2010. []

(20) Jones, Alexander Raymond. “Claudius Ptolemaeus.” __Encyclopedia Britannica Online__. 20 July 2010. []

(21) Jones, Alexander Raymond. “Claudius Ptolemaeus.” __Encyclopedia Britannica Online__. 20 July 2010. []

(22) Greene, Nick. “Ptolemy Biography: Journey to the Center of the Universe- Earth- Astronomy & Geography.” __About.com: Space & Astronomy__. 14 July 2010. []

(23) Jones, Alexander Raymond. “Claudius Ptolemaeus.” __Encyclopedia Britannica Online__. 20 July 2010. []