Ptolemy (100?-165? A.D.) was one of the greatest astronomers and geographers of ancient times. He was also known as Claudius Ptolemaeus. Little is known about his life other than that he made his astronomical observations in Alexandra, Egypt.

Ptolemy’s observations are preserved in a 13 part work called the Mathematike Syntaxis, of Mathematical Composition. His work was admired so much that it became known as the Almagest, a word that is a combination Greek-Arabic term meaning the greatest.


Ptolemy’s system of astronomy, written in his book the Syntaxis, was accepted until 1543. In his system, he placed the earth at the center of the earth and put the stars on a huge rotating sphere. Between the earth and stars, he placed the sun and planets which moved around a point close to the earth. He described the motions of planets by having them move according to complex mathematical constructions.

Ptolemy used three mathematical constructions, the eccentric, epicycle, and equant, to account for the movements of the planets. These made his model much more complicated but allowed him to explain the movements from a geocentric point of view with a fair degree of accuracy.

An eccentric construction is one which is not centered on the earth. An example of this is a circle which has its center not at the center of the earth, but on a point in space. Using this kind of construction violated the concept of the earth being at the center of the universe but to most astronomers, it was an acceptable compromise.

Figure 1: The eccentric. The center of this construction (C) is not earth (E).

The second construction, the epicycle, is where a planet moves around a small circle which itself moves around a larger circle. It is equivalent to moving the center of an eccentric circle. By using this construction and choosing appropriate speeds for each circle, Ptolemy was able to account for the retrograde motion of the planets.

Figure 2: The epicycle. The planet (P) revolves around the center of the epicycle (D) which in turn revolves around the center of the larger circle (C).

The third construction was the equant. In this construction, the center of motion of a point on a large circle was separated from the center of the circle. The point on the large circle was made to move uniformly around the equant point. By using this construction, Ptolemy was able to account for small changes in speed of the planets. For instance, the point on the circumference of the large circle would travel through each of the parts of the circle in equal times and would slow down as it gets closer to the equant point.

Figure 3: The equant. The planet (P) revolves around the center of the circle (C) but moves uniformly around the center of motion (M). The planet goes through each section of the circle in an equal amount of time so it would speed up as it gets farther from M.

For most planets, Ptolemy used all three of these constructions. His system accounted for the movements of the planets according to the accuracy of that time but it was incredibly complex and thus doomed. An example of the three constructions combined is given below.

Figure 4: The eccentric, epicycle and equant combined. The planet (P) revolves around the center of the epicycle (D) which moves around the center of circle (C) but moves uniformly around the center of motion (M). The earth (E) is not at the center of motion or the center of the eccentric.

Ptolemy devoted two parts of his work to a catalog of the stars. In it, he developed a mathematical description for the placement of stars. He placed the stars on a celestial sphere and gave each a celestial longitude and latitude. He cataloged 1022 stars grouped in 48 different constellations.


Ptolemy also wrote about geography and believed that the earth was a sphere. In his book Geography, he starts with an excellent theory of map projection. He also gives a list of places along with their longitudes and latitudes, but exaggerated the size of the land mass from Spain to China. This mistake led Christopher Columbus to make his historical voyage.


In his book Optics, Ptolemy wrote about the refraction of light when it passes from one substance to another, such as in the upper atmosphere. In his book he gave a table of refractions and was the first person to discover this phenomenon. This phenomenon is the reason that stars "twinkle".


Ptolemy wrote a four volume book about astrology. His serious treatment of the subject helped to spread the study of astrology.

In 1977, Robert R. Newton published his book The Crime of Claudius Ptolemy in which he accused Ptolemy of being the “most successful fraud in history”. Newton charged Ptolemy with faking the observations of his predecessors to better suit his theory. The historians of science said that the figures Ptolemy quoted were the ones who agreed the best with his theory out of a larger body of observers. Their conclusion, however, is that the case against Ptolemy is not proven.

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