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Ptolemy of Alexandria / TAHL-uh-mee /

or Claudius Ptolemaeus (Latin) 

c. 100 – c. 178
Astronomer, Geographer, and Mathematician
Mathematics Ranking 8th of 46
Ptolemy - BOOK - Burundi.JPG

This portrait of Ptolemy floats in his geocentric universe.

Its millenary predominance will soon be overcome by the

scientific revolution that will emerge from Copernicus’

heliocentric theories. The inscription refers to the birth of

Copernicus, the Earth in the middle of the panisphere, the sun at the bottom right. Stamp from the Republic of

Burundi in 1973.

Ptolemy of Alexandria considered the Earth the center of the universe (the “Ptolemaic system”). Virtually nothing is known about Ptolemy’s life.

Mathematics—Trigonometry, Astronomy

Ptolemy wrote the Mathematiki Syntaxis (Mathematical Collection, 460 pages), which was by far the most influential and significant trigonometric work of all antiquity.(1) Trigonometry deals with the relations of the sides and angles of triangles and with the relevant functions of any angles. The terms sine, cosine, and tangent describe various relationships between the sides of a right-angled triangle. His book was also the most influential astronomical work from the time it was written until the sixteenth century, and it was copied and analyzed countless   times.(2)


The Mathematiki Syntaxis, a work in 13 books, contained a complete mathematical description of the Greek model of the universe with parameters for the various motions of the sun, moon, and planets. He proposed a way of calculating the movements of the planets on the assumption that they, along with the sun and the stars, were embedded in clear spheres that revolved around the Earth. The system of Ptolemy, called the Ptolemaic system, prevailed in astronomy for nearly 1,500 years, until the correct model of the solar system, with the sun at the center and planets in motion, including Earth, was developed from the ideas of Nicolaus Copernicus in the 1500s.(3)


The book was the culmination of Greek astronomy. It is also the major source of knowledge about the work of Hipparchus, probably the greatest astronomer of antiquity (the time between 3,000 B.C.E. and c. 475 C.E., the fall of the Roman Empire).(4) Like Euclid’s Elements, it replaced all earlier works on its subject. More than any other book, it gave impetus to the notion that astronomers could create a mathematical model—that is, a quantitative description of natural phenomena—that would yield reliable predictions. Virtually all subsequent astronomical works, both in the Islamic world and in the West, up to and including the work of Copernicus, were based on Ptolemy’s encyclopedic masterpiece. Many centuries after it was written, it became known as the megisti syntaxis (the greatest collection), to distinguish it from lesser astronomical works. Islamic scientists then began to call the book al-magisti, and ever since it has been known as the Almagest.



(1) Carl B. Boyer, A History of Mathematics, 2nd Edition (New York, 1991), p. 164.

(2) Victor J. Katz, A History of Mathematics – An Introduction, 2nd edition (Reading, 1998), p. 145.

(3) E.D. Hirsch, Jr., Joseph F. Kett, James Trefil, The Dictionary of Cultural Literacy – What Every American Needs to Know, 2nd Edition (Boston, 1993), p. 205.

(4) Encyclopaedia Britannica, Micropaedia, Volume 9, 1993, 15th Edition, p. 775.

Key References: There is no biography of Ptolemy. A full English text of Almagest is the translation by R. Catesby Taliaferro published in Great Books of the Western World, v. 16, 1952. Ptolemy’s geographical work is discussed by J. O. Thomson in History of Ancient Geography, 1948 and Jerry Brotton in A History of the World in 12 Maps, 2012.


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