Ptolemy (born c. 100ce—died c. 170ce) was anEgyptianastronomer,mathematician, andgeographer of Greekdescent who flourished inAlexandria during the 2nd centuryce. In several fields his writings represent the culminating achievement ofGreco-Roman science, particularly hisgeocentric (Earth-centred) model of theuniverse now known as thePtolemaic system.

Virtually nothing is known about Ptolemy’s life except what can be inferred from his writings. His first major astronomical work, theAlmagest, was completed about 150ce and contains reports of astronomical observations that Ptolemy had made over the preceding quarter of a century. The size and content of his subsequent literary production suggests that he lived until about 170ce.

Astronomer

The book that is now generally known as theAlmagest (from a hybrid of Arabic and Greek, “the greatest”) was called by PtolemyHē mathēmatikē syntaxis (“The Mathematical Collection”) because he believed that its subject, the motions of the heavenly bodies, could be explained in mathematical terms. The opening chapters presentempirical arguments for the basiccosmological framework within which Ptolemy worked.Earth, he argued, is a stationary sphere at the centre of a vastly largercelestial sphere that revolves at a perfectly uniform rate around Earth, carrying with it thestars,planets,Sun, andMoon—thereby causing their daily risings and settings. Through the course of a year the Sun slowly traces out a great circle, known as theecliptic, against the rotation of the celestial sphere. (TheMoon and planets similarly travel backward—hence, the planets were also known as “wandering stars”—against the “fixed stars” found in the ecliptic.) The fundamental assumption of theAlmagest is that the apparently irregular movements of the heavenly bodies are in reality combinations of regular, uniform, circular motions.

How much of theAlmagest is original is difficult to determine because almost all of the preceding technical astronomical literature is now lost. Ptolemy creditedHipparchus (mid-2nd centurybce) with essential elements of his solar theory, as well as parts of his lunar theory, while denying that Hipparchus constructed planetary models. Ptolemy made only a few vague anddisparaging remarks regarding theoretical work over the intervening three centuries, yet the study of the planets undoubtedly made great strides during that interval. Moreover, Ptolemy’sveracity, especially as an observer, has been controversial since the time of the astronomerTycho Brahe (1546–1601). Brahe pointed out that solar observations Ptolemy claimed to have made in 141 are definitely not genuine, and there are strong arguments for doubting that Ptolemy independently observed the more than 1,000 stars listed in hisstar catalog. What is not disputed, however, is the mastery of mathematical analysis that Ptolemy exhibited.

Ptolemy was preeminently responsible for the geocentric cosmology that prevailed in theIslamic world and inmedievalEurope. This was not due to theAlmagest so much as a latertreatise,Hypotheseis tōn planōmenōn (Planetary Hypotheses). In this work he proposed what is now called thePtolemaic system—a unified system in which each heavenly body is attached to its own sphere and the set of spheres nested so that it extends without gaps from Earth to the celestial sphere. The numerical tables in theAlmagest (which enabled planetary positions and other celestial phenomena to be calculated for arbitrary dates) had a profound influence on medievalastronomy, in part through a separate, revised version of the tables that Ptolemy published asProcheiroi kanones (“Handy Tables”). Ptolemy taught later astronomers how to use quantitative observations with recorded dates to revise cosmological models.

Britannica Quiz

Astronomy and Space Quiz

Ptolemy also attempted to placeastrology on a sound basis inApotelesmatika (“Astrological Influences”), later known as theTetrabiblos for its four volumes. He believed that astrology is alegitimate, though inexact, science that describes the physical effects of the heavens on terrestrial life. Ptolemy accepted the basic validity of the traditional astrological doctrines, but he revised the details toreconcile the practice with anAristotelianconception of nature, matter, and change. Of Ptolemy’s writings, theTetrabiblos is the most foreign to modern readers, who do not accept astral prognostication and a cosmology driven by the interplay of basic qualities such as hot, cold, wet, and dry.

Mathematician

Ptolemy has a prominent place in thehistory ofmathematics primarily because of the mathematical methods he applied to astronomical problems. His contributions totrigonometry are especially important. For instance, Ptolemy’s table of the lengths ofchords in a circle is the earliest surviving table of atrigonometric function. He also applied fundamental theorems in spherical trigonometry (apparently discovered half a century earlier byMenelaus of Alexandria) to the solution of many basic astronomical problems.

Access for the whole family!

Bundle Britannica Premium and Kids for the ultimate resource destination.

Subscribe

Among Ptolemy’s earliesttreatises, theHarmonics investigatedmusical theory while steering a middle course between an extreme empiricism and the mystical arithmetical speculations associated withPythagoreanism. Ptolemy’s discussion of the roles of reason and the senses in acquiring scientific knowledge have bearing beyond music theory.

Probably near the end of his life, Ptolemy turned to the study of visual perception inOptica (“Optics”), a work that only survives in a mutilated medieval Latin translation of an Arabic translation. The extent to which Ptolemy subjected visual perception to empirical analysis is remarkable when contrasted with other Greek writers onoptics. For example,Hero of Alexandria (mid-1st centuryce)asserted, purely for philosophical reasons, that an object and its mirror image must make equal angles to amirror. In contrast, Ptolemy established this principle by measuring angles ofincidence andreflection for planar and curved mirrors set upon a disk graduated in degrees. Ptolemy also measured how lines of sight arerefracted at the boundary between materials of different density, such asair,water, andglass, although he failed to discover the exact law relating the angles of incidence andrefraction (Snell’s law).