Everything about Claudius Ptolemaeus totally explained
» For the Macedonian general and ruler of Egypt, see Ptolemy I Soter; for others with "Ptolemy..." names, and history of those names, see Ptolemy (name).
Claudius Ptolemaeus (
Greek: Κλαύδιος Πτολεμαῖος
Klaúdios Ptolemaĩos; after
83 –
161 AD), known in English as
Ptolemy, was an ancient
mathematician,
geographer,
astronomer, and
astrologer. He lived in
Roman Egypt, and was probably born there in a town in the
Thebaid called
Ptolemais Hermiou; he died in
Alexandria in 161 AD.
Ptolemy was the author of several scientific treatises, three of which would be of continuing importance to later
Islamic and
European science. The first is the astronomical treatise now known as the
Almagest (in Greek, Η Μεγάλη Σύνταξις, "The Great Treatise", originally Μαθηματικἠ Σύνταξις, "Mathematical Treatise"). The second is the
Geography, which is a thorough discussion of the geographic knowledge of the
Greco-Roman world. The third is the astrological treatise known as the
Tetrabiblos ("Four books") in which he attempted to adapt
horoscopic astrology to the
Aristotelian natural philosophy of his day.
Name and origins
Beyond his being considered a member of Alexandria's
Greek society, few details of Ptolemy's life are known. He wrote in
Ancient Greek; some scholars have concluded that Ptolemy was a Greek,
He was often known in later
Arabic sources as "the
Upper Egyptian", suggesting that he may have had origins in southern
Egypt.
Ptolemy is a Greek name. It occurs once in Greek mythology, and is of Homeric form. It was quite common among the Macedonian upper class at the time of
Alexander the Great, and there are several among Alexander's army, one of whom made himself King of Egypt:
Ptolemy I Soter; all the Kings after him, until Rome conquered Egypt, were also
Ptolemies. There is no evidence on Ptolemy's ancestry, but most scholars consider it unlikely that Ptolemy was related to the royal family.
Claudius is a Roman name; it implies Ptolemy was a Roman citizen. It would have suited custom if the first Ptolemy who became a citizen (whether it was he or an ancestor) took the
nomen from a Roman called Claudius, who was in some sense responsible for the citizenship. If, as wasn't uncommon, this Roman was the Emperor, the citizenship would have been granted between
14 and
68 AD, when the
Claudii were Emperors. The astronomer would also have had a
praenomen, which remains unknown.
Astronomy
The
Almagest is the only surviving comprehensive ancient treatise on astronomy.
Babylonian astronomers had developed arithmetical techniques for calculating astronomical phenomena; Greek astronomers such as
Hipparchus had produced geometric models for calculating celestial motions; Ptolemy, however, claimed to have derived his geometrical models from selected astronomical observations by his predecessors spanning more than 800 years, though astronomers have for centuries suspected that his models' parameters were adopted
independently
of observations. Ptolemy presented his astronomical models in convenient tables, which could be used to compute the future or past position of the planets. The
Almagest also contains a
star catalogue, which is an appropriated version of a catalogue created by Hipparchus. Its list of forty-eight
constellations is ancestral to the modern system of constellations, but unlike the modern system they didn't cover the whole sky (only the sky Hipparchus could see). Through the Middle Ages it was spoken of as the authoritative text on astronomy, with its author becoming an almost mythical figure, called Ptolemy, King of Alexandria. The
Almagest was preserved, like most of Classical Greek science, in
Arabic manuscripts (hence its familiar name). Because of its reputation, it was widely sought and was
translated twice into Latin in the 12th century, once in Sicily and again in Spain. Ptolemy's model, like those of his predecessors, was
geocentric and was almost universally accepted until an equally systematic presentation of a
heliocentric geometrical model by
Nicolaus Copernicus.
His
Planetary Hypotheses went beyond the mathematical model of the
Almagest to present a physical realization of the universe as a set of nested spheres, in which he used the epicycles of his planetary model to compute the dimensions of the universe. He estimated the Sun was at an average distance of 1210 Earth radii while the radius of the sphere of the fixed stars was 20,000 times the radius of the Earth.
Ptolemy presented a useful tool for astronomical calculations in his
Handy Tables, which tabulated all the data needed to compute the positions of the Sun, Moon and planets, the rising and setting of the stars, and
eclipses of the Sun and Moon. Ptolemy's
Handy Tables provided the model for later astronomical tables or
zījes. In the
Phaseis (
Risings of the Fixed Stars) Ptolemy gave a
parapegma, a star
calendar or
almanac based on the appearances and disappearances of stars over the course of the solar year.
His model and computational methods were adopted and modified in the
Arabic speaking world and in
India, since they were of sufficient accuracy to satisfy the needs of astronomers, astrologers, timekeepers, calendar keepers, and
navigators.
Geography
Ptolemy's other main work is his
Geographia. This too is a compilation of what was known about the world's
geography in the
Roman Empire during his time. He relied somewhat on the work of an earlier geographer,
Marinos of Tyre, and on
gazetteers of the Roman and ancient
Persian Empire, but most of his sources beyond the perimeter of the Empire were unreliable.
The first part of the
Geographia is a discussion of the data and of the methods he used. As with the model of the solar system in the
Almagest, Ptolemy put all this information into a grand scheme. Following Marinos, he assigned
coordinates to all the places and geographic features he knew, in a
grid that spanned the globe.
Latitude was measured from the
equator, as it's today, but Ptolemy preferred in
book 8 to express it as the length of the longest day rather than
degrees of arc (the length of the
midsummer day increases from 12h to 24h as you go from the equator to the
polar circle). In books 2 through 7, he used degrees and put the
meridian of 0
longitude at the most western land he knew, the "
Blessed Islands", probably the
Cape Verde islands
(not the
Canary Islands, as long accepted) as suggested by the location of the six dots labelled the "FORTUNATA" islands near the left extreme of the blue sea of Ptolemy's map here reproduced.
Ptolemy also devised and provided instructions on how to create maps both of the whole inhabited world (
oikoumenè) and of the Roman provinces. In the second part of the
Geographia he provided the necessary
topographic lists, and captions for the maps. His
oikoumenè spanned 180 degrees of longitude from the Blessed Islands in the
Atlantic Ocean to the middle of
China, and about 80 degrees of latitude from The
Shetlands to anti-Meroe (east coast of
Africa); Ptolemy was well aware that he knew about only a quarter of the globe, and an erroneous extension of China southward blocked off any awareness of the Pacific Ocean.
The maps in surviving manuscripts of Ptolemy's
Geographia, however, date only from about 1300, after the text was rediscovered by
Maximus Planudes. It seems likely that the topographical tables in books 2-7 are cumulative texts - texts which were altered and added to as new knowledge became available in the centuries after Ptolemy (Bagrow 1945). This means that information contained in different parts of the Geography is likely to be of different date.
Maps based on scientific principles had been made since the time of
Eratosthenes (
3rd century BC), but Ptolemy improved
projections. It is known that a world map based on the
Geographia was on display in
Autun,
France in late Roman times. In the
15th century Ptolemy's
Geographia began to be printed with engraved maps; the earliest printed edition with engraved maps was produced in Bologna in 1477, followed quickly by a Roman edition in 1478 (Campbell, 1987). An edition printed at
Ulm in 1482, including woodcut maps, was the first one printed north of the
Alps. The maps look distorted as compared to modern maps, because Ptolemy's data were inaccurate. One reason is that Ptolemy estimated the size of the Earth as too small: while
Eratosthenes found 700
stadia for a great circle degree on the globe, in the
Geographia Ptolemy uses 500
stadia. It is highly probable that these were the same
stadion since Ptolemy switched from the former scale to the latter, between the
Syntaxis and the
Geographia and severely readjusted longitude degrees accordingly. If they both used the Attic
stadion of about
185 meters, then the older estimate is 1/6 too large, and Ptolemy's value is 1/6 too small, a difference recently
explained as due to ancient scientists' use of simple methods of measuring the earth, which were corrupted either high or low by a factor of 5/6, due to air's bending of horizontal light rays by 1/6 of the earth's curvature. See also
Ancient Greek units of measurement and
History of geodesy.
Because Ptolemy derived many of his key latitudes from crude longest day values, his latitudes are erroneous on average by roughly a degree (2 degrees for Byzantium, 4 degrees for Carthage), though capable ancient astronomers knew their latitudes to more like a minute. (Ptolemy's own latitude was in error by 14'.) He agreed (
Geographia 1.4) that longitude was best determined by simultaneous observation of lunar eclipses, yet he was so out of touch with the scientists of his day that he knew of no such data more recent than 500 years ago (Arbela eclipse). When switching from 700 stadia per degree to 500, he (or Marinos) expanded longitude differences between cities accordingly (a point 1st realized by P.Gosselin in 1790), resulting in serious over-stretching of the earth's east-west scale in degrees, though not distance. Achieving highly precise longitude remained a problem in geography until the invention of the
marine chronometer at the end of the 18th century. It must be added that his original topographic list can't be reconstructed: the long tables with numbers were transmitted to posterity through copies containing many scribal errors, and people have always been adding or improving the topographic data: this is a testimony to the persistent popularity of this influential work in the
history of cartography.
Astrology
Ptolemy's treatise on
astrology, the
Tetrabiblos, was the most popular astrological work of antiquity and also enjoyed great influence in the
Islamic world and the
medieval Latin West. The
Tetrabiblos is an extensive and continually reprinted treatise on the ancient principles of
horoscopic astrology in four books (Greek
tetra means "four",
biblos is "book"). That it didn't quite attain the unrivalled status of the
Almagest was perhaps because it didn't cover some popular areas of the subject, particularly
electional astrology (interpreting astrological charts for a particular moment to determine the outcome of a course of action to be initiated at that time), and
medical astrology.
The great popularity that the
Tetrabiblos did possess might be attributed to its nature as an exposition of the art of astrology and as a compendium of astrological lore, rather than as a manual. It speaks in general terms, avoiding illustrations and details of practice. Ptolemy was concerned to defend astrology by defining its limits,
compiling astronomical data that he believed was reliable and dismissing practices (such as considering the
numerological significance of names) that he believed to be without sound basis.
Much of the content of the
Tetrabiblos may well have been collected from earlier sources; Ptolemy's achievement was to order his material in a systematic way, showing how the subject could, in his view, be rationalized. It is, indeed, presented as the second part of the study of astronomy of which the
Almagest was the first, concerned with the influences of the celestial bodies in the
sublunar sphere. Thus explanations of a sort are provided for the astrological effects of the
planets, based upon their combined effects of heating, cooling, moistening, and drying.
Ptolemy's astrological outlook was quite practical: he thought that astrology was like
medicine, that's
conjectural, because of the many variable factors to be taken into account: the
race,
country, and
upbringing of a person affects an individual's personality as much if not more than the positions of the Sun, Moon, and planets at the precise moment of their birth, so Ptolemy saw astrology as something to be used in life but in no way relied on entirely.
Music
Ptolemy also wrote an influential work,
Harmonics, on
music theory and the mathematics of music. After criticizing the approaches of his predecessors, Ptolemy argued for basing musical intervals on mathematical ratios (in contrast to the followers of
Aristoxenus and in agreement with the followers of
Pythagoras) backed up by empirical observation (in contrast to the overly theoretical approach of the
Pythagoreans). Ptolemy wrote about how musical notes could be translated into mathematical equations and vice versa in
Harmonics. This is called Pythagorean tuning because it was first discovered by Pythagoras. However, Pythagoras believed that the mathematics of music should be based on the specific ratio of 3:2 whereas Ptolemy merely believed that it should just generally involve
tetrachords and
octaves. He presented his own divisions of the tetrachord and the octave, which he derived with the help of a
monochord. Ptolemy's astronomical interests also appeared in a discussion of the "
music of the spheres."
Other works
His
Optics, a work which survives only in a poor Arabic translation and in about twenty manuscripts of a Latin translation of the Arabic, made by
Eugene of Palermo (circa 1154). In it he writes about properties of
light, including
reflection,
refraction, and
color. The work is a significant part of the early
history of optics.
Named after Ptolemy
Footnotes
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