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Claudius Ptolemy (; , ; ; – 160s/170s AD) was a Greco-Roman
mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
,
astronomer An astronomer is a scientist in the field of astronomy who focuses on a specific question or field outside the scope of Earth. Astronomers observe astronomical objects, such as stars, planets, natural satellite, moons, comets and galaxy, galax ...
,
astrologer Astrology is a range of Divination, divinatory practices, recognized as pseudoscientific since the 18th century, that propose that information about human affairs and terrestrial events may be discerned by studying the apparent positions ...
,
geographer A geographer is a physical scientist, social scientist or humanist whose area of study is geography, the study of Earth's natural environment and human society, including how society and nature interacts. The Greek prefix "geo" means "earth" a ...
, and
music theorist Music theory is the study of theoretical frameworks for understanding the practices and possibilities of music. '' The Oxford Companion to Music'' describes three interrelated uses of the term "music theory": The first is the " rudiments", that ...
who wrote about a dozen scientific
treatise A treatise is a Formality, formal and systematic written discourse on some subject concerned with investigating or exposing the main principles of the subject and its conclusions."mwod:treatise, Treatise." Merriam-Webster Online Dictionary. Acc ...
s, three of which were important to later
Byzantine The Byzantine Empire, also known as the Eastern Roman Empire, was the continuation of the Roman Empire centred on Constantinople during late antiquity and the Middle Ages. Having survived the events that caused the fall of the Western Roman E ...
,
Islamic Islam is an Abrahamic religions, Abrahamic monotheistic religion based on the Quran, and the teachings of Muhammad. Adherents of Islam are called Muslims, who are estimated to number Islam by country, 2 billion worldwide and are the world ...
, and Western European science. The first was his astronomical treatise now known as the ''
Almagest The ''Almagest'' ( ) is a 2nd-century Greek mathematics, mathematical and Greek astronomy, astronomical treatise on the apparent motions of the stars and planetary paths, written by Ptolemy, Claudius Ptolemy ( ) in Koine Greek. One of the most i ...
'', originally entitled ' (, ', ). The second is the ''
Geography Geography (from Ancient Greek ; combining 'Earth' and 'write', literally 'Earth writing') is the study of the lands, features, inhabitants, and phenomena of Earth. Geography is an all-encompassing discipline that seeks an understanding o ...
'', which is a thorough discussion on maps and the geographic knowledge of the
Greco-Roman world The Greco-Roman world , also Greco-Roman civilization, Greco-Roman culture or Greco-Latin culture (spelled Græco-Roman or Graeco-Roman in British English), as understood by modern scholars and writers, includes the geographical regions and co ...
. The third is the astrological treatise in which he attempted to adapt horoscopic astrology to the Aristotelian
natural philosophy Natural philosophy or philosophy of nature (from Latin ''philosophia naturalis'') is the philosophical study of physics, that is, nature and the physical universe, while ignoring any supernatural influence. It was dominant before the develop ...
of his day. This is sometimes known as the ' (, 'On the Effects') but more commonly known as the ' (from the
Koine Greek Koine Greek (, ), also variously known as Hellenistic Greek, common Attic, the Alexandrian dialect, Biblical Greek, Septuagint Greek or New Testament Greek, was the koiné language, common supra-regional form of Greek language, Greek spoken and ...
meaning 'four books'; ). The
Catholic Church The Catholic Church (), also known as the Roman Catholic Church, is the List of Christian denominations by number of members, largest Christian church, with 1.27 to 1.41 billion baptized Catholics Catholic Church by country, worldwid ...
promoted his work, which included the only mathematically sound geocentric model of the
Solar System The Solar SystemCapitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Sola ...
, and unlike most Greek mathematicians, Ptolemy's writings (foremost the ''Almagest'') never ceased to be copied or commented upon, both in
late antiquity Late antiquity marks the period that comes after the end of classical antiquity and stretches into the onset of the Early Middle Ages. Late antiquity as a period was popularized by Peter Brown (historian), Peter Brown in 1971, and this periodiza ...
and in the
Middle Ages In the history of Europe, the Middle Ages or medieval period lasted approximately from the 5th to the late 15th centuries, similarly to the post-classical period of global history. It began with the fall of the Western Roman Empire and ...
. However, it is likely that only a few truly mastered the mathematics necessary to understand his works, as evidenced particularly by the many abridged and watered-down introductions to Ptolemy's astronomy that were popular among the Arabs and Byzantines. His work on
epicycle In the Hipparchian, Ptolemaic, and Copernican systems of astronomy, the epicycle (, meaning "circle moving on another circle") was a geometric model used to explain the variations in speed and direction of the apparent motion of the Moon, ...
s has come to symbolize a very complex theoretical model built in order to explain a false assumption.


Biography

Ptolemy's date of birth and birthplace are both unknown. The 14th-century astronomer Theodore Meliteniotes wrote that Ptolemy's birthplace was
Ptolemais Hermiou Ptolemais Hermiou, or Ptolemais in the Thebaid, was a city and metropolitan archbishopric in Greco-Roman Egypt and remains a Catholic titular see. Today, the city of El Mansha ()-Bsoi () in the Sohag Governorate is located where the ancient cit ...
, a Greek city in the
Thebaid The Thebaid or Thebais (, ''Thēbaïs'') was a region in ancient Egypt, comprising the 13 southernmost nome (Egypt), nomes of Upper Egypt, from Abydos, Egypt, Abydos to Aswan. Pharaonic history The Thebaid acquired its name from its proximit ...
region of Egypt (now El Mansha, Sohag Governorate). This attestation is quite late, however, and there is no evidence to support it. It is known that Ptolemy lived in or around the city of
Alexandria Alexandria ( ; ) is the List of cities and towns in Egypt#Largest cities, second largest city in Egypt and the List of coastal settlements of the Mediterranean Sea, largest city on the Mediterranean coast. It lies at the western edge of the Nile ...
, in the Roman province of Egypt under Roman rule. He had a Latin name, Claudius, which is generally taken to imply he was a
Roman citizen Citizenship in ancient Rome () was a privileged political and legal status afforded to free individuals with respect to laws, property, and governance. Citizenship in ancient Rome was complex and based upon many different laws, traditions, and cu ...
. He was familiar with Greek philosophers and used Babylonian observations and Babylonian lunar theory. In half of his extant works, Ptolemy addresses a certain Syrus, a figure of whom almost nothing is known but who likely shared some of Ptolemy's astronomical interests. Ptolemy died in Alexandria. Ptolemy's year of death is not directly recorded by primary sources, and has to be inferred from the scale of his work. Suggested years of death include , , , and .


Naming and nationality

Ptolemy's Greek name'', Ptolemaeus'' (, ''Ptolemaîos''), is an ancient Greek personal name. It occurs once in
Greek mythology Greek mythology is the body of myths originally told by the Ancient Greece, ancient Greeks, and a genre of ancient Greek folklore, today absorbed alongside Roman mythology into the broader designation of classical mythology. These stories conc ...
and is of Homeric form. It was common among the Macedonian upper class at the time of
Alexander the Great Alexander III of Macedon (; 20/21 July 356 BC – 10/11 June 323 BC), most commonly known as Alexander the Great, was a king of the Ancient Greece, ancient Greek kingdom of Macedonia (ancient kingdom), Macedon. He succeeded his father Philip ...
and there were several of this name among Alexander's army, one of whom made himself
pharaoh Pharaoh (, ; Egyptian language, Egyptian: ''wikt:pr ꜥꜣ, pr ꜥꜣ''; Meroitic language, Meroitic: 𐦲𐦤𐦧, ; Biblical Hebrew: ''Parʿō'') was the title of the monarch of ancient Egypt from the First Dynasty of Egypt, First Dynasty ( ...
in 323 BC:
Ptolemy I Soter Ptolemy I Soter (; , ''Ptolemaîos Sōtḗr'', "Ptolemy the Savior"; 367 BC – January 282 BC) was a Macedonian Greek general, historian, and successor of Alexander the Great who went on to found the Ptolemaic Kingdom centered on Egypt. Pto ...
, the first pharaoh of the
Ptolemaic Kingdom The Ptolemaic Kingdom (; , ) or Ptolemaic Empire was an ancient Greek polity based in Ancient Egypt, Egypt during the Hellenistic period. It was founded in 305 BC by the Ancient Macedonians, Macedonian Greek general Ptolemy I Soter, a Diadochi, ...
. Almost all subsequent pharaohs of Egypt, with a few exceptions, were named
Ptolemy Claudius Ptolemy (; , ; ; – 160s/170s AD) was a Greco-Roman mathematician, astronomer, astrologer, geographer, and music theorist who wrote about a dozen scientific treatises, three of which were important to later Byzantine science, Byzant ...
until Egypt became a Roman province in 30 BC, ending the Macedonian family's rule. The name ''Claudius'' is a Roman name, belonging to the ''gens'' Claudia; the peculiar multipart form of the whole name ''Claudius Ptolemaeus'' is a Roman custom, characteristic of Roman citizens. This indicates that Ptolemy would have been a
Roman citizen Citizenship in ancient Rome () was a privileged political and legal status afforded to free individuals with respect to laws, property, and governance. Citizenship in ancient Rome was complex and based upon many different laws, traditions, and cu ...
. Gerald Toomer, the translator of Ptolemy's ''Almagest'' into English, suggests that citizenship was probably granted to one of Ptolemy's ancestors by either the emperor
Claudius Tiberius Claudius Caesar Augustus Germanicus ( ; ; 1 August 10 BC – 13 October AD 54), or Claudius, was a Roman emperor, ruling from AD 41 to 54. A member of the Julio-Claudian dynasty, Claudius was born to Nero Claudius Drusus, Drusus and Ant ...
or the emperor
Nero Nero Claudius Caesar Augustus Germanicus ( ; born Lucius Domitius Ahenobarbus; 15 December AD 37 – 9 June AD 68) was a Roman emperor and the final emperor of the Julio-Claudian dynasty, reigning from AD 54 until his ...
. The 9th century Persian
astronomer An astronomer is a scientist in the field of astronomy who focuses on a specific question or field outside the scope of Earth. Astronomers observe astronomical objects, such as stars, planets, natural satellite, moons, comets and galaxy, galax ...
Abu Ma'shar al-Balkhi mistakenly presents Ptolemy as a member of Ptolemaic Egypt's royal lineage, stating that the descendants of the Alexandrine general and Pharaoh
Ptolemy I Soter Ptolemy I Soter (; , ''Ptolemaîos Sōtḗr'', "Ptolemy the Savior"; 367 BC – January 282 BC) was a Macedonian Greek general, historian, and successor of Alexander the Great who went on to found the Ptolemaic Kingdom centered on Egypt. Pto ...
were wise "and included Ptolemy the Wise, who composed the book of the ''Almagest''". Abu Ma'shar recorded a belief that a different member of this royal line "composed the book on astrology and attributed it to Ptolemy". Historical confusion on this point can be inferred from Abu Ma'shar's subsequent remark: "It is sometimes said that the very learned man who wrote the book of astrology also wrote the book of the ''Almagest''. The correct answer is not known." Not much positive evidence is known on the subject of Ptolemy's ancestry, apart from what can be drawn from the details of his name, although modern scholars have concluded that Abu Ma'shar's account is erroneous. It is no longer doubted that the astronomer who wrote the ''
Almagest The ''Almagest'' ( ) is a 2nd-century Greek mathematics, mathematical and Greek astronomy, astronomical treatise on the apparent motions of the stars and planetary paths, written by Ptolemy, Claudius Ptolemy ( ) in Koine Greek. One of the most i ...
'' also wrote the '' Tetrabiblos'' as its astrological counterpart. In later
Arabic Arabic (, , or , ) is a Central Semitic languages, Central Semitic language of the Afroasiatic languages, Afroasiatic language family spoken primarily in the Arab world. The International Organization for Standardization (ISO) assigns lang ...
sources, he was often known as "the
Upper Egypt Upper Egypt ( ', shortened to , , locally: ) is the southern portion of Egypt and is composed of the Nile River valley south of the delta and the 30th parallel North. It thus consists of the entire Nile River valley from Cairo south to Lake N ...
ian", suggesting he may have had origins in southern
Egypt Egypt ( , ), officially the Arab Republic of Egypt, is a country spanning the Northeast Africa, northeast corner of Africa and Western Asia, southwest corner of Asia via the Sinai Peninsula. It is bordered by the Mediterranean Sea to northe ...
. Arabic astronomers,
geographers A geographer is a physical scientist, social scientist or humanist whose area of study is geography, the study of Earth's natural environment and human society, including how society and nature interacts. The Greek prefix "geo" means "earth" ...
, and
physicists A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe. Physicists generally are interested in the root or ultimate cau ...
referred to his name in
Arabic Arabic (, , or , ) is a Central Semitic languages, Central Semitic language of the Afroasiatic languages, Afroasiatic language family spoken primarily in the Arab world. The International Organization for Standardization (ISO) assigns lang ...
as ''Baṭlumyus'' (). Ptolemy wrote in
Koine Greek Koine Greek (, ), also variously known as Hellenistic Greek, common Attic, the Alexandrian dialect, Biblical Greek, Septuagint Greek or New Testament Greek, was the koiné language, common supra-regional form of Greek language, Greek spoken and ...
, and can be shown to have used Babylonian astronomical data. He might have been a Roman citizen, but was ethnically either a
Greek Greek may refer to: Anything of, from, or related to Greece, a country in Southern Europe: *Greeks, an ethnic group *Greek language, a branch of the Indo-European language family **Proto-Greek language, the assumed last common ancestor of all kno ...
or at least a Hellenized Egyptian. George Sarton (1936). "The Unity and Diversity of the Mediterranean World", ''Osiris'' 2, p. 406–463 29


Astronomical writings

Astronomy was the subject to which Ptolemy devoted the most time and effort; about half of all the works that survived deal with astronomical matters, and even others such as the ''Geography'' and the ''Tetrabiblos'' have significant references to astronomy.


''Mathēmatikē Syntaxis''

Ptolemy's ''
Almagest The ''Almagest'' ( ) is a 2nd-century Greek mathematics, mathematical and Greek astronomy, astronomical treatise on the apparent motions of the stars and planetary paths, written by Ptolemy, Claudius Ptolemy ( ) in Koine Greek. One of the most i ...
'' (originally , ) is the only surviving comprehensive ancient treatise on astronomy. Although Babylonian astronomers had developed arithmetical techniques for calculating and predicting astronomical phenomena, these were not based on any underlying model of the heavens; early Greek astronomers, on the other hand, provided qualitative geometrical models to "save the appearances" of celestial phenomena without the ability to make any predictions. The earliest person who attempted to merge these two approaches was
Hipparchus Hipparchus (; , ;  BC) was a Ancient Greek astronomy, Greek astronomer, geographer, and mathematician. He is considered the founder of trigonometry, but is most famous for his incidental discovery of the precession of the equinoxes. Hippar ...
, who produced geometric models that not only reflected the arrangement of the planets and stars but could be used to calculate celestial motions. Ptolemy, following Hipparchus, derived each of his geometrical models for the Sun, Moon, and the planets from selected astronomical observations done in the spanning of more than 800 years; however, many astronomers have for centuries suspected that some of his models' parameters were adopted independently of observations. Ptolemy presented his astronomical models alongside convenient tables, which could be used to compute the future or past position of the planets. The ''Almagest'' also contains a
star catalogue A star catalogue is an astronomical catalogue that lists stars. In astronomy, many stars are referred to simply by catalogue numbers. There are a great many different star catalogues which have been produced for different purposes over the year ...
, which is a version of a catalogue created by Hipparchus. Its list of forty-eight
constellation A constellation is an area on the celestial sphere in which a group of visible stars forms Asterism (astronomy), a perceived pattern or outline, typically representing an animal, mythological subject, or inanimate object. The first constellati ...
s is ancestral to the modern system of constellations but, unlike the modern system, they did not cover the whole sky (only what could be seen with the naked eye in the northern hemisphere). For over a thousand years, the ''Almagest'' was the authoritative text on astronomy across Europe, the Middle East, and North Africa. The ''Almagest'' was preserved, like many extant Greek scientific works, in Arabic manuscripts; the modern title is thought to be an Arabic corruption of the Greek name ('The greatest treatise'), as the work was presumably known during
late antiquity Late antiquity marks the period that comes after the end of classical antiquity and stretches into the onset of the Early Middle Ages. Late antiquity as a period was popularized by Peter Brown (historian), Peter Brown in 1971, and this periodiza ...
. Because of its reputation, it was widely sought and translated twice into Latin in the 12th century, once in Sicily and again in Spain. Ptolemy's planetary models, like those of the majority of his predecessors, were geocentric and almost universally accepted until the reappearance of
heliocentric Heliocentrism (also known as the heliocentric model) is a Superseded theories in science#Astronomy and cosmology, superseded astronomical model in which the Earth and Solar System, planets orbit around the Sun at the center of the universe. His ...
models during the
Scientific Revolution The Scientific Revolution was a series of events that marked the emergence of History of science, modern science during the early modern period, when developments in History of mathematics#Mathematics during the Scientific Revolution, mathemati ...
.


Modern reassessment

Under the scrutiny of modern scholarship, and the cross-checking of observations contained in the ''Almagest'' against figures produced through backwards extrapolation, various patterns of errors have emerged within the work. A prominent miscalculation is Ptolemy's use of measurements that he claimed were taken at noon, but which systematically produce readings now shown to be off by half an hour, as if the observations were taken at 12:30 pm. The overall quality of Ptolemy's observations has been challenged by several modern scientists, but prominently by Robert R. Newton in his 1977 book ''The Crime of Claudius Ptolemy'', which asserted that Ptolemy fabricated many of his observations to fit his theories. Newton accused Ptolemy of systematically inventing data or doctoring the data of earlier astronomers, and labelled him "the most successful fraud in the history of science". One striking error noted by Newton was an autumn equinox said to have been observed by Ptolemy and "measured with the greatest care" at 2pm on 25 September 132, when the equinox should have been observed around 9:55am the day prior. In attempting to disprove Newton, Herbert Lewis also found himself agreeing that "Ptolemy was an outrageous fraud," and that "all those result capable of statistical analysis point beyond question towards fraud and against accidental error". The charges laid by Newton and others have been the subject of wide discussions and received significant push back from other scholars against the findings.
Owen Gingerich Owen Jay Gingerich (; March 24, 1930 – May 28, 2023) was an American astronomer who had been professor emeritus of astronomy and of the history of science at Harvard University and a senior astronomer emeritus at the Smithsonian Astrophysical Ob ...
, while agreeing that the ''Almagest'' contains "some remarkably fishy numbers", including in the matter of the 30-hour displaced equinox, which he noted aligned perfectly with predictions made by Hipparchus 278 years earlier, rejected the qualification of fraud. Objections were also raised by Bernard Goldstein, who questioned Newton's findings and suggested that he had misunderstood the secondary literature, while noting that issues with the accuracy of Ptolemy's observations had long been known. Other authors have pointed out that instrument warping or atmospheric refraction may also explain some of Ptolemy's observations at a wrong time. In 2022 the first Greek fragments of Hipparchus' lost star catalog were discovered in a palimpsest and they debunked accusations made by the French astronomer
Jean Baptiste Joseph Delambre Jean Baptiste Joseph, chevalier Delambre (19 September 1749 – 19 August 1822) was a French mathematician, astronomer, historian of astronomy, and geodesist. He was also director of the Paris Observatory, and author of well-known books on the ...
in the early 1800s which were repeated by R. R. Newton. Specifically, it proved Hipparchus was not the sole source of Ptolemy's catalog, as they both had claimed, and proved that Ptolemy did not simply copy Hipparchus' measurements and adjust them to account for precession of the equinoxes, as they had claimed. Scientists analyzing the charts concluded:
It also confirms that Ptolemy’s Star Catalogue was not based solely on data from Hipparchus’ Catalogue.
... These observations are consistent with the view that Ptolemy composed his star catalogue by combining various sources, including Hipparchus’ catalogue, his own observations and, possibly, those of other authors.


''Handy Tables''

The '' Handy Tables'' () are a set of astronomical tables, together with canons for their use. To facilitate astronomical calculations, Ptolemy tabulated all the data needed to compute the positions of the Sun, Moon and planets, the rising and setting of the stars, and
eclipses An eclipse is an astronomical event which occurs when an astronomical object or spacecraft is temporarily obscured, by passing into the shadow of another body or by having another body pass between it and the viewer. This alignment of three ...
of the Sun and Moon, making it a useful tool for astronomers and astrologers. The tables themselves are known through
Theon of Alexandria Theon of Alexandria (; ; ) was a Greek scholar and mathematician who lived in Alexandria, Egypt. He edited and arranged Euclid's '' Elements'' and wrote commentaries on works by Euclid and Ptolemy. His daughter Hypatia also won fame as a mathema ...
's version. Although Ptolemy's ''Handy Tables'' do not survive as such in Arabic or in Latin, they represent the prototype of most Arabic and Latin astronomical tables or '' zījes''. Additionally, the introduction to the ''Handy Tables'' survived separately from the tables themselves (apparently part of a gathering of some of Ptolemy's shorter writings) under the title ''Arrangement and Calculation of the Handy Tables''.


''Planetary Hypotheses''

The ''Planetary Hypotheses'' (, ) is a
cosmological Cosmology () is a branch of physics and metaphysics dealing with the nature of the universe, the cosmos. The term ''cosmology'' was first used in English in 1656 in Thomas Blount's ''Glossographia'', with the meaning of "a speaking of the wo ...
work, probably one of the last written by Ptolemy, in two books dealing with the structure of the universe and the laws that govern celestial motion. Ptolemy goes beyond the mathematical models of the ''Almagest'' to present a physical realization of the universe as a set of nested spheres, in which he used the
epicycle In the Hipparchian, Ptolemaic, and Copernican systems of astronomy, the epicycle (, meaning "circle moving on another circle") was a geometric model used to explain the variations in speed and direction of the apparent motion of the Moon, ...
s of his planetary model to compute the dimensions of the universe. He estimated the Sun was at an average distance of (now known to actually be while the radius of the sphere of the fixed stars was the radius of the Earth. The work is also notable for having descriptions on how to build instruments to depict the planets and their movements from a geocentric perspective, much as an
orrery An orrery is a mechanical Solar System model, model of the Solar System that illustrates or predicts the relative positions and motions of the planets and natural satellite, moons, usually according to the heliocentric model. It may also represent ...
would have done for a
heliocentric Heliocentrism (also known as the heliocentric model) is a Superseded theories in science#Astronomy and cosmology, superseded astronomical model in which the Earth and Solar System, planets orbit around the Sun at the center of the universe. His ...
one, presumably for didactic purposes.


Other astronomical works

The ''Analemma'' is a short treatise where Ptolemy provides a method for specifying the location of the Sun in three pairs of locally oriented coordinate arcs as a function of the declination of the Sun, the terrestrial latitude, and the hour. The key to the approach is to represent the solid configuration in a plane diagram that Ptolemy calls the ''
analemma In astronomy, an analemma (; ) is a diagram showing the position of the Sun in the sky as seen from a fixed location on Earth at the same Solar time#Mean solar time, mean solar time over the course of a year. The change of position is a result ...
''. In another work, the ''Phaseis'' (''Risings of the Fixed Stars''), Ptolemy gave a ''parapegma'', a star
calendar A calendar is a system of organizing days. This is done by giving names to periods of time, typically days, weeks, months and years. A calendar date, date is the designation of a single and specific day within such a system. A calendar is ...
or
almanac An almanac (also spelled almanack and almanach) is a regularly published listing of a set of current information about one or multiple subjects. It includes information like weather forecasting, weather forecasts, farmers' sowing, planting dates ...
, based on the appearances and disappearances of stars over the course of the solar year. The '' Planisphaerium'' (, ) contains 16 propositions dealing with the projection of the celestial circles onto a plane. The text is lost in Greek (except for a fragment) and survives in Arabic and Latin only. Ptolemy also erected an inscription in a temple at
Canopus Canopus is the brightest star in the southern constellation of Carina (constellation), Carina and the list of brightest stars, second-brightest star in the night sky. It is also Bayer designation, designated α Carinae, which is Rom ...
, around 146–147 AD, known as the ''Canobic Inscription''. Although the inscription has not survived, someone in the sixth century transcribed it, and manuscript copies preserved it through the Middle Ages. It begins: "To the saviour god, Claudius Ptolemy (dedicates) the first principles and models of astronomy", following by a catalogue of numbers that define a system of celestial mechanics governing the motions of the Sun, Moon, planets, and stars. In 2023, archaeologists were able to read a manuscript which gives instructions for the construction of an astronomical tool called a '' meteoroscope'' ( or ). The text, which comes from an eighth-century manuscript which also contains Ptolemy's ''Analemma'', was identified on the basis of both its content and linguistic analysis as being by Ptolemy. Ptolemy is also though to have produced his Table of Noteworthy Cities as an aid to his astronomical tables.


Other writings


''Geography''

Ptolemy's second most well-known work is his ''Geographike Hyphegesis'' (; ), known as the ''
Geography Geography (from Ancient Greek ; combining 'Earth' and 'write', literally 'Earth writing') is the study of the lands, features, inhabitants, and phenomena of Earth. Geography is an all-encompassing discipline that seeks an understanding o ...
'', a handbook on how to draw maps using geographical coordinates for parts of the Roman world known at the time. He relied on previous work by an earlier geographer,
Marinus of Tyre Marinus of Tyre (, ''Marînos ho Týrios'';  70–130) was a List of Graeco-Roman geographers, geographer, Cartography, cartographer and mathematician, who founded mathematical geography and provided the underpinnings of Claudius Ptolemy's i ...
, as well as on
gazetteer A gazetteer is a geographical dictionary or wikt:directory, directory used in conjunction with a map or atlas.Aurousseau, 61. It typically contains information concerning the geographical makeup, social statistics and physical features of a co ...
s of the Roman and ancient
Persian Empire The Achaemenid Empire or Achaemenian Empire, also known as the Persian Empire or First Persian Empire (; , , ), was an Iranian empire founded by Cyrus the Great of the Achaemenid dynasty in 550 BC. Based in modern-day Iran, it was the larg ...
. He also acknowledged ancient astronomer
Hipparchus Hipparchus (; , ;  BC) was a Ancient Greek astronomy, Greek astronomer, geographer, and mathematician. He is considered the founder of trigonometry, but is most famous for his incidental discovery of the precession of the equinoxes. Hippar ...
for having provided the elevation of the north celestial pole for a few cities. Although
maps A map is a symbolic depiction of interrelationships, commonly spatial, between things within a space. A map may be annotated with text and graphics. Like any graphic, a map may be fixed to paper or other durable media, or may be displayed on ...
based on scientific principles had been made since the time of
Eratosthenes Eratosthenes of Cyrene (; ;  – ) was an Ancient Greek polymath: a Greek mathematics, mathematician, geographer, poet, astronomer, and music theory, music theorist. He was a man of learning, becoming the chief librarian at the Library of A ...
(), Ptolemy improved on
map projection In cartography, a map projection is any of a broad set of Transformation (function) , transformations employed to represent the curved two-dimensional Surface (mathematics), surface of a globe on a Plane (mathematics), plane. In a map projection, ...
s. The first part of the ''Geography'' is a discussion of the data and of the methods he used. Ptolemy notes the supremacy of astronomical data over land measurements or travelers' reports, though he possessed these data for only a handful of places. Ptolemy's real innovation, however, occurs in the second part of the book, where he provides a catalogue of 8,000 localities he collected from Marinus and others, the biggest such database from antiquity. About of these places and geographic features have assigned
coordinate In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine and standardize the position of the points or other geometric elements on a manifold such as Euclidean space. The coordinates are ...
s so that they can be placed in a grid that spanned the globe.
Latitude In geography, latitude is a geographic coordinate system, geographic coordinate that specifies the north-south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from −90° at t ...
was measured from the
equator The equator is the circle of latitude that divides Earth into the Northern Hemisphere, Northern and Southern Hemisphere, Southern Hemispheres of Earth, hemispheres. It is an imaginary line located at 0 degrees latitude, about in circumferen ...
, as it is today, but Ptolemy preferred to express it as '' climata'', the length of the longest day rather than degrees of arc: The length of the
midsummer Midsummer is a celebration of the season of summer, taking place on or near the date of the summer solstice in the Northern Hemisphere; the longest Daytime, day of the year. The name "midsummer" mainly refers to summer solstice festivals of Eu ...
day increases from 12h to 24h as one goes from the equator to the
polar circle A polar circle is a geographic term for a conditional circular line (arc) referring either to the Arctic Circle or the Antarctic Circle. These are two of the keynote circles of latitude (parallels). On Earth, the Arctic Circle is currentl ...
. One of the places Ptolemy noted specific coordinates for was the now-lost stone tower which marked the midpoint on the ancient
Silk Road The Silk Road was a network of Asian trade routes active from the second century BCE until the mid-15th century. Spanning over , it played a central role in facilitating economic, cultural, political, and religious interactions between the ...
, and which scholars have been trying to locate ever since. In the third part of the ''Geography'', Ptolemy gives instructions on how to create maps both of the whole inhabited world ('' oikoumenē'') and of the Roman provinces, including the necessary topographic lists, and captions for the maps. His ''oikoumenē'' spanned 180 degrees of longitude from the Blessed Islands in the
Atlantic Ocean The Atlantic Ocean is the second largest of the world's five borders of the oceans, oceanic divisions, with an area of about . It covers approximately 17% of Earth#Surface, Earth's surface and about 24% of its water surface area. During the ...
to the middle of
China China, officially the People's Republic of China (PRC), is a country in East Asia. With population of China, a population exceeding 1.4 billion, it is the list of countries by population (United Nations), second-most populous country after ...
, and about 80 degrees of latitude from
Shetland Shetland (until 1975 spelled Zetland), also called the Shetland Islands, is an archipelago in Scotland lying between Orkney, the Faroe Islands, and Norway, marking the northernmost region of the United Kingdom. The islands lie about to the ...
to anti-Meroe (east coast of
Africa Africa is the world's second-largest and second-most populous continent after Asia. At about 30.3 million km2 (11.7 million square miles) including adjacent islands, it covers 20% of Earth's land area and 6% of its total surfac ...
); Ptolemy was well aware that he knew about only a quarter of the globe, and an erroneous extension of China southward suggests his sources did not reach all the way to the Pacific Ocean. It seems likely that the topographical tables in the second part of the work (Books 2–7) are cumulative texts, which were altered as new knowledge became available in the centuries after Ptolemy. This means that information contained in different parts of the ''Geography'' is likely to be of different dates, in addition to containing many scribal errors. However, although the regional and
world maps A world map is a map of most or all of the surface of Earth. World maps, because of their scale, must deal with the problem of map projection, projection. Maps rendered in two dimensions by necessity distort the display of the three-dimensiona ...
in surviving manuscripts date from (after the text was rediscovered by
Maximus Planudes Maximus Planudes (, ''Máximos Planoúdēs''; ) was a Byzantine Greek monk, scholar, anthologist, translator, mathematician, grammarian and theologian at Constantinople. Through his translations from Latin into Greek and from Greek into Latin, ...
), there are some scholars who think that such maps go back to Ptolemy himself.


''Tetrabiblos''

Ptolemy wrote an astrological treatise, in four parts, known by the Greek term '' Tetrabiblos'' () or by its Latin equivalent ''Quadripartitum''. Its original title is unknown, but may have been a term found in some Greek manuscripts, ''Apotelesmatiká'' (''biblía''), roughly meaning "(books) on the Effects" or "Outcomes", or "Prognostics". As a source of reference, the ''Tetrabiblos'' is said to have "enjoyed almost the authority of a Bible among the astrological writers of a thousand years or more". It was first translated from Arabic into Latin by Plato of Tivoli (Tiburtinus) in 1138, while he was in Spain. Much of the content of the ''Tetrabiblos'' was 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 sublunary sphere. Thus explanations of a sort are provided for the astrological effects of the
planets A planet is a large, rounded astronomical body that is generally required to be in orbit around a star, stellar remnant, or brown dwarf, and is not one itself. The Solar System has eight planets by the most restrictive definition of the te ...
, based upon their combined effects of heating, cooling, moistening, and drying. Ptolemy dismisses other astrological practices, such as considering the numerological significance of names, that he believed to be without sound basis, and leaves out popular topics, such as electional astrology (interpreting astrological charts to determine courses of action) and medical astrology, for similar reasons. The great respect in which later astrologers held the ''Tetrabiblos'' derived from its nature as an exposition of theory, rather than as a manual. A collection of one hundred
aphorism An aphorism (from Greek ἀφορισμός: ''aphorismos'', denoting 'delimitation', 'distinction', and 'definition') is a concise, terse, laconic, or memorable expression of a general truth or principle. Aphorisms are often handed down by tra ...
s about astrology called the '' Centiloquium'', ascribed to Ptolemy, was widely reproduced and commented on by Arabic, Latin, and Hebrew scholars, and often bound together in medieval manuscripts after the ''Tetrabiblos'' as a kind of summation. It is now believed to be a much later pseudepigraphical composition. The identity and date of the actual author of the work, referred to now as Pseudo-Ptolemy, remains the subject of conjecture.


''Harmonics''

Ptolemy's ''Harmonics'' () is a work in three books on
music theory Music theory is the study of theoretical frameworks for understanding the practices and possibilities of music. ''The Oxford Companion to Music'' describes three interrelated uses of the term "music theory": The first is the "Elements of music, ...
and the mathematics behind musical scales ''Harmonics'' begins with a definition of harmonic theory, with a long exposition on the relationship between reason and sense perception in corroborating theoretical assumptions. After criticizing the approaches of his predecessors, Ptolemy argues for basing musical intervals on mathematical ratios (as opposed to the ideas advocated by followers of
Aristoxenus Aristoxenus of Tarentum (; born 375, fl. 335 BC) was a Ancient Greece, Greek Peripatetic school, Peripatetic philosopher, and a pupil of Aristotle. Most of his writings, which dealt with philosophy, ethics and music, have been lost, but one musi ...
), backed up by empirical observation (in contrast to the excessively theoretical approach of the
Pythagoreans Pythagoreanism originated in the 6th century BC, based on and around the teachings and beliefs held by Pythagoras and his followers, the Pythagoreans. Pythagoras established the first Pythagorean community in the Ancient Greece, ancient Greek co ...
). Ptolemy introduces the ''harmonic canon'' (Greek name) or ''
monochord A monochord, also known as sonometer (see below), is an ancient musical and scientific laboratory instrument, involving one (mono-) string ( chord). The term ''monochord'' is sometimes used as the class-name for any musical stringed instrument ...
'' (Latin name), which is an experimental musical apparatus that he used to measure relative pitches, and used to describe to his readers how to demonstrate the relations discussed in the following chapters for themselves. After the early exposition on to build and use monochord to test proposed tuning systems, Ptolemy proceeds to discuss Pythagorean tuning (and how to demonstrate that their idealized musical scale fails in practice). The Pythagoreans believed that the mathematics of music should be based on only the one specific ratio of 3:2, the
perfect fifth In music theory, a perfect fifth is the Interval (music), musical interval corresponding to a pair of pitch (music), pitches with a frequency ratio of 3:2, or very nearly so. In classical music from Western culture, a fifth is the interval f ...
, and believed that tunings mathematically exact to their system would prove to be melodious, if only the extremely large numbers involved could be calculated (by hand). To the contrary, Ptolemy believed that musical scales and tunings should in general involve multiple different ratios arranged to fit together evenly into smaller
tetrachord In music theory, a tetrachord (; ) is a series of four notes separated by three interval (music), intervals. In traditional music theory, a tetrachord always spanned the interval of a perfect fourth, a 4:3 frequency proportion (approx. 498 cent (m ...
s (combinations of four pitch ratios which together make a
perfect fourth A fourth is a interval (music), musical interval encompassing four staff positions in the music notation of Western culture, and a perfect fourth () is the fourth spanning five semitones (half steps, or half tones). For example, the ascending int ...
) and
octave In music, an octave (: eighth) or perfect octave (sometimes called the diapason) is an interval between two notes, one having twice the frequency of vibration of the other. The octave relationship is a natural phenomenon that has been referr ...
s. Ptolemy reviewed standard (and ancient, disused) musical tuning practice of his day, which he then compared to his own subdivisions of the
tetrachord In music theory, a tetrachord (; ) is a series of four notes separated by three interval (music), intervals. In traditional music theory, a tetrachord always spanned the interval of a perfect fourth, a 4:3 frequency proportion (approx. 498 cent (m ...
and the
octave In music, an octave (: eighth) or perfect octave (sometimes called the diapason) is an interval between two notes, one having twice the frequency of vibration of the other. The octave relationship is a natural phenomenon that has been referr ...
, which he derived experimentally using a
monochord A monochord, also known as sonometer (see below), is an ancient musical and scientific laboratory instrument, involving one (mono-) string ( chord). The term ''monochord'' is sometimes used as the class-name for any musical stringed instrument ...
/ harmonic canon. The volume ends with a more speculative exposition of the relationships between harmony, the soul (''psyche''), and the planets ( harmony of the spheres). Although Ptolemy's ''Harmonics'' never had the influence of his ''Almagest'' or ''Geography'', it is nonetheless a well-structured treatise and contains more methodological reflections than any other of his writings. In particular, it is a nascent form of what in the following millennium developed into the scientific method, with specific descriptions of the experimental apparatus that he built and used to test musical conjectures, and the empirical musical relations he identified by testing pitches against each other: He was able to accurately measure relative pitches based on the ratios of vibrating lengths two separate sides of the same single string, hence which were assured to be under equal tension, eliminating one source of error. He analyzed the empirically determined ratios of "pleasant" pairs of pitches, and then synthesised all of them into a coherent mathematical description, which persists to the present as
just intonation In music, just intonation or pure intonation is a musical tuning, tuning system in which the space between notes' frequency, frequencies (called interval (music), intervals) is a natural number, whole number ratio, ratio. Intervals spaced in thi ...
– the standard for comparison of consonance in the many other, less-than exact but more facile compromise tuning systems. During the
Renaissance The Renaissance ( , ) is a Periodization, period of history and a European cultural movement covering the 15th and 16th centuries. It marked the transition from the Middle Ages to modernity and was characterized by an effort to revive and sur ...
, Ptolemy's ideas inspired
Kepler Johannes Kepler (27 December 1571 – 15 November 1630) was a German astronomer, mathematician, astrologer, natural philosopher and writer on music. He is a key figure in the 17th-century Scientific Revolution, best known for his laws of p ...
in his own musings on the harmony of the world ('' Harmonice Mundi'', Appendix to Book V).


Optics

The ''Optica'' (
Koine Greek Koine Greek (, ), also variously known as Hellenistic Greek, common Attic, the Alexandrian dialect, Biblical Greek, Septuagint Greek or New Testament Greek, was the koiné language, common supra-regional form of Greek language, Greek spoken and ...
: ), known as the ''Optics'', is a work that survives only in a somewhat poor Latin version, which, in turn, was translated from a lost Arabic version by Eugenius of Palermo (). In it, Ptolemy writes about properties of sight (not light), including reflection,
refraction In physics, refraction is the redirection of a wave as it passes from one transmission medium, medium to another. The redirection can be caused by the wave's change in speed or by a change in the medium. Refraction of light is the most commo ...
, and
colour Color (or colour in Commonwealth English; see spelling differences) is the visual perception based on the electromagnetic spectrum. Though color is not an inherent property of matter, color perception is related to an object's light absorp ...
. The work is a significant part of the early
history of optics Optics began with the development of lenses by the ancient Egyptians and Mesopotamians, followed by theories on light and vision developed by ancient Greek philosophers, and the development of geometrical optics in the Greco-Roman world. The w ...
and influenced the more famous and superior 11th-century ''
Book of Optics The ''Book of Optics'' (; or ''Perspectiva''; ) is a seven-volume treatise on optics and other fields of study composed by the medieval Arab scholar Ibn al-Haytham, known in the West as Alhazen or Alhacen (965–c. 1040 AD). The ''Book ...
'' by
Ibn al-Haytham Ḥasan Ibn al-Haytham (Latinization of names, Latinized as Alhazen; ; full name ; ) was a medieval Mathematics in medieval Islam, mathematician, Astronomy in the medieval Islamic world, astronomer, and Physics in the medieval Islamic world, p ...
. Ptolemy offered explanations for many phenomena concerning illumination and colour, size, shape, movement, and binocular vision. He also divided illusions into those caused by physical or optical factors and those caused by judgmental factors. He offered an obscure explanation of the Sun or
Moon illusion The Moon illusion is the optical illusion of the Moon appearing larger near the horizon than it does higher up in the sky. It has been known since ancient times and recorded by various cultures. The explanation of this illusion is still debate ...
(the enlarged apparent size on the horizon) based on the difficulty of looking upwards. The work is divided into three major sections. The first section (Book II) deals with direct vision from first principles and ends with a discussion of binocular vision. The second section (Books III-IV) treats reflection in plane, convex, concave, and compound mirrors. The last section (Book V) deals with
refraction In physics, refraction is the redirection of a wave as it passes from one transmission medium, medium to another. The redirection can be caused by the wave's change in speed or by a change in the medium. Refraction of light is the most commo ...
and includes the earliest surviving table of refraction from air to water, for which the values (with the exception of the 60° angle of incidence) show signs of being obtained from an arithmetic progression. However, according to Mark Smith, Ptolemy's table was based in part on real experiments. Ptolemy's theory of vision consisted of rays (or flux) coming from the eye forming a cone, the vertex being within the eye, and the base defining the visual field. The rays were sensitive, and conveyed information back to the observer's intellect about the distance and orientation of surfaces. Size and shape were determined by the visual angle subtended at the eye combined with perceived distance and orientation. This was one of the early statements of size-distance invariance as a cause of perceptual size and shape constancy, a view supported by the Stoics.


Philosophy

Although mainly known for his contributions to astronomy and other scientific subjects, Ptolemy also engaged in
epistemological Epistemology is the branch of philosophy that examines the nature, origin, and limits of knowledge. Also called "the theory of knowledge", it explores different types of knowledge, such as propositional knowledge about facts, practical knowled ...
and
psychological Psychology is the scientific study of mind and behavior. Its subject matter includes the behavior of humans and nonhumans, both consciousness, conscious and Unconscious mind, unconscious phenomena, and mental processes such as thoughts, feel ...
discussions across his corpus. He wrote a short essay entitled ''On the Criterion and Hegemonikon'' (), which may have been one of his earliest works. Ptolemy deals specifically with how humans obtain scientific knowledge (i.e., the "criterion" of truth), as well as with the nature and structure of the human ''psyche'' or soul, particularly its ruling faculty (i.e., the ''hegemonikon''). Ptolemy argues that, to arrive at the truth, one should use both reason and sense perception in ways that complement each other. ''On the Criterion'' is also noteworthy for being the only one of Ptolemy's works that is devoid of
mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
. Elsewhere, Ptolemy affirms the supremacy of mathematical knowledge over other forms of knowledge. Like Aristotle before him, Ptolemy classifies mathematics as a type of theoretical philosophy; however, Ptolemy believes mathematics to be superior to
theology Theology is the study of religious belief from a Religion, religious perspective, with a focus on the nature of divinity. It is taught as an Discipline (academia), academic discipline, typically in universities and seminaries. It occupies itse ...
or
metaphysics Metaphysics is the branch of philosophy that examines the basic structure of reality. It is traditionally seen as the study of mind-independent features of the world, but some theorists view it as an inquiry into the conceptual framework of ...
because the latter are conjectural while only the former can secure certain knowledge. This view is contrary to the Platonic and Aristotelian traditions, where theology or metaphysics occupied the highest honour. Despite being a minority position among ancient philosophers, Ptolemy's views were shared by other mathematicians such as
Hero of Alexandria Hero of Alexandria (; , , also known as Heron of Alexandria ; probably 1st or 2nd century AD) was a Greek mathematician and engineer who was active in Alexandria in Egypt during the Roman era. He has been described as the greatest experimental ...
.


Named after Ptolemy

There are several characters and items named after Ptolemy, including: * The crater Ptolemaeus on the
Moon The Moon is Earth's only natural satellite. It Orbit of the Moon, orbits around Earth at Lunar distance, an average distance of (; about 30 times Earth diameter, Earth's diameter). The Moon rotation, rotates, with a rotation period (lunar ...
* The crater Ptolemaeus on
Mars Mars is the fourth planet from the Sun. It is also known as the "Red Planet", because of its orange-red appearance. Mars is a desert-like rocky planet with a tenuous carbon dioxide () atmosphere. At the average surface level the atmosph ...
* The asteroid 4001 Ptolemaeus * Messier 7, sometimes known as the Ptolemy Cluster, an open cluster of stars in the constellation of Scorpius * The Ptolemy stone used in the mathematics courses at both St. John's College campuses in the U.S. * Ptolemy's theorem on distances in a
cyclic quadrilateral In geometry, a cyclic quadrilateral or inscribed quadrilateral is a quadrilateral (four-sided polygon) whose vertex (geometry), vertices all lie on a single circle, making the sides Chord (geometry), chords of the circle. This circle is called ...
, and its generalization, Ptolemy's inequality, to non-cyclic quadrilaterals * Ptolemaic graphs, the graphs whose distances obey Ptolemy's inequality * Ptolemy Project, a project at University of California, Berkeley, aimed at modeling, simulating and designing concurrent, real-time,
embedded system An embedded system is a specialized computer system—a combination of a computer processor, computer memory, and input/output peripheral devices—that has a dedicated function within a larger mechanical or electronic system. It is e ...
s * Ptolemy Slocum, actor


See also

*
Equant Equant (or punctum aequans) is a mathematical concept developed by Claudius Ptolemy in the 2nd century AD to account for the observed motion of the planets. The equant is used to explain the observed speed change in different stages of the plane ...
* Messier 7 – Ptolemy Cluster, star cluster described by Ptolemaeus *
Pei Xiu Pei Xiu (224–3 April 271), courtesy name Jiyan, was a Chinese cartographer, geographer, politician, and writer of the state of Cao Wei during the late Three Kingdoms period and Jin dynasty (265–420), Jin dynasty of China. He was very m ...
* Ptolemy's Canon – a dated list of kings used by ancient astronomers. *
Ptolemy's table of chords The table of chords, created by the Greece, Greek astronomer, geometer, and geographer Ptolemy in Egypt during the 2nd century AD, is a trigonometric table in Book I, chapter 11 of Ptolemy's ''Almagest'', a treatise on mathematical astron ...
*
Zhang Heng Zhang Heng (; AD 78–139), formerly romanization of Chinese, romanized Chang Heng, was a Chinese polymathic scientist and statesman who lived during the Han dynasty#Eastern Han (25–220 AD), Eastern Han dynasty. Educated in the capital citi ...


Notes


Footnotes


Citations


Bibliography


Works of Ptolemy

* * * * * * * * * — medieval Arabic translations and an English translation of those


References

* * * * * * — The most recent edition of the Greek text of Ptolemy's astrological work, based on earlier editions by F. Boll and E. Boer. * — Latin text with French translation * * * — Until Stückelberger (2006), this was the most recent edition of the complete Greek text. * * Peerlings, R.H.J., Laurentius F., van den Bovenkamp J.,(2018) ''New findings and discoveries in the 1507/8 Rome edition of Ptolemy's Cosmography'', In Quaerendo 48: 139–162, 2018. * * * * — This is the only complete English translation of Ptolemy's ''Geography'', but it is marred by numerous mistakes; and placenames are given in Latinised forms, rather than in the Greek, as in the original. * — Massive 2 vol, academic edition of ''Geography'' by a team of a dozen scholars that takes account of all known manuscripts, with facing Greek and German text, with footnotes on manuscript variations, color maps, and a CD with the geographical data. * * ''Ptolemy's Almagest'', Translated and annotated by G. J. Toomer, 1998. Princeton University Press *


Further reading

* * *


External links


''Almagest'' books 1–13
The complete text of Heiberg's edition (PDF) Greek.
''Almagest'' books 1–6
with preface at archive.org
Extracts of Ptolemy on the country of the Seres (China)
(English translation)
''Geography''
digitised codex made in Italy between 1460 and 1477, translated to Latin by Jacobus Angelus a
Somni
Also known as ''Codex Valentinus'', it is the oldest manuscript of the codices with maps of Ptolemy with the donis projections.

at LacusCurtius (English translation, incomplete)
Ptolemaeus Arabus et Latinus (PAL)
Project, dedicated to the edition and study of the Arabic and Latin versions of Ptolemy’s astronomical and astrological texts and related material.

at LacusCurtius (Transcription of the
Loeb Classical Library The Loeb Classical Library (LCL; named after James Loeb; , ) is a monographic series of books originally published by Heinemann and since 1934 by Harvard University Press. It has bilingual editions of ancient Greek and Latin literature, ...
's English translation)
''Tetrabiblos''
entire J.M. Ashmand's 1822 translation.
Hieronymi Cardani ... In Cl. Ptolemaei ... IIII De astrorum judiciis
From the Rare Book and Special Collection Division at the
Library of Congress The Library of Congress (LOC) is a research library in Washington, D.C., serving as the library and research service for the United States Congress and the ''de facto'' national library of the United States. It also administers Copyright law o ...

Almagestū Cl. Ptolemei
From the Rare Book and Special Collection Division at the
Library of Congress The Library of Congress (LOC) is a research library in Washington, D.C., serving as the library and research service for the United States Congress and the ''de facto'' national library of the United States. It also administers Copyright law o ...
* * Franz Boll (1894),
Studien über Claudius Ptolemaeus. Ein Beitrag zur Geschichte der griechischen Philosophie und Astrologie
In: ''Neue Jahrbücher für Philologie und Pädagogik'', Supplementband 21,2. Teubner, Leipzig, pp. 49–244. * * * * *

– at Paul Stoddard's Animated Virtual Planetarium, Northern Illinois University *

– at Rosemary Kennett's website at
Syracuse University Syracuse University (informally 'Cuse or SU) is a Private university, private research university in Syracuse, New York, United States. It was established in 1870 with roots in the Methodist Episcopal Church but has been nonsectarian since 1920 ...

Flash animation of Ptolemy's universe.
(best in Internet Explorer)
High resolution images
of works by Ptolemy in .jpg and .tiff format. Online Galleries, History of Science Collections,
University of Oklahoma The University of Oklahoma (OU) is a Public university, public research university in Norman, Oklahoma, United States. Founded in 1890, it had existed in Oklahoma Territory near Indian Territory for 17 years before the two territories became the ...
Libraries.
Codex Vaticanus graecus 1291 (Vat.gr.1291) in Vatican Digital Library
- Complete reproduction of the 9th century manuscript of Ptolemy's ''Handy Tables''. *
Database of the Arabic and Latin versions of Ptolemy’s astronomical and astrological texts and related material
{{Authority control 100s births 2nd-century deaths 1st-century Romans 2nd-century astronomers 2nd-century Romans 2nd-century geographers 2nd-century Greek philosophers 2nd-century mathematicians Ancient Greek astrologers Ancient Greek astronomers Ancient Greek geographers Ancient Greek mathematicians Ancient Greek music theorists Ancient Roman geographers Astrological writers Claudii Epigrammatists of the Greek Anthology