Claudius Ptolemy (; grc-gre,
Πτολεμαῖος, ; la, Claudius Ptolemaeus; AD)
was a
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, structure, space, models, and change.
History
On ...
,
astronomer
An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the scope of Earth. They observe astronomical objects such as stars, planets, natural satellite, moons, comets and galaxy, g ...
,
astrologer
Astrology is a range of divinatory practices, recognized as pseudoscientific since the 18th century, that claim to discern information about human affairs and terrestrial events by studying the apparent positions of celestial objects. Dif ...
,
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 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 are needed to understand music notation (ke ...
, who wrote about a dozen scientific
treatises
A treatise is a formal and systematic written discourse on some subject, generally longer and treating it in greater depth than an essay, and more concerned with investigating or exposing the principles of the subject and its conclusions."Treat ...
, three of which were of importance to later
Byzantine
The Byzantine Empire, also referred to as the Eastern Roman Empire or Byzantium, was the continuation of the Roman Empire primarily in its eastern provinces during Late Antiquity and the Middle Ages, when its capital city was Constantinopl ...
,
Islamic
Islam (; ar, ۘالِإسلَام, , ) is an Abrahamic monotheistic religion centred primarily around the Quran, a religious text considered by Muslims to be the direct word of God (or '' Allah'') as it was revealed to Muhammad, the mai ...
, and
Western European
Western Europe is the western region of Europe. The region's countries and territories vary depending on context.
The concept of "the West" appeared in Europe in juxtaposition to "the East" and originally applied to the ancient Mediterranean ...
science. The first is the astronomical treatise now known as the ''
Almagest
The ''Almagest'' is a 2nd-century Greek-language mathematical and astronomical treatise on the apparent motions of the stars and planetary paths, written by Claudius Ptolemy ( ). One of the most influential scientific texts in history, it canoni ...
'', although it was originally entitled the ''Mathēmatikē Syntaxis'' or ''Mathematical Treatise'', and later known as ''The Greatest Treatise''. The second is the ''
Geography
Geography (from Greek: , ''geographia''. Combination of Greek words ‘Geo’ (The Earth) and ‘Graphien’ (to describe), literally "earth description") is a field of science devoted to the study of the lands, features, inhabitants, and ...
'', which is a thorough discussion on maps and the geographic knowledge of the
Greco-Roman world
The Greco-Roman civilization (; also Greco-Roman culture; spelled Graeco-Roman in the Commonwealth), as understood by modern scholars and writers, includes the geographical regions and countries that culturally—and so historically—were di ...
. The third is the astrological treatise in which he attempted to adapt
horoscopic astrology
Horoscopic astrology is a form of astrology that uses a horoscope, a visual representation of the heavens, for a specific moment in time in order to interpret the inherent meaning underlying the alignment of the planets in astrology, planets at th ...
to the
Aristotelian natural philosophy
Natural philosophy or philosophy of nature (from Latin ''philosophia naturalis'') is the philosophical study of physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior throu ...
of his day. This is sometimes known as the ''Apotelesmatika'' (lit. "On the Effects") but more commonly known as the ''
Tetrábiblos'', from the
Koine Greek
Koine Greek (; Koine el, ἡ κοινὴ διάλεκτος, hē koinè diálektos, the common dialect; ), also known as Hellenistic Greek, common Attic, the Alexandrian dialect, Biblical Greek or New Testament Greek, was the common supra-reg ...
meaning "Four Books", or by its Latin equivalent ''Quadripartite''.
Unlike most ancient
Greek mathematicians
Greek may refer to:
Greece
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 ...
, Ptolemy's writings (foremost the ''
Almagest
The ''Almagest'' is a 2nd-century Greek-language mathematical and astronomical treatise on the apparent motions of the stars and planetary paths, written by Claudius Ptolemy ( ). One of the most influential scientific texts in history, it canoni ...
'') never ceased to be copied or commented upon, both in
Late Antiquity
Late antiquity is the time of transition from classical antiquity to the Middle Ages, generally spanning the 3rd–7th century in Europe and adjacent areas bordering the Mediterranean Basin. The popularization of this periodization in English ha ...
and in the
Middle Ages
In the history of Europe, the Middle Ages or medieval period lasted approximately from the late 5th to the late 15th centuries, similar to the post-classical period of global history. It began with the fall of the Western Roman Empire a ...
. 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 alike.
Biography
Ptolemy lived in or around the city of
Alexandria
Alexandria ( or ; ar, ٱلْإِسْكَنْدَرِيَّةُ ; grc-gre, Αλεξάνδρεια, Alexándria) is the second largest city in Egypt, and the largest city on the Mediterranean coast. Founded in by Alexander the Great, Alexandria ...
, in the
Roman province of Egypt
, conventional_long_name = Roman Egypt
, common_name = Egypt
, subdivision = Province
, nation = the Roman Empire
, era = Late antiquity
, capital = Alexandria
, title_leader = Praefectus Augustalis
, image_map = Roman E ...
under
Roman rule, had a Latin name (which several historians have taken to imply he was also a
Roman citizen
Citizenship in ancient Rome (Latin: ''civitas'') 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, t ...
), cited 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.
The 14th-century astronomer
Theodore Meliteniotes
Theodore Meliteniotes ( el, Θεόδωρος Μελιτηνιώτης; Constantinople, c. 1320 - 8 March 1393) was a Byzantine Greek astronomer, a ''sakellarios'' (treasurer) in the Byzantine bureaucracy, a supporter of Gregory Palamas and an oppon ...
gave his birthplace as the prominent Greek city
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 city ...
() in the
Thebaid
The Thebaid or Thebais ( grc-gre, Θηβαΐς, ''Thēbaïs'') was a region in ancient Egypt, comprising the 13 southernmost nomes of Upper Egypt, from Abydos to Aswan.
Pharaonic history
The Thebaid acquired its name from its proximity to ...
(). This attestation is quite late, however, and there is no evidence to support it.
[; The only place mentioned in any of Ptolemy's observations is Alexandria, and there is no reason to suppose that he ever lived anywhere else. The statement by Theodore Meliteniotes that he was born in Ptolemais Hermiou (in Upper Egypt) could be correct, but it is late (ca. 1360) and unsupported.]
Claudius Ptolemy died in Alexandria around 168.
Naming and nationality
![Ptolemy urania](https://upload.wikimedia.org/wikipedia/commons/2/2e/Ptolemy_urania.jpg)
Ptolemy's Greek name'',
Ptolemaeus
Claudius Ptolemy (; grc-gre, Πτολεμαῖος, ; la, Claudius Ptolemaeus; AD) was a mathematician, astronomer, astrologer, geographer, and music theorist, who wrote about a dozen scientific treatises, three of which were of importanc ...
'' (, ''Ptolemaîos''), is an
ancient Greek personal name. It occurs once in
Greek mythology
A major branch of classical mythology, Greek mythology is the body of myths originally told by the Ancient Greece, ancient Greeks, and a genre of Ancient Greek folklore. These stories concern the Cosmogony, origin and Cosmology#Metaphysical co ...
and is of
Homeric form. It was common among the
Macedonian upper class at the time of
Alexander the Great
Alexander III of Macedon ( grc, wikt:Ἀλέξανδρος, Ἀλέξανδρος, Alexandros; 20/21 July 356 BC – 10/11 June 323 BC), commonly known as Alexander the Great, was a king of the Ancient Greece, ancient Greek kingdom of Maced ...
and there were several of this name among Alexander's army, one of whom made himself
pharaoh
Pharaoh (, ; Egyptian: ''pr ꜥꜣ''; cop, , Pǝrro; Biblical Hebrew: ''Parʿō'') is the vernacular term often used by modern authors for the kings of ancient Egypt who ruled as monarchs from the First Dynasty (c. 3150 BC) until the an ...
in 323 BC:
Ptolemy I Soter
Ptolemy I Soter (; gr, Πτολεμαῖος Σωτήρ, ''Ptolemaîos Sōtḗr'' "Ptolemy the Savior"; c. 367 BC – January 282 BC) was a Macedonian Greek general, historian and companion of Alexander the Great from the Kingdom of Macedon ...
, the first pharaoh of the
Ptolemaic Kingdom. Almost all subsequent pharaohs of Egypt, with a few exceptions, were named
Ptolemies
The Ptolemaic dynasty (; grc, Πτολεμαῖοι, ''Ptolemaioi''), sometimes referred to as the Lagid dynasty (Λαγίδαι, ''Lagidae;'' after Ptolemy I's father, Lagus), was a Macedonian Greek royal dynasty which ruled the Ptolemaic K ...
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. Several historians have made the deduction that this indicates that Ptolemy would have been a
Roman citizen
Citizenship in ancient Rome (Latin: ''civitas'') 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, t ...
. 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) was the fourth Roman emperor, ruling from AD 41 to 54. A member of the Julio-Claudian dynasty, Claudius was born to Nero Claudius Drusus, Drusu ...
or the emperor
Nero
Nero Claudius Caesar Augustus Germanicus ( ; born Lucius Domitius Ahenobarbus; 15 December AD 37 – 9 June AD 68), was the fifth Roman emperor and final emperor of the Julio-Claudian dynasty, reigning from AD 54 un ...
.
The 9th century
Persian
Persian may refer to:
* People and things from Iran, historically called ''Persia'' in the English language
** Persians, the majority ethnic group in Iran, not to be conflated with the Iranic peoples
** Persian language, an Iranian language of the ...
astronomer
An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the scope of Earth. They observe astronomical objects such as stars, planets, natural satellite, moons, comets and galaxy, g ...
Abu Ma'shar al-Balkhi
Abu Ma'shar al-Balkhi, Latinized as Albumasar (also ''Albusar'', ''Albuxar''; full name ''Abū Maʿshar Jaʿfar ibn Muḥammad ibn ʿUmar al-Balkhī'' ;
, AH 171–272), was an early Persian Muslim astrologer, thought to be the greatest ast ...
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 (; gr, Πτολεμαῖος Σωτήρ, ''Ptolemaîos Sōtḗr'' "Ptolemy the Savior"; c. 367 BC – January 282 BC) was a Macedonian Greek general, historian and companion of Alexander the Great from the Kingdom of Macedon ...
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". We can infer historical confusion on this point 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."
[Abu Ma'shar, ''De magnis coniunctionibus'', ed.-transl. K. Yamamoto, Ch. Burnett, Leiden, 2000, 2 vols. (Arabic & Latin text); 4.1.4.] 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.
[ Jones (2010). "Ptolemy's Doctrine of the Terms and Its Reception" by Stephan Heilen, p. 68.] It is no longer doubted that the astronomer who wrote the ''Almagest'' also wrote the ''
Tetrabiblos
''Tetrabiblos'' () 'four books', also known in Greek as ''Apotelesmatiká'' () "Effects", and in Latin as ''Quadripartitum'' "Four Parts", is a text on the philosophy and practice of astrology, written in the 2nd century AD by the Alexandrian ...
'' as its astrological counterpart. In later
Arabic
Arabic (, ' ; , ' or ) is a Semitic languages, Semitic language spoken primarily across the Arab world.Semitic languages: an international handbook / edited by Stefan Weninger; in collaboration with Geoffrey Khan, Michael P. Streck, Janet C ...
sources, he was often known as "the
Upper Egypt
Upper Egypt ( ar, صعيد مصر ', shortened to , , locally: ; ) is the southern portion of Egypt and is composed of the lands on both sides of the Nile that extend upriver from Lower Egypt in the north to Nubia in the south.
In ancient ...
ian", suggesting he may have had origins in southern
Egypt
Egypt ( ar, مصر , ), officially the Arab Republic of Egypt, is a transcontinental country spanning the northeast corner of Africa and southwest corner of Asia via a land bridge formed by the Sinai Peninsula. It is bordered by the Mediter ...
.
Martin Bernal
Martin Gardiner Bernal (; 10 March 1937 – 9 June 2013)
was a British scholar of modern Chinese political history. He was a Professor of Government and Near Eastern Studies at Cornell University. He is best known for his work ''Black Athena'', a ...
(1992). "Animadversions on the Origins of Western Science", ''Isis'' 83 (4), p. 596–607 02, 606 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" a ...
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 caus ...
referred to his name in
Arabic
Arabic (, ' ; , ' or ) is a Semitic languages, Semitic language spoken primarily across the Arab world.Semitic languages: an international handbook / edited by Stefan Weninger; in collaboration with Geoffrey Khan, Michael P. Streck, Janet C ...
as ''Baṭlumyus'' ( ar, بَطْلُمْيوس).
Ptolemy wrote in
ancient Greek
Ancient Greek includes the forms of the Greek language used in ancient Greece and the ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: Mycenaean Greek (), Dark Ages (), the Archaic peri ...
and can be shown to have utilized
Babylonian astronomical data. He might have been a Roman citizen, but was ethnically either a
Greek
Greek may refer to:
Greece
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 ...
["Ptolemy". Britannica Concise Encyclopedia. Encyclopædia Britannica, Inc., 2006.] or at least a
Hellenized
Hellenization (other British spelling Hellenisation) or Hellenism is the adoption of Greek culture, religion, language and identity by non-Greeks. In the ancient period, colonization often led to the Hellenization of indigenous peoples; in the ...
Egyptian.
[ But what we really want to know is to what extent the Alexandrian mathematicians of the period from the 1st to the 5th centuries CE were Greek. Certainly, all of them wrote in Greek and were part of the Greek intellectual community of Alexandria. Most modern studies conclude that the Greek community coexisted ... So should we assume that Ptolemy and Diophantus, Pappus and Hypatia were ethnically Greek, that their ancestors had come from Greece at some point in the past but had remained effectively isolated from the Egyptians? It is, of course, impossible to answer this question definitively. But research in papyri dating from the early centuries of the common era demonstrates that a significant amount of intermarriage took place between the Greek and Egyptian communities ... And it is known that Greek marriage contracts increasingly came to resemble Egyptian ones. In addition, even from the founding of Alexandria, small numbers of Egyptians were admitted to the privileged classes in the city to fulfill numerous civic roles. Of course, it was essential in such cases for the Egyptians to become "Hellenized", to adopt Greek habits and the Greek language. Given that the Alexandrian mathematicians mentioned here were active several hundred years after the founding of the city, it would seem at least equally possible that they were ethnically Egyptian as that they remained ethnically Greek. In any case, it is unreasonable to portray them with purely European features when no physical descriptions exist.]George Sarton
George Alfred Leon Sarton (; 31 August 1884 – 22 March 1956) was a Belgian-born American chemist and historian. He is considered the founder of the discipline of the history of science as an independent field of study. His most influential works ...
(1936). "The Unity and Diversity of the Mediterranean World", ''Osiris'' 2, p. 406–463 29
Astronomy
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.
[Jones, A. (2020). The ancient Ptolemy. ln Ptolemy's ''Science of the Stars in the Middle Ages'' (D. Juste, B. van Dalen, D. N. Hasse, C. Burnett, Turnhout, Brepols, Eds.) Ptolemaeus Arabus et Latinus Studies 1, 13-3]
/ref>
''Mathēmatikē Syntaxis''
Ptolemy's ''Mathēmatikē Syntaxis'' (Ancient Greek
Ancient Greek includes the forms of the Greek language used in ancient Greece and the ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: Mycenaean Greek (), Dark Ages (), the Archaic peri ...
: ''Μαθηματικὴ Σύνταξις'', lit. "Mathematical Systematic Treatise"), better known as the ''Almagest
The ''Almagest'' is a 2nd-century Greek-language mathematical and astronomical treatise on the apparent motions of the stars and planetary paths, written by Claudius Ptolemy ( ). One of the most influential scientific texts in history, it canoni ...
'', is the only surviving comprehensive ancient treatise on astronomy. Although Babylonian astronomers
Babylonian astronomy was the study or recording of celestial objects during the early history of Mesopotamia.
Babylonian astronomy seemed to have focused on a select group of stars and constellations known as Ziqpu stars. These constellations m ...
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 that attempted to merge these two approaches was Hipparchus
Hipparchus (; el, Ἵππαρχος, ''Hipparkhos''; BC) was a 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 equi ...
, who produced geometric model
__NOTOC__
Geometric modeling is a branch of applied mathematics and computational geometry that studies methods and algorithms for the mathematical description of shapes.
The shapes studied in geometric modeling are mostly two- or three-dimensio ...
s 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 years, ...
, which is a version of a catalogue created by Hipparchus
Hipparchus (; el, Ἵππαρχος, ''Hipparkhos''; BC) was a 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 equi ...
. 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 origins of the e ...
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). 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
Arabic (, ' ; , ' or ) is a Semitic languages, Semitic language spoken primarily across the Arab world.Semitic languages: an international handbook / edited by Stefan Weninger; in collaboration with Geoffrey Khan, Michael P. Streck, Janet C ...
manuscripts; the modern title is thought to be an Arabic corruption of the Greek name ''Hē Megistē Syntaxis'' (lit. "The greatest treatise"), as the work was presumably known in Late Antiquity
Late antiquity is the time of transition from classical antiquity to the Middle Ages, generally spanning the 3rd–7th century in Europe and adjacent areas bordering the Mediterranean Basin. The popularization of this periodization in English ha ...
. 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
In astronomy, the geocentric model (also known as geocentrism, often exemplified specifically by the Ptolemaic system) is a superseded description of the Universe with Earth at the center. Under most geocentric models, the Sun, Moon, stars, an ...
and almost universally accepted until the reappearance of heliocentric
Heliocentrism (also known as the Heliocentric model) is the astronomical model in which the Earth and planets revolve around the Sun at the center of the universe. Historically, heliocentrism was opposed to geocentrism, which placed the Earth at ...
models during the scientific revolution
The Scientific Revolution was a series of events that marked the emergence of modern science during the early modern period, when developments in mathematics, physics, astronomy, biology (including human anatomy) and chemistry transfo ...
.
''Handy Tables''
The ''Handy Tables'' (Ancient Greek
Ancient Greek includes the forms of the Greek language used in ancient Greece and the ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: Mycenaean Greek (), Dark Ages (), the Archaic peri ...
: ''Πρόχειροι κανόνες'') 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 that 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 ce ...
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 (; grc, Θέων ὁ Ἀλεξανδρεύς; 335 – c. 405) was a Greek scholar and mathematician who lived in Alexandria, Egypt. He edited and arranged Euclid's '' Elements'' and wrote commentaries on works ...
’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'' (Ancient Greek
Ancient Greek includes the forms of the Greek language used in ancient Greece and the ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: Mycenaean Greek (), Dark Ages (), the Archaic peri ...
: ''Ὑποθέσεις τῶν πλανωμένων'', lit. "Hypotheses of the Planets") is a cosmological
Cosmology () is a branch of physics and metaphysics dealing with the nature of the universe. The term ''cosmology'' was first used in English in 1656 in Thomas Blount's ''Glossographia'', and in 1731 taken up in Latin by German philosopher ...
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, Sun ...
s of his planetary model to compute the dimensions of the universe. He estimated the Sun was at an average distance of 1,210 Earth radii (now known to actually be ~23,450 radii), while the radius of the sphere of the fixed stars was 20,000 times 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
In astronomy, the geocentric model (also known as geocentrism, often exemplified specifically by the Ptolemaic system) is a superseded description of the Universe with Earth at the center. Under most geocentric models, the Sun, Moon, stars, an ...
perspective, much like an orrery
An orrery is a mechanical model of the Solar System that illustrates or predicts the relative positions and motions of the planets and moons, usually according to the heliocentric model. It may also represent the relative sizes of these bodies; ...
would have done for a heliocentric
Heliocentrism (also known as the Heliocentric model) is the astronomical model in which the Earth and planets revolve around the Sun at the center of the universe. Historically, heliocentrism was opposed to geocentrism, which placed the Earth at ...
one, presumably for didactic purposes.
Other works
The ''Analemma'' is a short treatise where Ptolemy provides a method for specifying the location of the sun in three pairs of locally orientated 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 mean solar time, as that position varies over the course of a year. The diagram will resemble a figure ei ...
''.
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 date is the designation of a single and specific day within such a system. A calendar is also a physi ...
or almanac
An almanac (also spelled ''almanack'' and ''almanach'') is an annual publication listing a set of current information about one or multiple subjects. It includes information like weather forecasts, farmers' planting dates, tide tables, and other ...
, based on the appearances and disappearances of stars over the course of the solar year.
The ''Planisphaerium
The ''Planisphaerium'' is a work by Ptolemy. The title can be translated as "celestial plane" or "star chart". In this work Ptolemy explored the mathematics of mapping figures inscribed in the celestial sphere onto a plane by what is now known ...
'' (Ancient Greek
Ancient Greek includes the forms of the Greek language used in ancient Greece and the ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: Mycenaean Greek (), Dark Ages (), the Archaic peri ...
: ''Ἅπλωσις ἐπιφανείας σφαίρας'', lit. 'Simplification of the Sphere') 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 Lat ...
, 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.
Cartography
Ptolemy's second most well-known work is his ''Geographike Hyphegesis'' (Ancient Greek
Ancient Greek includes the forms of the Greek language used in ancient Greece and the ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: Mycenaean Greek (), Dark Ages (), the Archaic peri ...
: ''Γεωγραφικὴ Ὑφήγησις''; lit. "Guide to Drawing the Earth"), known as the ''Geography
Geography (from Greek: , ''geographia''. Combination of Greek words ‘Geo’ (The Earth) and ‘Graphien’ (to describe), literally "earth description") is a field of science devoted to the study of the lands, features, inhabitants, and ...
'', a handbook on how to draw maps using geographical coordinates
The geographic coordinate system (GCS) is a spherical or ellipsoidal coordinate system for measuring and communicating positions directly on the Earth as latitude and longitude. It is the simplest, oldest and most widely used of the various ...
for parts of the Roman world
The culture of ancient Rome existed throughout the almost 1200-year history of the civilization of Ancient Rome. The term refers to the culture of the Roman Republic, later the Roman Empire, which at its peak covered an area from present-day Lo ...
known at the time.[Isaksen L. (2011). Lines, damned lines and statistics: unearthing structure in Ptolemy’s Geographia. ''e-Perimetron'', ''6''(4), 254-260]
/ref> He relied on previous work by an earlier geographer, Marinos of Tyre, Marinus of Tyre, as well as on gazetteer
A gazetteer is a geographical index or 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 country, region, or co ...
s of the Roman and ancient Persian Empire
The Achaemenid Empire or Achaemenian Empire (; peo, wikt:𐎧𐏁𐏂𐎶, 𐎧𐏁𐏂, , ), also called the First Persian Empire, was an History of Iran#Classical antiquity, ancient Iranian empire founded by Cyrus the Great in 550 BC. Bas ...
. He also acknowledged ancient astronomer Hipparchus
Hipparchus (; el, Ἵππαρχος, ''Hipparkhos''; BC) was a 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 equi ...
for having provided the elevation of the north celestial pole
The north and south celestial poles are the two points in the sky where Earth's axis of rotation, indefinitely extended, intersects the celestial sphere. The north and south celestial poles appear permanently directly overhead to observers at ...
for a few cities. Although maps
A map is a symbolic depiction emphasizing relationships between elements of some space, such as objects, regions, or themes.
Many maps are static, fixed to paper or some other durable medium, while others are dynamic or interactive. Although ...
based on scientific principles had been made since the time of Eratosthenes
Eratosthenes of Cyrene (; grc-gre, Ἐρατοσθένης ; – ) was a Greek polymath: a mathematician, geographer, poet, astronomer, and music theorist. He was a man of learning, becoming the chief librarian at the Library of Alexandria ...
(c. 276–195 BC), Ptolemy improved on map projection
In cartography, map projection is the term used to describe a broad set of transformations employed to represent the two-dimensional curved surface of a globe on a plane. In a map projection, coordinates, often expressed as latitude and longitud ...
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 6,300 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 the position of the points or other geometric elements on a manifold such as Euclidean space. The order of the coordinates is sign ...
s so that they can be placed in a grid
Grid, The Grid, or GRID may refer to:
Common usage
* Cattle grid or stock grid, a type of obstacle is used to prevent livestock from crossing the road
* Grid reference, used to define a location on a map
Arts, entertainment, and media
* News g ...
that spanned the globe. Latitude
In geography, latitude is a 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 the south pole to 90° at the north pol ...
was measured from the equator
The equator is a circle of latitude, about in circumference, that divides Earth into the Northern and Southern hemispheres. It is an imaginary line located at 0 degrees latitude, halfway between the North and South poles. The term can als ...
, as it is today, but Ptolemy preferred to express it as '' climata'', the length of the longest day rather than degrees of arc
A degree (in full, a degree of arc, arc degree, or arcdegree), usually denoted by ° (the degree symbol), is a measurement of a plane angle in which one full rotation is 360 degrees.
It is not an SI unit—the SI unit of angular measure is th ...
: the length of the midsummer
Midsummer is a celebration of the season of summer usually held at a date around the summer solstice. It has pagan pre-Christian roots in Europe.
The undivided Christian Church designated June 24 as the feast day of the early Christian mart ...
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 currently ...
. 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 Eurasian trade routes active from the second century BCE until the mid-15th century. Spanning over 6,400 kilometers (4,000 miles), it played a central role in facilitating economic, cultural, political, and reli ...
, 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
The ecumene ( US spelling) or oecumene ( UK spelling; grc-gre, οἰκουμένη, oikouménē, inhabited) is an ancient Greek term for the known, the inhabited, or the habitable world. In Greek antiquity, it referred to the portions of the worl ...
'') and of the Roman provinces, including the necessary topographic
Topography is the study of the forms and features of land surfaces. The topography of an area may refer to the land forms and features themselves, or a description or depiction in maps.
Topography is a field of geoscience and planetary scie ...
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 oceans, with an area of about . It covers approximately 20% of Earth's surface and about 29% of its water surface area. It is known to separate the " Old World" of Africa, Europe ...
to the middle of China
China, officially the People's Republic of China (PRC), is a country in East Asia. It is the world's most populous country, with a population exceeding 1.4 billion, slightly ahead of India. China spans the equivalent of five time zones and ...
, and about 80 degrees of latitude from Shetland
Shetland, also called the Shetland Islands and formerly Zetland, is a subarctic archipelago in Scotland lying between Orkney, the Faroe Islands and Norway. It is the northernmost region of the United Kingdom.
The islands lie about to the no ...
to anti-Meroe (east coast of Africa
Africa is the world's second-largest and second-most populous continent, after Asia in both cases. At about 30.3 million km2 (11.7 million square miles) including adjacent islands, it covers 6% of Earth's total surface area ...
); 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 projection. Maps rendered in two dimensions by necessity distort the display of the three-dimensional surface of the ...
in surviving manuscripts date from c. 1300 AD (after the text was rediscovered by Maximus Planudes
Maximus Planudes ( grc-gre, Μάξιμος Πλανούδης, ''Máximos Planoúdēs''; ) was a Byzantine Greek monk, scholar, anthologist, translator, mathematician, grammarian and theologian at Constantinople. Through his translations from La ...
), there are some scholars who think that such maps go back to Ptolemy himself.
Astrology
Ptolemy wrote an astrological treatise, in four parts, known by the Greek term ''Tetrabiblos
''Tetrabiblos'' () 'four books', also known in Greek as ''Apotelesmatiká'' () "Effects", and in Latin as ''Quadripartitum'' "Four Parts", is a text on the philosophy and practice of astrology, written in the 2nd century AD by the Alexandrian ...
'' (lit. "Four Books") 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 Plato Tiburtinus ( la, Plato Tiburtinus, "Plato of Tivoli"; fl. 12th century) was a 12th-century Italian mathematician, astronomer and translator who lived in Barcelona from 1116 to 1138. He is best known for translating Hebrew and Arabic document ...
(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 In Aristotelian physics and Greek astronomy, the sublunary sphere is the region of the geocentric cosmos
The cosmos (, ) is another name for the Universe. Using the word ''cosmos'' implies viewing the universe as a complex and orderly system or ...
. Thus explanations of a sort are provided for the astrological effects of the planets
A planet is a large, rounded astronomical body that is neither a star nor its remnant. The best available theory of planet formation is the nebular hypothesis, which posits that an interstellar cloud collapses out of a nebula to create a young ...
, based upon their combined effects of heating, cooling, moistening, and drying. Ptolemy dismisses other astrological practices, such as considering the numerological
Numerology (also known as arithmancy) is the belief in an occult, divine or mystical relationship between a number and one or more coinciding events. It is also the study of the numerical value, via an alphanumeric system, of the letters in ...
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
Medical astrology (traditionally known as iatromathematics) is an ancient applied branch of astrology based mostly on ''melothesia'' (Gr. μελοθεσία), the association of various parts of the body, diseases, and drugs with the nature of the ...
, for similar reasons.
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.
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
The ''Centiloquium'' (= "one hundred sayings"), also called ''Ptolemy's Centiloquium'', is a collection of one hundred aphorisms about astrology and astrological rules. It is first recorded at the start of the tenth century CE, when a commentary ...
'', 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 pseudepigraph
Pseudepigrapha (also :wikt:anglicized, anglicized as "pseudepigraph" or "pseudepigraphs") are false attribution, falsely attributed works, texts whose claimed author is not the true author, or a work whose real author attributed it to a figure ...
ical composition. The identity and date of the actual author of the work, referred to now as Pseudo-Ptolemy, remains the subject of conjecture.
Music
Ptolemy wrote an earlier work entitled ''Harmonikon'' (Ancient Greek
Ancient Greek includes the forms of the Greek language used in ancient Greece and the ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: Mycenaean Greek (), Dark Ages (), the Archaic peri ...
: ''Ἁρμονικόν''), known as the ''Harmonics'', on music theory
Music theory is the study of 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 are needed to understand music notation (ke ...
and the mathematics behind musical scales in three books. It 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 (in contrast to the followers of Aristoxenus
Aristoxenus of Tarentum ( el, Ἀριστόξενος ὁ Ταραντῖνος; born 375, fl. 335 BC) was a Greek Peripatetic philosopher, and a pupil of Aristotle. Most of his writings, which dealt with philosophy, ethics and music, have been ...
), backed up by empirical observation (in contrast to the overly 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 Greek colony of Kroton, ...
).
Ptolemy introduces the harmonic canon, an experimental apparatus that would be used for the demonstrations in the next chapters, then proceeds to discuss Pythagorean tuning
Pythagorean tuning is a system of musical tuning in which the frequency ratios of all intervals are based on the ratio 3:2.Bruce Benward and Marilyn Nadine Saker (2003). ''Music: In Theory and Practice'', seventh edition, 2 vols. (Boston: Mc ...
. Pythagoreans 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 tetrachord
In music theory, a tetrachord ( el, τετράχορδoν; lat, tetrachordum) is a series of four notes separated by three intervals. In traditional music theory, a tetrachord always spanned the interval of a perfect fourth, a 4:3 frequency propo ...
s and octave
In music, an octave ( la, octavus: eighth) or perfect octave (sometimes called the diapason) is the interval between one musical pitch and another with double its frequency. The octave relationship is a natural phenomenon that has been refer ...
s. He presented his own divisions of the tetrachord and the octave, which he derived with the help of 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 h ...
. The book ends with a more speculative exposition of the relationships between harmony, the soul (''psyche''), and the planets (harmony of the spheres
The ''musica universalis'' (literally universal music), also called music of the spheres or harmony of the spheres, is a philosophical concept that regards proportions in the movements of celestial bodies – the Sun, Moon, and planets – as a f ...
).
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. During the Renaissance
The Renaissance ( , ) , from , with the same meanings. is a period in European history marking the transition from the Middle Ages to modernity and covering the 15th and 16th centuries, characterized by an effort to revive and surpass ideas ...
, 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 o ...
in his own musings on the harmony of the world (''Harmonice Mundi
''Harmonice Mundi (Harmonices mundi libri V)''The full title is ''Ioannis Keppleri Harmonices mundi libri V'' (''The Five Books of Johannes Kepler's The Harmony of the World''). (Latin: ''The Harmony of the World'', 1619) is a book by Johannes ...
'', Appendix to Book V).
Optics
The ''Optica'' (Ancient Greek
Ancient Greek includes the forms of the Greek language used in ancient Greece and the ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: Mycenaean Greek (), Dark Ages (), the Archaic peri ...
: Ὀπτικά), 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 Eugenius of Palermo (also Eugene) ( la, Eugenius Siculus, el, Εὐγενἠς Εὐγένιος ὁ τῆς Πανόρμου, it, Eugenio da Palermo; 1130 – 1202) was an '' amiratus'' (admiral) of the Kingdom of Sicily in the late twelfth cen ...
(). In it, Ptolemy writes about properties of sight (not light), including reflection Reflection or reflexion may refer to:
Science and technology
* Reflection (physics), a common wave phenomenon
** Specular reflection, reflection from a smooth surface
*** Mirror image, a reflection in a mirror or in water
** Signal reflection, in ...
, refraction
In physics, refraction is the redirection of a wave as it passes from one 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 commonly observed phenomeno ...
, and colour
Color (American English) or colour (British English) is the visual perceptual property deriving from the spectrum of light interacting with the photoreceptor cells of the eyes. Color categories and physical specifications of color are associ ...
. 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 wo ...
and influenced the more famous and superior 11th-century ''Book of Optics
The ''Book of Optics'' ( ar, كتاب المناظر, Kitāb al-Manāẓir; la, De Aspectibus or ''Perspectiva''; it, Deli Aspecti) is a seven-volume treatise on optics and other fields of study composed by the medieval Arab scholar Ibn al- ...
'' by Ibn al-Haytham
Ḥasan Ibn al-Haytham, Latinized as Alhazen (; full name ; ), was a medieval mathematician, astronomer, and physicist of the Islamic Golden Age from present-day Iraq.For the description of his main fields, see e.g. ("He is one of the prin ...
. 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 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 Reflection or reflexion may refer to:
Science and technology
* Reflection (physics), a common wave phenomenon
** Specular reflection, reflection from a smooth surface
*** Mirror image, a reflection in a mirror or in water
** Signal reflection, in ...
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 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 commonly observed phenomeno ...
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 (; ), or the theory of knowledge, is the branch of philosophy concerned with knowledge. Epistemology is considered a major subfield of philosophy, along with other major subfields such as ethics, logic, and metaphysics.
Episte ...
and psychological
Psychology is the scientific study of mind and behavior. Psychology includes the study of conscious and unconscious phenomena, including feelings and thoughts. It is an academic discipline of immense scope, crossing the boundaries between t ...
discussions across his corpus. He wrote a short essay entitled ''On the Criterion and Hegemonikon'' (Ancient Greek
Ancient Greek includes the forms of the Greek language used in ancient Greece and the ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: Mycenaean Greek (), Dark Ages (), the Archaic peri ...
: ''Περὶ Κριτηρίου καὶ Ἡγεμονικοῡ''), 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 an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
.
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 systematic study of the nature of the divine and, more broadly, of religious belief. It is taught as an academic discipline, typically in universities and seminaries. It occupies itself with the unique content of analyzing the ...
or metaphysics
Metaphysics is the branch of philosophy that studies the fundamental nature of reality, the first principles of being, identity and change, space and time, causality, necessity, and possibility. It includes questions about the nature of conscio ...
because the latter are conjectural while only the former can secure certain knowledge. This view is contrary to the Platonic
Plato's influence on Western culture was so profound that several different concepts are linked by being called Platonic or Platonist, for accepting some assumptions of Platonism, but which do not imply acceptance of that philosophy as a whole. It ...
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 (; grc-gre, Ἥρων ὁ Ἀλεξανδρεύς, ''Heron ho Alexandreus'', also known as Heron of Alexandria ; 60 AD) was a Greece, Greek mathematician and engineer who was active in his native city of Alexandria, Roman Egy ...
.
Named after Ptolemy
There are several characters or items named after Ptolemy, including:
* The crater Ptolemaeus
Claudius Ptolemy (; grc-gre, Πτολεμαῖος, ; la, Claudius Ptolemaeus; AD) was a mathematician, astronomer, astrologer, geographer, and music theorist, who wrote about a dozen scientific treatises, three of which were of importanc ...
on the Moon
The Moon is Earth's only natural satellite. It is the fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth (comparable to the width of ...
* The crater Ptolemaeus
Claudius Ptolemy (; grc-gre, Πτολεμαῖος, ; la, Claudius Ptolemaeus; AD) was a mathematician, astronomer, astrologer, geographer, and music theorist, who wrote about a dozen scientific treatises, three of which were of importanc ...
on Mars
Mars is the fourth planet from the Sun and the second-smallest planet in the Solar System, only being larger than Mercury (planet), Mercury. In the English language, Mars is named for the Mars (mythology), Roman god of war. Mars is a terr ...
* The asteroid 4001 Ptolemaeus
* Messier 7
Messier 7 or M7, also designated NGC 6475 and sometimes known as the Ptolemy Cluster, is an open cluster of stars in the constellation of Scorpius. The cluster is easily detectable with the naked eye, close to the "stinger" of Scorpius. With a d ...
, sometimes known as the Ptolemy Cluster, an open cluster of stars in the constellation of Scorpius
* The Ptolemy stone
St. John's College is a private liberal arts college with dual campuses in Annapolis, Maryland, and Santa Fe, New Mexico. St. John's is one of the oldest institutions of higher learning in the United States as the successor institution of King W ...
used in the mathematics courses at both St. John's College campuses in the U.S.
* Ptolemy's theorem
In Euclidean geometry, Ptolemy's theorem is a relation between the four sides and two diagonals of a cyclic quadrilateral (a quadrilateral whose vertices lie on a common circle). The theorem is named after the Greek astronomer and mathematician ...
on distances in a cyclic quadrilateral
In Euclidean geometry, a cyclic quadrilateral or inscribed quadrilateral is a quadrilateral whose vertices all lie on a single circle. This circle is called the ''circumcircle'' or ''circumscribed circle'', and the vertices are said to be ''c ...
, and its generalization, Ptolemy's inequality
In Euclidean geometry, Ptolemy's inequality relates the six distances determined by four points in the plane or in a higher-dimensional space. It states that, for any four points , , , and , the following inequality holds:
:\overline\cdot \overline ...
, to non-cyclic quadrilaterals
* Ptolemaic graph
In graph theory, a Ptolemaic graph is an undirected graph whose shortest path distances obey Ptolemy's inequality, which in turn was named after the Greek astronomer and mathematician Ptolemy. The Ptolemaic graphs are exactly the graphs that ar ...
s, the graphs whose distances obey Ptolemy's inequality
* Ptolemy Project
The Ptolemy Project is an ongoing project aimed at modeling, simulating, and designing concurrent, real-time, embedded systems. The focus of the Ptolemy Project is on assembling concurrent components. The principal product of the project is the Pto ...
, a project at University of California, Berkeley, aimed at modeling, simulating and designing concurrent, real-time, embedded systems
* Ptolemy Slocum
Ptolemy Slocum (born 20 November 1975) is an American actor, known for his role as Sylvester in ''Westworld''.
Slocum was born in the Kenyan capital Nairobi. He was named after the Greek astronomer Claudius Ptolemy and has been active as an actor ...
, actor
Works
*
*
*
*
*
*
*
*
* ''Planisphaerium'', medieval Arabic translations and an English translation thereof, https://www.sciamvs.org/files/SCIAMVS_08_037-139_Sidoli_Berggren.pdf
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
Messier 7 or M7, also designated NGC 6475 and sometimes known as the Ptolemy Cluster, is an open cluster of stars in the constellation of Scorpius. The cluster is easily detectable with the naked eye, close to the "stinger" of Scorpius. With a d ...
– Ptolemy Cluster, star cluster described by Ptolemaeus
* Pei Xiu
Pei Xiu (224–271), 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 of China. He was very much trusted by Sima Zhao, and pa ...
* Ptolemy's Canon The Canon of Kings was a dated list of kings used by ancient astronomers as a convenient means to date astronomical phenomena, such as eclipses. The Canon was preserved by the astronomer Claudius Ptolemy, and is thus known sometimes as Ptolemy's Can ...
– a dated list of kings used by ancient astronomers.
* Ptolemy's table of chords
The table of chords, created by the 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 astronomy. It ...
* Zhang Heng
Zhang Heng (; AD 78–139), formerly romanized as Chang Heng, was a Chinese polymathic scientist and statesman who lived during the Han dynasty. Educated in the capital cities of Luoyang and Chang'an, he achieved success as an astronomer, ma ...
Footnotes
References
*
* Berggren, J. Lennart, and Alexander Jones. 2000. ''Ptolemy's ''Geography'': An Annotated Translation of the Theoretical Chapters''. Princeton and Oxford: Princeton University Press
Princeton University Press is an independent publisher with close connections to Princeton University. Its mission is to disseminate scholarship within academia and society at large.
The press was founded by Whitney Darrow, with the financial su ...
. .
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* Hübner, Wolfgang, ed. 1998. ''Claudius Ptolemaeus, Opera quae exstant omnia'' Vol III/Fasc 1: ΑΠΟΤΕΛΕΣΜΑΤΙΚΑ (= Tetrabiblos). De Gruyter. (Bibliotheca scriptorum Graecorum et Romanorum Teubneriana). (The most recent edition of the Greek text of Ptolemy's astrological work, based on earlier editions by F. Boll and E. Boer.)
* Lejeune, A. (1989) ''L'Optique de Claude Ptolémée dans la version latine d'après l'arabe de l'émir Eugène de Sicile.'' atin text with French translation Collection de travaux de l'Académie International d'Histoire des Sciences, No. 31. Leiden: E.J.Brill.
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* Nobbe, C. F. A., ed. 1843. Claudii Ptolemaei Geographia. 3 vols. Leipzig: Carolus Tauchnitus. (Until Stückelberger (2006), this was the most recent edition of the complete Greek text.)
* Peerlings, R.H.J., Laurentius F., van den Bovenkamp J.,(2017) ''The watermarks in the Rome editions of Ptolemy's Cosmography and more'', In Quaerendo 47: 307–327, 2017.
* 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.
* Ptolemy. 1930. ''Die Harmonielehre des Klaudios Ptolemaios'', edited by Ingemar Düring. Göteborgs högskolas årsskrift 36, 1930:1. Göteborg: Elanders boktr. aktiebolag. Reprint, New York: Garland Publishing, 1980.
* Ptolemy. 2000. ''Harmonics'', translated and commentary by Jon Solomon. Mnemosyne, Bibliotheca Classica Batava, Supplementum, 0169–8958, 203. Leiden and Boston: Brill Publishers
Brill Academic Publishers (known as E. J. Brill, Koninklijke Brill, Brill ()) is a Dutch international academic publisher founded in 1683 in Leiden, Netherlands. With offices in Leiden, Boston, Paderborn and Singapore, Brill today publishes 27 ...
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* Smith, A.M. (1996) ''Ptolemy's theory of visual perception: An English translation of the Optics with introduction and commentary.'' Transactions of the American Philosophical Society, Vol. 86, Part 2. Philadelphia: The American Philosophical Society.
* .
* Stevenson, Edward Luther (trans. and ed.). 1932. ''Claudius Ptolemy: The Geography''. New York: New York Public Library. Reprint, New York: Dover, 1991. (This is the only complete English translation of Ptolemy's most famous work. Unfortunately, it is marred by numerous mistakes and the placenames are given in Latinised forms, rather than in the original Greek).
* Stückelberger, Alfred, and Gerd Graßhoff (eds). 2006. ''Ptolemaios, Handbuch der Geographie, Griechisch-Deutsch''. 2 vols. Basel: Schwabe Verlag. . (Massive 1018 pp. scholarly edition by a team of a dozen scholars that takes account of all known manuscripts, with facing Greek and German text, footnotes on manuscript variations, color maps, and a CD with the geographical data)
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* ''Ptolemy's Almagest'', Translated and annotated by G. J. Toomer
Gerald James Toomer (born 23 November 1934) is a historian of astronomy and mathematics who has written numerous books and papers on ancient Greek and medieval Islamic astronomy. In particular, he translated Ptolemy's '' Almagest'' into Englis ...
. Princeton University Press, 1998
* Sir Thomas Heath, A History of Greek Mathematics, Oxford : Clarendon Press, 1921.
External links
Ptolemy's Tetrabiblos at LacusCurtius
(Transcription of the Loeb Classical Library
The Loeb Classical Library (LCL; named after James Loeb; , ) is a series of books originally published by Heinemann in London, but is currently published by Harvard University Press. The library contains important works of ancient Greek and L ...
's English translation)
Entire ''Tetrabiblos'' of J.M. Ashmand's 1822 translation.
(English translation, incomplete)
(English translation)
The complete text of Heiberg's edition (PDF) Greek.
''Almagest'' books 1–6
with preface at archive.org
The Internet Archive is an American digital library with the stated mission of "universal access to all knowledge". It provides free public access to collections of digitized materials, including websites, software applications/games, music, ...
''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.
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 the research library that officially serves the United States Congress and is the ''de facto'' national library of the United States. It is the oldest federal cultural institution in the country. The library is ...
Almagestū Cl. Ptolemei
From the Rare Book and Special Collection Division at the Library of Congress
The Library of Congress (LOC) is the research library that officially serves the United States Congress and is the ''de facto'' national library of the United States. It is the oldest federal cultural institution in the country. The library is ...
* 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.
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– at Paul Stoddard's Animated Virtual Planetarium, Northern Illinois University
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– at Rosemary Kennett's website at the Syracuse University
Syracuse University (informally 'Cuse or SU) is a Private university, private research university in Syracuse, New York. Established in 1870 with roots in the Methodist Episcopal Church, the university has been nonsectarian since 1920. Locate ...
Flash animation of Ptolemy's universe.
(best in Internet Explorer)
Online Galleries, History of Science Collections, University of Oklahoma Libraries
High resolution images of works by Ptolemy in .jpg and .tiff format.
Codex Vaticanus graecus 1291 (Vat.gr.1291) in Vatican Digital Library
- Complete reproduction of the 9th century manuscript of Ptolemy's ''Handy Tables''.
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