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Claudius Ptolemy (; grc-koi, Κλαύδιος Πτολεμαῖος, , ; la, Claudius Ptolemaeus; AD) was a
mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Greek: ) includes the study of such topics as numbers ( and ), formulas and related structures (), shapes and spaces in which they are contained ( ...

mathematician
,
astronomer An astronomer is a in the field of who focuses their studies on a specific question or field outside the scope of . They observe s such as s, s, , s and – in either (by analyzing the data) or . Examples of topics or fields astronomers stud ...

astronomer
,
astrologer Astrology is a pseudoscience Pseudoscience consists of statements, beliefs, or practices that claim to be both scientific and factual but are incompatible with the scientific method The scientific method is an Empirical evidenc ...

astrologer
,
geographer A geographer is a physical scientist, social scientist or humanist whose area of study is geography Geography (from Greek: , ''geographia'', literally "earth description") is a field of science devoted to the study of the lands, feat ...
, and
music theorist Music theory is the study of the practices and possibilities of music Music is the of arranging s in time through the of melody, harmony, rhythm, and timbre. It is one of the aspects of all human societies. General include common elem ...
, who wrote about a dozen scientific
treatises A treatise is a Formality, 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 conclusio ...
, 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 in its eastern provinces during Late Antiquity and the Middle Ages, when its capital city was Constantinople. It surviv ...

Byzantine
,
Islamic Islam (; ar, اَلْإِسْلَامُ, al-’Islām, "submission o God Oh God may refer to: * An exclamation; similar to "oh no", "oh yes", "oh my", "aw goodness", "ah gosh", "ah gawd"; see interjection ''Oh, God!'' franchise * ''Oh, ...
, and
Western European Western Europe is the western region of Europe. The region's countries and territories vary depending on context. Beginning with foreign exploration during the Age of Discovery, roughly from the 15th century, the concept of ''Europe'' as "the W ...
science. The first is the astronomical treatise now known as the ''
Almagest The ''Almagest'' is a 2nd-century Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its population is appr ...
'', 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 Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its population is approximately 10. ...
'', which is a thorough discussion on maps and the geographic knowledge of the
Greco-Roman world File:Merida Roman Theatre2.jpg, Roman Theatre of Mérida, Spain. The term "Greco-Roman world" (also "Greco-Roman culture" or ; spelled Graeco-Roman in the Commonwealth of Nations, Commonwealth), as understood by modern scholars and writers, r ...
. The third is the astrological treatise in which he attempted to adapt horoscopic astrology to the
Aristotelian Aristotelian may refer to: * Aristotle (384–322 BCE), Greek philosopher * Aristotelianism, the philosophical tradition begun by Aristotle * Aristotelian ethics * Aristotelian logic, term logic * Aristotelian physics, the natural sciences * Aristot ...
natural philosophy Natural philosophy or philosophy of nature (from ''philosophia naturalis'') was the study of and the physical that was dominant before the development of . From the ancient world, at least since , to the 19th century, ''natural philosophy' ...
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 (, , Greek approximately ;. , , , lit. "Common Greek"), also known as Alexandrian dialect, common Attic, Hellenistic or Biblical Greek, was the koiné language, common supra-regional form of Greek language, Greek spoken and written d ...
meaning "Four Books", or by its Latin equivalent ''Quadripartite''. Unlike most ancient Greek mathematicians, Ptolemy's writings (foremost the ''
Almagest The ''Almagest'' is a 2nd-century Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its population is appr ...
'') never ceased to be copied or commented upon, both in
Late Antiquity Late antiquity is a used by historians to describe the time of transition from to the in and adjacent areas bordering the . The popularization of this periodization in English has generally been credited to historian , after the publication o ...
and in the
Middle Ages In the history of Europe The history of Europe concerns itself with the discovery and collection, the study, organization and presentation and the interpretation of past events and affairs of the people of Europe since the beginning of w ...
. 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, الإسكندرية ; arz, اسكندرية ; : Rakodī; el, Αλεξάνδρεια ''Alexandria'') is the in after and , in , and a major economic centre. With a total population of 5,200,000, Alexandria is the ...

Alexandria
, in the Roman province of Egypt under , had a Latin name (which several historians have taken to imply he was also 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. *Women in Ancient Rome, Roman women had a limited form of citizenship. They were not allowed 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 la, Constantinopolis , alternate_name = Byzantion (earlier Greek name), Nova Roma ("New Rome"), Miklagard/Miklagarth (Old Norse), Tsarigrad (Slavs, Slavic), Q ...
gave his birthplace as the prominent Greek city
Ptolemais Hermiou Ptolemais Hermiou, or Ptolemais in the Thebaid The Thebaid or Thebais ( grc-gre, Θηβαΐς, ''Thēbaïs'') was a region in Roman Egypt, ancient Egypt, comprising the 13 southernmost nome (Egypt), nomes of Upper Egypt, from Abydos, Egypt, Aby ...
() in the
Thebaid The Thebaid or Thebais ( grc-gre, Θηβαΐς, ''Thēbaïs'') was a region In geography Geography (from Greek: , ''geographia'', literally "earth description") is a field of science devoted to the study of the lands, features, inha ...
(). This attestation is quite late, however, and there is no evidence to support it.; G. J. Toomer, "Ptolemy (or Claudius Ptolemaeus)"
''Complete Dictionary of Scientific Biography''
2008. Retrieved from Encyclopedia.com. 21 January 2013. Concerning the possibility that Ptolemy might have been born in Ptolemais Hermiou, Toomer writes:
Ptolemy died in Alexandria around 168.


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 myth Myth is a folklore genre Folklore is the expressive body of culture shared by a particular group of people; it encompasses the tradition A tradition is a belief A belief is an Attitude (psyc ...
and is of Homeric form. It was common among the
Macedonian Macedonian most often refers to someone or something from or related to Macedonia (disambiguation), Macedonia. Macedonian may specifically refer to: People Modern * Macedonians (ethnic group), the South Slavic ethnic group primarily associated w ...
upper class at the time of
Alexander the Great Alexander III of Macedon ( grc-gre, Αλέξανδρος}, ; 20/21 July 356 BC – 10/11 June 323 BC), commonly known as Alexander the Great, was a king (''basileus ''Basileus'' ( el, βασιλεύς) is a Greek term and title A title ...

Alexander the Great
and there were several of this name among Alexander's army, one of whom made himself
pharaoh Pharaoh ( , ; cop, , Pǝrro) is the common title now used for the monarch A monarch is a head of state A head of state (or chief of state) is the public persona A persona (plural personae or personas), depending on the conte ...

pharaoh
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 Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδ ...
, the first pharaoh of the
Ptolemaic Kingdom The Ptolemaic Kingdom (; grc-koi, Πτολεμαϊκὴ βασιλεία, Ptolemaïkḕ basileía) was an Ancient Greece, Ancient Greek state based in Egypt during the Hellenistic period, Hellenistic Period. It was founded in 305 BC by Ptolemy ...
. Almost all subsequent pharaohs of Egypt, with a few exceptions, were named
Ptolemies The Ptolemaic dynasty (; grc, Πτολεμαῖοι, ''Ptolemaioi''), the Thirty-third dynasty of Egypt, sometimes referred to as the Lagid dynasty (Λαγίδαι, ''Lagidae;'' after Ptolemy I Ptolemy I Soter (; gr, Πτολεμαῖο ...
until 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 () was a privileged political and legal status afforded to free individuals with respect to laws, property, and governance. *Women in Ancient Rome, Roman women had a limited form of citizenship. They were not allowed 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 Claudius ( ; Tiberius Claudius Caesar Augustus Germanicus; 1 August 10 BC – 13 October AD 54) was the fourth Roman emperor The Roman emperor was the ruler of the Roman Empire during the History of the Roman Empire, imperial p ...

Claudius
or the emperor
Nero Nero ( ; full name: Nero Claudius Caesar Augustus Germanicus; 15 December AD 37 – 9 June AD 68) was the fifth emperor of Rome. He was Adoption in Ancient Rome, adopted by the Roman emperor Claudius at the age of 13 and s ...

Nero
. The 9th century
Persian Persian may refer to: * People and things from Iran, historically called ''Persia'' in the English language ** Persians, Persian people, the majority ethnic group in Iran, not to be conflated with the Iranian peoples ** Persian language, an Iranian ...
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 Maʻshar 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 Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδ ...
were wise "and included Ptolemy the Wise, who composed the book of the ''Almagest''". Abu Maʻshar 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 Maʿshar'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 Maʻshar, ''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 Maʻshar'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#REDIRECT Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast E ...
'' as its astrological counterpart. In later
Arabic Arabic (, ' or , ' or ) is a Semitic language The Semitic languages are a branch of the Afroasiatic language family originating in the Middle East The Middle East is a list of transcontinental countries, transcontinental region ...

Arabic
sources, he was often known as "the
Upper Egypt Upper Egypt ( ar, صعيد مصر ', shortened to , , locally: ; ) is the southern portion of Egypt Egypt ( ar, مِصر, Miṣr), officially the Arab Republic of Egypt, is a transcontinental country This is a list of countries lo ...
ian", suggesting he may have had origins in southern
Egypt Egypt ( ar, مِصر, Miṣr), officially the Arab Republic of Egypt, is a transcontinental country This is a list of countries located on more than one continent A continent is one of several large landmasses. Generally identi ...

Egypt
.
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'', ...
(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 Geography (from Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), offic ...
and
physicists A physicist is a scientist A scientist is a person who conducts scientific research The scientific method is an Empirical evidence, empirical method of acquiring knowledge that has characterized the development of science since at lea ...
referred to his name in
Arabic Arabic (, ' or , ' or ) is a Semitic language The Semitic languages are a branch of the Afroasiatic language family originating in the Middle East The Middle East is a list of transcontinental countries, transcontinental region ...

Arabic
as ''Baṭlumyus'' ( ar, بَطْلُمْيوس). Ptolemy wrote in
ancient Greek Ancient Greek includes the forms of the Greek language Greek ( el, label=Modern Greek Modern Greek (, , or , ''Kiní Neoellinikí Glóssa''), generally referred to by speakers simply as Greek (, ), refers collectively to the diale ...
and can be shown to have utilized Babylonian astronomical data. He might have been a Roman citizen, but was ethnically either a
Greek#REDIRECT Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its population is approximately 10.7 million as of ...
"Ptolemy". Britannica Concise Encyclopedia. Encyclopædia Britannica, Inc., 2006. or at least a
Hellenized Hellenization (other British spelling Hellenisation) or Hellenism is the historical spread of ancient Greek Ancient Greek includes the forms of the Greek language used in ancient Greece and the classical antiquity, ancient world from ar ...
Egyptian.
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. He has a significant import ...
(1936). "The Unity and Diversity of the Mediterranean World", ''Osiris'' 2, p. 406–463


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 Greek ( el, label=Modern Greek Modern Greek (, , or , ''Kiní Neoellinikí Glóssa''), generally referred to by speakers simply as Greek (, ), refers collectively to the diale ...
: ''Μαθηματικὴ Σύνταξις'', lit. "Mathematical Systematic Treatise"), better known as the ''
Almagest The ''Almagest'' is a 2nd-century Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its population is appr ...
'', 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 that attempted to merge these two approaches was
Hipparchus Hipparchus of Nicaea (; 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 precession of the ...
, who produced
geometric model __NOTOC__ Geometric modeling is a branch of applied mathematics Applied mathematics is the application of mathematical methods by different fields such as physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epist ...
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 (English in the Commonwealth of Nations, Commonwealth English) or star catalog (American English) is an astronomical catalogue that lists stars. In astronomy, many stars are referred to simply by catalogue numbers. There are a gre ...
, 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 a perceived outline or pattern, typically representing an animal, mythological person or creature, or an inanimate object. The origins of the earliest ...

constellation
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, and its author soon became an almost legendary figure: Ptolemy, King of Alexandria. The ''Almagest'' was preserved, like many extant Greek scientific works, in
Arabic Arabic (, ' or , ' or ) is a Semitic language The Semitic languages are a branch of the Afroasiatic language family originating in the Middle East The Middle East is a list of transcontinental countries, transcontinental region ...

Arabic
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 a periodization Periodization is the process or study of categorizing the past into discrete, quantified named blocks of time.Adam Rabinowitz. It’s about time: historical periodization and Linked Ancient World Data'. Inst ...
. 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 , the geocentric model (also known as geocentrism, often exemplified specifically by the Ptolemaic system) is a description of the with at the center. Under the geocentric model, the , , s, and all Earth. The geocentric model was the pre ...

geocentric
and almost universally accepted until the reappearance of
heliocentric Heliocentrism is the astronomical Astronomy (from el, ἀστρονομία, literally meaning the science that studies the laws of the stars) is a natural science that studies celestial objects and phenomena. It uses mathematics ...

heliocentric
models during the
scientific revolution The Scientific Revolution was a series of events that marked the emergence In philosophy Philosophy (from , ) is the study of general and fundamental questions, such as those about reason, Metaphysics, existence, Epistemology, ...

scientific revolution
.


''Handy Tables''

The ''Handy Tables'' (
Ancient Greek Ancient Greek includes the forms of the Greek language Greek ( el, label=Modern Greek Modern Greek (, , or , ''Kiní Neoellinikí Glóssa''), generally referred to by speakers simply as Greek (, ), refers collectively to the diale ...
: ''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 ECLiPSe is a software system for the development and deployment of Constraint Programming Constraint programming (CP) is a paradigm for solving combinatorial problems that draws on a wide range of techniques from artificial intelligence ...
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 Greeks, Greek scholar and mathematician who lived in Alexandria, Egypt. He edited and arranged Euclid's ''Euclid's Elements, Elements'' and wrot ...
’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 Greek ( el, label=Modern Greek Modern Greek (, , or , ''Kiní Neoellinikí Glóssa''), generally referred to by speakers simply as Greek (, ), refers collectively to the diale ...
: ''Ὑποθέσεις τῶν πλανωμένων'', lit. "Hypotheses of the Planets") is a
cosmological Cosmology (from Greek#REDIRECT Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its population is appro ...
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 heliocentrism, Copernican systems of astronomy, the epicycle (from grc, ἐπίκυκλος, literally ''upon the circle'', meaning ''circle moving on another circle'') was a geometric model used ...

epicycle
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 , the geocentric model (also known as geocentrism, often exemplified specifically by the Ptolemaic system) is a description of the with at the center. Under the geocentric model, the , , s, and all Earth. The geocentric model was the pre ...
perspective, much like 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 Scientific modelling, model ...
would have done for a
heliocentric Heliocentrism is the astronomical Astronomy (from el, ἀστρονομία, literally meaning the science that studies the laws of the stars) is a natural science that studies celestial objects and phenomena. It uses mathematics ...
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 Astronomy (from el, ἀστρονομία, literally meaning the science that studies the laws of the stars) is a natural science that studies astronomical object, celestial objects and celestial event, phenomena. It uses ...

analemma
''. 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, specific day within such a system. A calendar is also ...

calendar
or
almanac An almanac (also spelled ''almanack'' and ''almanach'') is an annual publication Annual publications, more often simply called annuals, are periodical publications appearing regularly once per year."Annuals", in ''Encyclopedia of library and info ...
, based on the appearances and disappearances of stars over the course of the solar year. The ''Planispherium'' (
Ancient Greek Ancient Greek includes the forms of the Greek language Greek ( el, label=Modern Greek Modern Greek (, , or , ''Kiní Neoellinikí Glóssa''), generally referred to by speakers simply as Greek (, ), refers collectively to the diale ...
: ''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 A constellation is an area on the celestial sphere in which a group of visible stars forms a perceived outline or pattern, typically representing an animal, mythological ...
, around 146-147 CE, 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 savior god, Claudius Ptolemy (dedicates) the first principles and models of astronomy," following by a catalog 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 Greek ( el, label=Modern Greek Modern Greek (, , or , ''Kiní Neoellinikí Glóssa''), generally referred to by speakers simply as Greek (, ), refers collectively to the diale ...
: ''Γεωγραφικὴ Ὑφήγησις''; lit. "Guide to Drawing the Earth"), known as the ''
Geography Geography (from Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its population is approximately 10. ...
'', a handbook on how to draw maps using
geographical coordinates A geographic coordinate system (GCS) is a coordinate system associated with position (geometry), positions on Earth (geographic position). A GCS can give positions: *as Geodetic coordinates, spherical coordinate system using latitude, long ...
for parts of the
Roman world The culture of ancient Rome existed throughout the almost 1200-year history of the civilization  A civilization (or civilisation) is a that is characterized by , , a form of government, and systems of communication (such as ). Ci ...

Roman world
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 or used in conjunction with a map or .Aurousseau, 61. It typically contains information concerning the geographical makeup, and physical features of a country, region, or continent. Content of a gazetteer can incl ...

gazetteer
s of the Roman and ancient
Persian Empire The Achaemenid Empire (; peo, wikt:𐎧𐏁𐏂𐎶, 𐎧𐏁𐏂, translit=Xšāça, translation=The Empire), also called the First Persian Empire, was an ancient Iranian peoples, Iranian empire based in Western Asia founded by Cyrus the Grea ...

Persian Empire
. He also acknowledged ancient astronomer
Hipparchus Hipparchus of Nicaea (; 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 precession of the ...
for having provided the elevation of the
north celestial pole The north and south celestial poles are the two imaginary points in the sky where Earth's rotation around a fixed axis, axis of rotation, indefinitely extended, intersects the celestial sphere. The north and south celestial poles appear perman ...
for a few cities. Although
maps A map is a symbol A symbol is a mark, sign, or word In linguistics, a word of a spoken language can be defined as the smallest sequence of phonemes that can be uttered in isolation with semantic, objective or pragmatics, practical meani ...

maps
based on scientific principles had been made since the time of
Eratosthenes Eratosthenes of Cyrene (; grc-gre, Ἐρατοσθένης ;  – ) was a Greek polymath A polymath ( el, πολυμαθής, , "having learned much"; la, homo universalis, "universal human") is an individual whose knowledge spans a ...

Eratosthenes
(c. 276-195 BCE), Ptolemy improved on
map projection In cartography, a map projection is a way to flatten a globe's surface into a plane in order to make a map. This requires a systematic transformation of the latitudes and longitudes of locations from the Surface (mathematics), surface of the globe ...
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 Geometry (from the grc, γεωμετρία; ''wikt:γῆ, geo-'' "earth", ''wikt:μέτρον, -metron'' "measurement") is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space t ...

coordinate
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 gri ...
that spanned the globe.
Latitude In geography Geography (from Greek: , ''geographia'', literally "earth description") is a field of science devoted to the study of the lands, features, inhabitants, and phenomena of the Earth and planets. The first person to use the ...

Latitude
was measured from the
equator The Equator is a circle of latitude, about in circumference, that divides Earth into the Northern Hemisphere, Northern and Southern Hemisphere, Southern hemispheres. It is an imaginary line located at 0 degrees latitude, halfway between the N ...

equator
, as it is today, but Ptolemy preferred to express it as '' climata'', the length of the longest day rather than
degrees of arc Image:Degree diagram.svg, One degree (shown in red) andeighty nine degrees (shown in blue) A degree (in full, a degree of arc, arc degree, or arcdegree), usually denoted by ° (the degree symbol), is a measurement of a plane (mathematics), plane ...
: the length of the
midsummer Midsummer is the period of time in the middle of the summer. The exact dates vary among different cultures, but is primarily held close to the summer solstice The summer solstice, also known as estival solstice or midsummer, occurs when one of ...

midsummer
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 The Arctic Circle is one of the two s and the most northerly of the five major as shown on maps of . It marks the northernmo ...

polar circle
. 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 Topography is the study of the forms and features of land surfaces. The topography of an area could refer to the surface forms and features themselves, or a description (especially their depiction in maps). Topography is a field of geoscience ...
lists, and captions for the maps. His ''oikoumenē'' spanned 180 degrees of longitude from the Blessed Islands in the to the middle of
China China (), officially the People's Republic of China (PRC; ), is a country in East Asia East Asia is the eastern region of Asia Asia () is Earth's largest and most populous continent, located primarily in the Eastern Hemisphere ...

China
, and about 80 degrees of latitude from
Shetland Shetland ( on, Hjaltland; sco, Shetland; nrn, Hjetland), also called the Shetland Islands and formerly Zetland, is a subarctic archipelago An archipelago ( ), sometimes called an island group or island chain, is a chain, cluster or co ...

Shetland
to anti-Meroe (east coast of
Africa Africa is the world's second-largest and second-most populous continent A continent is any of several large landmass A landmass, or land mass, is a large region In geography Geography (from Greek: , ''geographia'', ...

Africa
); 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 in surviving manuscripts date from c. 1300 CE (after the text was rediscovered by
Maximus Planudes Maximus Planudes ( grc-gre, Μάξιμος Πλανούδης, ''Máximos Planoúdēs''; ) was a Byzantine The Byzantine Empire, also referred to as the Eastern Roman Empire, or Byzantium, was the continuation of the Roman Empire in its eas ...
), 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#REDIRECT Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast E ...
'' (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 (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 sphereIn Aristotelian physics and Greek astronomy Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its population is appr ...
. Thus explanations of a sort are provided for the astrological effects of the
planets A planet is an astronomical body orbit In physics, an orbit is the gravitationally curved trajectory of an physical body, object, such as the trajectory of a planet around a star or a natural satellite around a planet. Normally, orbit r ...

planets
, based upon their combined effects of heating, cooling, moistening, and drying. Ptolemy dismisses other astrological practices, such as considering the
numerological Numerology is any belief in the divine or mysticism, mystical relationship between a number and one or more Coincidence#Interpretation, coinciding events. It is also the study of the numerical value of the letters in words, names, and ideas. I ...
significance of names, that he believed to be without sound basis, and leaves out popular topics, such as
electional astrology Electional astrology, also known as ''event'' astrology, is a branch found in most traditions of astrology Astrology is a pseudoscience that claims to divination, divine information about human affairs and terrestrial events by studying ...
(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 s ...
, 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 Ancient Greek, Greek ἀφορισμός: ''aphorismos'', denoting 'delimitation', 'distinction', and 'definition') is a concise, terse, laconic, or memorable expression of a general truth or principle. They are often handed do ...
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 w ...
'', 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.


Music

Ptolemy wrote an earlier work entitled ''Harmonikon'' (
Ancient Greek Ancient Greek includes the forms of the Greek language Greek ( el, label=Modern Greek Modern Greek (, , or , ''Kiní Neoellinikí Glóssa''), generally referred to by speakers simply as Greek (, ), refers collectively to the diale ...
: ''Ἁρμονικόν''), known as the ''Harmonics'', on music theory 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), backed up by empirical observation (in contrast to the overly theoretical approach of the Pythagoreans). 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. 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 tetrachords and octaves. He presented his own divisions of the tetrachord and the octave, which he derived with the help of a monochord. The book ends with a more speculative exposition of the relationships between harmony, the soul (''psyche''), and the planets (Musica universalis, 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. It also exherted a strong influenced during the Science in the Renaissance, Renaissance and the Scientific Revolution, seventeenth century; Kepler, for instance, read and was influenced by this work in his own musings on the harmony of the world (''Harmonices Mundi, Harmonice Mundi'', Appendix to Book V).


Optics

The ''Optica'' (
Ancient Greek Ancient Greek includes the forms of the Greek language Greek ( el, label=Modern Greek Modern Greek (, , or , ''Kiní Neoellinikí Glóssa''), generally referred to by speakers simply as Greek (, ), refers collectively to the diale ...
: ''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 (). In it, Ptolemy writes about properties of sight (not light), including Reflection (physics), reflection, refraction, and colour, color. The work is a significant part of the early history of optics and influenced the more famous and superior 11th-century ''Book of Optics'' by Ibn al-Haytham. Ptolemy offered explanations for many phenomena concerning illumination and color, 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 (physics), reflection in plane, convex, concave, and compound mirrors. The last section (Book V) deals with refraction 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 Epistemology, epistemological and Psychology, psychological 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 Greek ( el, label=Modern Greek Modern Greek (, , or , ''Kiní Neoellinikí Glóssa''), generally referred to by speakers simply as Greek (, ), refers collectively to the diale ...
: ''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 Greek mathematics, 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 or metaphysics because the latter are conjectural while only the former can secure certain knowledge. This view is contrary to the Platonism, Platonic and Aristotelianism, Aristotelian traditions, where theology or metaphysics occupied the highest honor. Despite being a minority position among ancient philosophers, Ptolemy's views were shared by other mathematicians such as Hero of Alexandria.


Named after Ptolemy

There are several characters or items named after Ptolemy, including: * The crater Ptolemaeus (lunar crater), Ptolemaeus on the Moon * The crater Ptolemaeus (Martian crater), Ptolemaeus on Mars * 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 (Annapolis/Santa Fe), St. John's College campuses in the U.S. * Ptolemy's theorem on distances in a cyclic quadrilateral, 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 systems * Ptolemy Slocum, actor


Works

* * * * * * * *


See also

* Equant * Messier 7 – Ptolemy Cluster, star cluster described by Ptolemaeus * Pei Xiu * Canon of Kings, Ptolemy's Canon – a dated list of kings used by ancient astronomers. * Ptolemy's table of chords * Zhang Heng


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. . * * 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.'' [Latin text with French translation]. Collection de travaux de l'Académie International d'Histoire des Sciences, No. 31. Leiden: E.J.Brill. * * 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. * . * * 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) * * ''Ptolemy's Almagest'', Translated and annotated by G. J. Toomer. 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'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 Internet Archive, archive.org
''Geography''
digitized 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
Almagestū Cl. Ptolemei
From the Rare Book and Special Collection Division at the Library of Congress * 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 the Syracuse University
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''. {{Authority control Ptolemy, 100 births 170 deaths 1st-century Romans 2nd-century Romans 2nd-century philosophers 2nd-century poets Egyptian calendar Ancient Greek astrologers Ancient Greek astronomers Ancient Greek mathematicians Ancient Greek music theorists Astrological writers Claudii Egyptian astronomers Egyptian mathematicians Epigrammatists of the Greek Anthology 2nd-century Egyptian people Ancient Greek geographers Roman-era geographers 2nd-century geographers 2nd-century mathematicians