Ptolemy

Quality 0.50 · 23 views · Updated 2 months ago

Greco-Roman astronomer and geographer (c. 100–170)

title: "Ptolemy" type: doc version: 1 created: 2026-02-28 author: "Wikipedia contributors" status: active scope: public tags: ["ptolemy", "100s-births", "2nd-century-deaths", "1st-century-romans", "2nd-century-astronomers", "2nd-century-romans", "2nd-century-geographers", "2nd-century-greek-philosophers", "2nd-century-mathematicians", "ancient-greek-astrologers", "ancient-greek-astronomers", "ancient-greek-geographers", "ancient-greek-mathematicians", "ancient-greek-music-theorists", "ancient-roman-geographers", "astrological-writers", "claudii", "epigrammatists-of-the-greek-anthology"] description: "Greco-Roman astronomer and geographer (c. 100–170)" topic_path: "arts" source: "https://en.wikipedia.org/wiki/Ptolemy" license: "CC BY-SA 4.0" wikipedia_page_id: 0 wikipedia_revision_id: 0

::summary Greco-Roman astronomer and geographer (c. 100–170) ::

::data[format=table title="Infobox scientist"]

Field	Value
name	Ptolemy
native_name	Κλαύδιος Πτολεμαῖος
image	Ptolemy 1476 with armillary sphere model.jpg
caption	Portrait of Ptolemy by Justus van Gent and Pedro Berruguete (1476)
birth_date	AD 100
birth_place	Unknown
death_date	160s/170s
death_place	Alexandria, Egypt, Roman Empire
fields
known_for
citizenship	possibly Roman
::

Claudius Ptolemy (; , grc; ; – 160s/170s AD), who wrote about a dozen scientific treatises, three of which were important to later Byzantine, Islamic, and Western European science. The first was his astronomical treatise now known as the Almagest, originally entitled ** (Μαθηματικὴ Σύνταξις, **, ). The second is the Geography, which is a thorough discussion on maps and the geographic knowledge of the Greco-Roman world. The third is the astrological treatise in which he attempted to adapt horoscopic astrology to the Aristotelian natural philosophy of his day. This is sometimes known as the ** (Αποτελεσματικά, 'On the Effects') but more commonly known as the ** (from the Koine Greek meaning 'four books'; ).

The Catholic Church promoted his work, which included the only mathematically sound geocentric model of the Solar System, and unlike most Greek mathematicians, Ptolemy's writings (foremost the Almagest) never ceased to be copied or commented upon, both in late antiquity and in the Middle Ages. However, it is likely that only a few truly mastered the mathematics necessary to understand his works, as evidenced particularly by the many abridged and watered-down introductions to Ptolemy's astronomy that were popular among the Arabs and Byzantines. His work on epicycles is now seen as a very complex theoretical model built in order to explain a false tenet based on faith.

Biography

Ptolemy's date of birth and birthplace are both unknown. The 14th-century astronomer Theodore Meliteniotes wrote that Ptolemy's birthplace was Ptolemais Hermiou, a Greek city in the Thebaid region of Egypt (now El Mansha, Sohag Governorate). This attestation is quite late, however, and there is no evidence to support it.{{efn| "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 () and {{nobr|unsupported." — Toomer & Jones (2018) |last1=Toomer |first1=Gerald |author-link=Gerald Toomer |last2=Jones |first2=Alexander |year=2018 |orig-date=2008 |title=Ptolemy (or Claudius Ptolemaeus) |encyclopedia=Complete Dictionary of Scientific Biography |publisher=Encyclopedia.com |url=http://www.encyclopedia.com/topic/Ptolemy.aspx |access-date=21 January 2013

It is known that Ptolemy lived in or around the city of Alexandria, in the Roman province of Egypt under Roman rule. |title=A History of Greek Mathematics |url=https://archive.org/details/ahistorygreekma00heatgoog |last=Heath |first=Sir Thomas |publisher=Clarendon Press |year=1921|location=Oxford |pages=vii, 273 He had a Latin name, Claudius, which is generally taken to imply he was a Roman citizen. |last=Neugebauer |first=Otto E. |author-link=Otto E. Neugebauer |title=A History of Ancient Mathematical Astronomy |url=https://books.google.com/books?id=vO5FCVIxz2YC&pg=PA834 |year=2004 |publisher=Springer Science & Business Media |isbn=978-3-540-06995-9 |page=834}};

|first1=Gerald |last1=Toomer |author-link=Gerald Toomer |entry=Ptolemy (or Claudius Ptolemaeus) |entry-url=http://www.encyclopedia.com/topic/Ptolemy.aspx |title=Complete Dictionary of Scientific Biography |orig-date=2008 |publisher=Encyclopedia.com | date= 2018 | last2= Jones | first2= Alexander He was familiar with Greek philosophers and used Babylonian observations and Babylonian lunar theory. In half of his extant works, Ptolemy addresses a certain Syrus, a figure of whom almost nothing is known but who likely shared some of Ptolemy's astronomical interests. |last=Tolsa Domènech |first=Cristian |year=2013 |title=Claudius Ptolemy and self-promotion: A study on Ptolemy's intellectual milieu in Roman Alexandria |url=http://diposit.ub.edu/dspace/bitstream/2445/48989/1/CTD_THESIS.pdf |s2cid=191297168 |institution= Universitat de Barcelona |degree= Doctoral

Ptolemy died in Alexandria. | last1 = Pecker | first1 = Jean Claude | author1-link=Jean Claude Pecker | last2 = Dumont | first2 = Simone | editor = Kaufman, Susan | year = 2001 | title=Understanding the Heavens: Thirty centuries of astronomical ideas from ancient thinking to modern cosmology | pages= 309–372 | publisher= Springer | isbn=3-540-63198-4 | doi= 10.1007/978-3-662-04441-4_7 | chapter=From pre-Galilean astronomy to the Hubble Space Telescope and beyond Ptolemy's year of death is not directly recorded by primary sources, and has to be inferred from the scale of his work. Suggested years of death include , , , and .

Naming and nationality

::figure[src="https://upload.wikimedia.org/wikipedia/commons/2/2e/Ptolemy_urania.jpg" caption="Ptolemaic Egypt]], with the same last name."] ::

Ptolemy is often called Ptolemaeus, which is a latinised version of his original ancient Greek personal name Πτολεμαῖος (Latin transcript: Ptolemaîos). It occurs once in Greek mythology and is of Homeric form. |first=Georg |last=Autenrieth |dictionary=A Homeric Dictionary |title=Πτολεμαῖος |url=https://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0073%3Aentry%3D*ptolemai%3Dos |via=perseus.tufts.edu |publisher=Tufts University It was common among the Macedonian upper class at the time of Alexander the Great and several people of this name were among Alexander's army, one of whom made himself pharaoh in 323 BC: Ptolemy I Soter, the first pharaoh of the Ptolemaic Kingdom. Almost all subsequent pharaohs of Egypt, with a few exceptions, were named Ptolemy until Egypt became a Roman province in 30 BC, ending the Macedonian family's rule. |url=https://www.metmuseum.org/toah/hd/ptol/hd_ptol.htm |title=Egypt in the Ptolemaic Period |last=Hill |first=Marsha |year=2006 |website=Metropolitan Museum of Art |access-date=4 April 2020

The name Claudius is a Roman name, belonging to the gens Claudia; the peculiar multipart form of the whole name Claudius Ptolemaeus is a Roman custom, characteristic of Roman citizens. This indicates that Ptolemy would have been a Roman citizen.

The 9th century Persian astronomer Abu Ma'shar al-Balkhi mistakenly presents Ptolemy as a member of Ptolemaic Egypt's royal lineage, stating that the descendants of the Alexandrine general and Pharaoh Ptolemy I Soter were wise "and included Ptolemy the Wise, who composed the book of the Almagest". Abu Ma'shar recorded a belief that a different member of this royal line "composed the book on astrology and attributed it to Ptolemy". Historical confusion on this point can be inferred from Abu Ma'shar's subsequent remark: "It is sometimes said that the very learned man who wrote the book of astrology also wrote the book of the Almagest. The correct answer is not known." |first=Abu |last=Ma'shar |others=editors & translators Yamamoto, K. & Burnett, Ch. |year=2000 |title=De magnis coniunctionibus |place=Leiden |at= 4.1.4 |language=ar, la 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.{{refn|name=Heilen-2010| |first=Stephan |last=Heilen |year=2010 |section=Ptolemy's doctrine of the terms and its reception |title=(Jones, 2010) |page=68 |editor-last=Jones |editor-first=A. |year=2010 |title=Ptolemy in Perspective: Use and criticism of his work from antiquity to the nineteenth century |publisher=Springer Netherlands |isbn=978-90-481-2787-0 |series=Archimedes |url=https://www.springer.com/us/book/9789048127870 It is no longer doubted that the astronomer who wrote the Almagest also wrote the Tetrabiblos as its astrological counterpart. suggesting he may have had origins in southern Egypt. |first=M. |last=Bernal |author-link=Martin Bernal |year=1992 |title=Animadversions on the origins of western science |journal=Isis |volume=83 |issue=4 |pages=596–607 |doi=10.1086/356291 |s2cid=143901637 }} Arabic astronomers, geographers, and physicists referred to his name in Arabic as Baṭlumyus (). |first=Hassan |last=Tahiri |year=2008 |section=The birth of scientific controversies, the dynamics of the Arabic tradition and its impact on the development of science: Ibn al-Haytham's challenge of Ptolemy's Almagest |editor1=Rahman, Shahid |editor2=Street, Tony |editor3=Tahiri, Hassan |title=The Unity of Science in the Arabic Tradition |volume=11 |publisher=Springer Science+Business Media / Springer Netherlands |isbn=978-1-4020-8404-1 |doi=10.1007/978-1-4020-8405-8 |section-url=https://link.springer.com/chapter/10.1007/978-1-4020-8405-8_7 |access-date=9 March 2024 |pages=183–225

Ptolemy wrote in Koine Greek, |last=Tomarchio |first=J. |year=2022 |title=A Sourcebook for Ancient Greek: Grammar, Poetry, and Prose |page=xv |publisher=CUA Press |isbn=9781949822205 |url=https://books.google.com/books?id=_dOUEAAAQBAJ and can be shown to have used Babylonian astronomical data. |first=A. |last=Aaboe |author-link=Asger Aaboe |year=2001 |title=Episodes from the Early History of Astronomy |place=New York, NY |publisher=Springer |pages=62–65 He might have been a Roman citizen, but was ethnically either a Greek |title=Ptolemy |encyclopedia=Britannica Concise Encyclopedia |publisher=Encyclopædia Britannica, Inc. |year=2006 or at least a Hellenized Egyptian.{{efn| "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 {{nobr|exist. — V.J. Katz (1998, p. 184) |first=Victor J. |last=Katz |year=1998 |title=A History of Mathematics: An introduction |page=184 |publisher=Addison Wesley |isbn=0-321-01618-1 George Sarton (1936). "The Unity and Diversity of the Mediterranean World", Osiris 2, p. 406–463 [429]. John Horace Parry (1981). The Age of Reconnaissance, p. 10. University of California Press.

Astronomical writings

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

''Mathēmatikē Syntaxis''

Main article: Almagest

Ptolemy's Almagest (originally , ) is the only surviving comprehensive ancient treatise on astronomy. Although Babylonian astronomers had developed arithmetical techniques for calculating and predicting astronomical phenomena, these were not based on any underlying model of the heavens; early Greek astronomers, on the other hand, provided qualitative geometrical models to "save the appearances" of celestial phenomena without the ability to make any predictions. |last=Schiefsky |first=M. |year=2012 |section=The creation of second-order knowledge in ancient Greek science as a process in the globalization of knowledge |url=https://mprl-series.mpg.de/studies/1/12/index.html |title=The Globalization of Knowledge in History |series=MPRL – Studies |place=Berlin |publisher=Max-Planck-Gesellschaft zur Förderung der Wissenschaften |language=en |isbn=978-3-945561-23-2

The earliest person who attempted to merge these two approaches was Hipparchus, who produced geometric models that not only reflected the arrangement of the planets and stars but could be used to calculate celestial motions. |last=Jones |first=Alexander |year=1991 |title=The adaptation of Babylonian methods in Greek numerical astronomy |journal=Isis |volume=82 |issue=3 |pages=440–453 |doi=10.1086/355836 |jstor=233225 |s2cid=92988054 |issn=0021-1753 |url=http://archive.nyu.edu/handle/2451/49537 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. |url=http://www.dioi.org/cot.htm#mjpg |title=Dennis Rawlins |publisher=The International Journal of Scientific History |access-date=7 October 2009

Ptolemy presented his astronomical models alongside convenient tables, which could be used to compute the future or past position of the planets. |first=Bernard R. |last=Goldstein |year=1997 |title=Saving the phenomena: The background to Ptolemy's planetary theory |journal=Journal for the History of Astronomy |volume=28 |issue=1 |pages=1–12 |doi=10.1177/002182869702800101 |bibcode=1997JHA....28....1G |s2cid=118875902 The Almagest also contains a star catalogue, which is a version of a catalogue created by Hipparchus. Its list of forty-eight constellations is ancestral to the modern system of constellations but, unlike the modern system, they did not cover the whole sky (only what could be seen with the naked eye in the northern hemisphere). |last=Swerdlow |first=N.M. |year=1992 |title=The enigma of Ptolemy's catalogue of stars |url=https://doi.org/10.1177/002182869202300303 |journal=Journal for the History of Astronomy |volume=23 |issue=3 |pages=173–183 |doi=10.1177/002182869202300303 |bibcode=1992JHA....23..173S |s2cid=116612700 |url-access=subscription For over a thousand years, the Almagest was the authoritative text on astronomy across Europe, the Middle East, and North Africa. S. C. McCluskey, 1998, Astronomies and Cultures in Early Medieval Europe, Cambridge: Cambridge Univ. Pr. pp. 20–21.

The Almagest was preserved, like many extant Greek scientific works, in Arabic manuscripts; the modern title is thought to be an Arabic corruption of the Greek name ('The greatest treatise'), as the work was presumably known during late antiquity. |last1=Krisciunas |first1=K. |last2=Bistué |first2=M. B. |year=2019 |title=Notes on the transmission of Ptolemy's Almagest and some geometrical mechanisms to the era of Copernicus |url=https://ri.conicet.gov.ar/handle/11336/136161 |journal=Repositorio Institucional CONICET Digital |volume=22 |issue=3 |page=492 |bibcode=2019JAHH...22..492K |issn=1440-2807 Because of its reputation, it was widely sought and translated twice into Latin in the 12th century, once in Sicily and again in Spain. Ptolemy's planetary models, like those of the majority of his predecessors, were geocentric and almost universally accepted until the reappearance of heliocentric models during the Scientific Revolution.

Modern reassessment

Under the scrutiny of modern scholarship, and the cross-checking of observations contained in the Almagest against figures produced through backwards extrapolation, various patterns of errors have emerged within the work. A prominent miscalculation is Ptolemy's use of measurements that he claimed were taken at noon, but which systematically produce readings now shown to be off by half an hour, as if the observations were taken at 12:30 pm.

The overall quality of Ptolemy's observations has been challenged by several modern scientists, but prominently by Robert R. Newton in his 1977 book The Crime of Claudius Ptolemy, which asserted that Ptolemy fabricated many of his observations to fit his theories. Newton accused Ptolemy of systematically inventing data or doctoring the data of earlier astronomers, and labelled him "the most successful fraud in the history of science". One striking error noted by Newton was an autumn equinox said to have been observed by Ptolemy and "measured with the greatest care" at 2pm on 25 September 132, when the equinox should have been observed around 9:55am the day prior. In attempting to disprove Newton, Herbert Lewis also found himself agreeing that "Ptolemy was an outrageous fraud," and that "all those result capable of statistical analysis point beyond question towards fraud and against accidental error".

The charges laid by Newton and others have been the subject of wide discussions and received significant push back from other scholars against the findings. Owen Gingerich, while agreeing that the Almagest contains "some remarkably fishy numbers", including in the matter of the 30-hour displaced equinox, which he noted aligned perfectly with predictions made by Hipparchus 278 years earlier, rejected the qualification of fraud. Objections were also raised by Bernard Goldstein, who questioned Newton's findings and suggested that he had misunderstood the secondary literature, while noting that issues with the accuracy of Ptolemy's observations had long been known. Other authors have pointed out that instrument warping or atmospheric refraction may also explain some of Ptolemy's observations at a wrong time. |last1=Bruin |first1=Franz |last2=Bruin |first2=Margaret |title=The equator ring, equinoxes, and atmospheric refraction |journal=Centaurus |year=1976 |volume=20 |issue=2 |page=89 |doi=10.1111/j.1600-0498.1976.tb00923.x |bibcode=1976Cent...20...89B |last1=Britton |first1=John Phillips |title=On the quality of solar and lunar observations and parameters in Ptolemy's Almagest |year=1967 |publisher=Yale University |degree=Ph.D.

In 2022 the first Greek fragments of Hipparchus' lost star catalog were discovered in a palimpsest and they debunked accusations made by the French astronomer Jean Baptiste Joseph Delambre in the early 1800s which were repeated by R. R. Newton. Specifically, it proved Hipparchus was not the sole source of Ptolemy's catalog, as they both had claimed, and proved that Ptolemy did not simply copy Hipparchus' measurements and adjust them to account for precession of the equinoxes, as they had claimed. Scientists analyzing the charts concluded:

::quote It also confirms that Ptolemy’s Star Catalogue was not based solely on data from Hipparchus’ Catalogue.

... These observations are consistent with the view that Ptolemy composed his star catalogue by combining various sources, including Hipparchus’ catalogue, his own observations and, possibly, those of other authors. {{cite journal |last1=Gysembergh |first1=Victor |last2=Williams |first2=Peter J. |last3=Zingg |first3=Emanuel |date=November 2022 |title=New evidence for Hipparchus' star catalogue revealed by multispectral imaging |journal=Journal for the History of Astronomy |volume=53 |issue=4 |pages=383–393 |doi=10.1177/00218286221128289 |bibcode=2022JHA....53..383G |issn=0021-8286 |url=https://journals.sagepub.com/doi/10.1177/00218286221128289 }}

''Handy Tables''

Main article: Handy Tables

The Handy Tables () are a set of astronomical tables, together with canons for their use. To facilitate astronomical calculations, Ptolemy tabulated all the data needed to compute the positions of the Sun, Moon and planets, the rising and setting of the stars, and eclipses of the Sun and Moon, making it a useful tool for astronomers and astrologers. The tables themselves are known through Theon of Alexandria'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. Juste, D. (2021). Ptolemy, Handy Tables. Ptolemaeus Arabus et Latinus, Works. https://ptolemaeus.badw.de/work/153

''Planetary Hypotheses''

::figure[src="https://upload.wikimedia.org/wikipedia/commons/7/7b/Bartolomeu_Velho_1568.jpg" caption="A depiction of the non-Ptolemaic Universe with no epicycles, possibly from 500 years before Ptolemy, as described in the ''Planetary Hypotheses'' by [[Bartolomeu Velho]] (1568)."] ::

The Planetary Hypotheses (, ) is a cosmological 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. |last=Murschel |first=A. |year=1995 |title=The structure and function of Ptolemy's physical hypotheses of planetary motion |journal=Journal for the History of Astronomy |volume=26 |issue=1 |pages=33–61 |doi=10.1177/002182869502600102 |bibcode=1995JHA....26...33M |s2cid=116006562 Ptolemy goes beyond the mathematical models of the Almagest to present a physical realization of the universe as a set of nested spheres, |first=Dennis |last=Duke |title=Ptolemy's cosmology |website= scs.fsu.edu/~dduke |type=academic pers. website |publisher=Florida State University |url=http://people.scs.fsu.edu/~dduke/ptolemy.html |url-status=dead |archive-url=https://web.archive.org/web/20091107202956/http://people.sc.fsu.edu/~dduke/ptolemy.html |archive-date=2009-11-07 in which he used the epicycles of his planetary model to compute the dimensions of the universe. He estimated the Sun was at an average distance of (now known to actually be while the radius of the sphere of the fixed stars was the radius of the Earth. |first=Bernard R. |last=Goldstein |year=1967 |title=The Arabic version of Ptolemy's planetary hypotheses |journal=Transactions of the American Philosophical Society |volume=57 |number=4 |pages=9–12 |doi=10.2307/1006040 |jstor=1006040

Other astronomical works

Analemma The Analemma is a short treatise where Ptolemy provides a method for specifying the location of the Sun in three pairs of locally oriented coordinate arcs as a function of the declination of the Sun, the terrestrial latitude, and the hour. The key to the approach is to represent the solid configuration in a plane diagram that Ptolemy calls the analemma.

Phaseis In another work, the Phaseis (Risings of the Fixed Stars), Ptolemy gave a parapegma, a star calendar or almanac, based on the appearances and disappearances of stars over the course of the solar year. |last1=Evans |first1=James |url=https://books.google.com/books?id=if9ZDwAAQBAJ&pg=PA286 |title=Geminos's Introduction to the Phenomena: A translation and study of a Hellenistic survey of astronomy |last2=Berggren |first2=J. Lennart |date=5 June 2018 |publisher=Princeton University Press |isbn=978-0-691-18715-0

Planisphaerium The Planisphaerium (, ) contains 16 propositions dealing with the projection of the celestial circles onto a plane. The text is lost in Greek (except for a fragment) and survives in Arabic and Latin only. |last=Juste |first=D. |year=2021 |title=Ptolemy, Planispherium. Ptolemaeus Arabus et Latinus, Works |url=https://ptolemaeus.badw.de/work/152?mark=%28%3Fis%29%28Planispherium%29

Ptolemy also erected an inscription in a temple at Canopus, 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. |last=Jones |first=A. |year=2005 |title=Ptolemy's Canobic Inscription and Heliodorus' observation reports |journal=SciAMVS |volume=6 |pages=53–97 |url=https://www.sciamvs.org/files/SCIAMVS_06_053-097_Jones.pdf

Ptolemy is also though to have produced his Table of Noteworthy Cities as an aid to his astronomical tables.

Other writings

''Geography''

Main article: Geography (Ptolemy)

::figure[src="https://upload.wikimedia.org/wikipedia/commons/f/f0/Claudius_Ptolemy-_The_World.jpg" caption="A printed map from the 15th century depicting Ptolemy's description of the ''[[Ecumene]]'' by Johannes Schnitzer (1482)."] ::

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. |last=Mittenhuber |first=F. |year=2010 |section=The tradition of texts and maps in Ptolemy's Geography |title=Ptolemy in Perspective: Use and criticism of his work from antiquity to the nineteenth century |series=Archimedes |volume=23 |pages=95–119 |place=Dordrecht, NL |publisher=Springer Netherlands |doi=10.1007/978-90-481-2788-7_4 |isbn=978-90-481-2788-7 About of these places and geographic features have assigned coordinates so that they can be placed in a grid that spanned the globe. Latitude was measured from the equator, as it is today, but Ptolemy preferred to express it as climata, the length of the longest day rather than degrees of arc: The length of the midsummer day increases from 12h to 24h as one goes from the equator to the polar circle. |last=Shcheglov |first=D.A. |date=2002–2007 |url=https://nw.academia.edu/DmitryShcheglov/Papers/142876/Hipparchus_Table_of_Climata_and_Ptolemys_Geography |title=Hipparchus' table of climata and Ptolemy's Geography |series=Orbis Terrarum |volume=9 (2003–2007) |pages=177–180 One of the places Ptolemy noted specific coordinates for was the now-lost stone tower which marked the midpoint on the ancient Silk Road, and which scholars have been trying to locate ever since. |last=Dean |first=Riaz |year=2022 |title=The Stone Tower: Ptolemy, the silk road, and a 2,000 year-old riddle |publisher=Penguin Viking |isbn=978-0670093625 |location=Delhi, IN |pages=xi, 135, 148, 160

In the third part of the Geography, Ptolemy gives instructions on how to create maps both of the whole inhabited world (oikoumenē) and of the Roman provinces, including the necessary topographic lists, and captions for the maps. His oikoumenē spanned 180 degrees of longitude from the Blessed Islands in the Atlantic Ocean to the middle of China, and about 80 degrees of latitude from Shetland to anti-Meroe (east coast of Africa); Ptolemy was well aware that he knew about only a quarter of the globe, and an erroneous extension of China southward suggests his sources did not reach all the way to the Pacific Ocean. ::figure[src="https://upload.wikimedia.org/wikipedia/commons/8/83/A_modern_reconstruction_of_Claudius_Ptolemy's_map_of_Europe_and_North_Africa_by_Kotsanas_Museum_of_Ancient_Greek_Technology.jpg" caption="Kotsanas Museum of Ancient Greek Technology]], Athens, Greece."] ::

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 (after the text was rediscovered by Maximus Planudes), there are some scholars who think that such maps go back to Ptolemy himself.

''Tetrabiblos''

Main article: Tetrabiblos

::figure[src="https://upload.wikimedia.org/wikipedia/commons/f/f3/Ptolemaeus_-_Quadripartitum,1622-_4658973.tif" caption="A copy of the ''Quadripartitum'' (1622)"] ::

Ptolemy wrote an astrological treatise, in four parts, known by the Greek term Tetrabiblos () or by its Latin equivalent Quadripartitum.{{refn| |first=H. Darrel |last=Rutkin |year=2010 |section=The use and abuse of Ptolemy's Tetrabiblos in Renaissance and early modern Europe |page=135 |title=Jones (2010) 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".{{refn|name=Robbins-1940-intro| |last=Robbins |first=Frank E. |section=Introduction |year=1940 |editor=Robbins, F.E. |title=Ptolemy Tetrabiblos It was first translated from Arabic into Latin by Plato of Tivoli (Tiburtinus) in 1138, while he was in Spain.

Much of the content of the Tetrabiblos was collected from earlier sources; Ptolemy's achievement was to order his material in a systematic way, showing how the subject could, in his view, be rationalized. It is, indeed, presented as the second part of the study of astronomy of which the Almagest was the first, concerned with the influences of the celestial bodies in the sublunary sphere. Thus explanations of a sort are provided for the astrological effects of the planets, based upon their combined effects of heating, cooling, moistening, and drying. |last=Riley |first=M. |date=1988 |title=Science and tradition in the Tetrabiblos |journal=Proceedings of the American Philosophical Society |volume=132 |issue=1 |pages=67–84 |jstor=3143825 |issn=0003-049X Ptolemy dismisses other astrological practices, such as considering the numerological significance of names, that he believed to be without sound basis, and leaves out popular topics, such as electional astrology (interpreting astrological charts to determine courses of action) and medical astrology, for similar reasons. |last=Riley |first=M. |date=1987 |title=Theoretical and practical astrology: Ptolemy and his colleagues |journal=Transactions of the American Philological Association |volume=117 |pages=235–256 |doi=10.2307/283969 |jstor=283969

The great respect in which later astrologers held the Tetrabiblos derived from its nature as an exposition of theory, rather than as a manual.

A collection of one hundred aphorisms about astrology called the Centiloquium, ascribed to Ptolemy, was widely reproduced and commented on by Arabic, Latin, and Hebrew scholars, and often bound together in medieval manuscripts after the Tetrabiblos as a kind of summation. It is now believed to be a much later pseudepigraphical composition. The identity and date of the actual author of the work, referred to now as Pseudo-Ptolemy, remains the subject of conjecture. |last=Boudet |first=J.-P. |year=2014 |section=Astrology between rational science and divine inspiration: The pseudo-Ptolemy's centiloquium |editor1-last=Rapisarda |editor1-first=S. |editor2-last=Niblaeus |editor2-first=E. |title=Dialogues among Books in Medieval Western Magic and Divination |series=Micrologus' library |volume=65 |pages=47–73 |publisher=Sismel edizioni del Galluzzo |isbn=9788884505811 |url=https://halshs.archives-ouvertes.fr/halshs-01628233 |access-date=19 August 2021

''Harmonics''

::figure[src="https://upload.wikimedia.org/wikipedia/commons/7/7a/Epogdoon.jpg" caption="A diagram showing [[Pythagorean tuning]]."] ::

Ptolemy introduces the harmonic canon (Greek name) or monochord (Latin name), which is an experimental musical apparatus that he used to measure relative pitches, and used to describe to his readers how to demonstrate the relations discussed in the following chapters for themselves. After the early exposition on to build and use monochord to test proposed tuning systems, Ptolemy proceeds to discuss Pythagorean tuning (and how to demonstrate that their idealized musical scale fails in practice). The Pythagoreans believed that the mathematics of music should be based on only the one specific ratio of 3:2, the perfect fifth, and believed that tunings mathematically exact to their system would prove to be melodious, if only the extremely large numbers involved could be calculated (by hand). To the contrary, Ptolemy believed that musical scales and tunings should in general involve multiple different ratios arranged to fit together evenly into smaller tetrachords (combinations of four pitch ratios which together make a perfect fourth) and octaves. |last=Barker |first=A. |year=1994 |title=Greek musicologists in the Roman Empire |journal=Apeiron |volume=27 |issue=4 |pages=53–74 |doi=10.1515/APEIRON.1994.27.4.53 |s2cid=170415282 |url=https://www.degruyter.com/document/doi/10.1515/APEIRON.1994.27.4.53/html |url-access=subscription |last=West |first=Martin Litchfield |author-link=Martin Litchfield West |year=1992 |title=Ancient Greek Music |place=Oxford, UK |publisher=Oxford University Press |isbn=0-19-814975-1 Ptolemy reviewed standard (and ancient, disused) musical tuning practice of his day, which he then compared to his own subdivisions of the tetrachord and the octave, which he derived experimentally using a monochord / harmonic canon. The volume ends with a more speculative exposition of the relationships between harmony, the soul (psyche), and the planets (harmony of the spheres). |last=Feke |first=J. |year=2012 |title=Mathematizing the soul: The development of Ptolemy's psychological theory from On the Kritêrion and Hêgemonikon to the Harmonics |journal=Studies in History and Philosophy of Science Part A |volume=43 |issue=4 |pages=585–594 |doi=10.1016/j.shpsa.2012.06.006 |bibcode=2012SHPSA..43..585F |url=https://www.sciencedirect.com/science/article/abs/pii/S0039368112000428 |url-access=subscription

Although Ptolemy's Harmonics never had the influence of his Almagest or Geography, it is nonetheless a well-structured treatise and contains more methodological reflections than any other of his writings. In particular, it is a nascent form of what in the following millennium developed into the scientific method, with specific descriptions of the experimental apparatus that he built and used to test musical conjectures, and the empirical musical relations he identified by testing pitches against each other: He was able to accurately measure relative pitches based on the ratios of vibrating lengths two separate sides of the same single string, hence which were assured to be under equal tension, eliminating one source of error. He analyzed the empirically determined ratios of "pleasant" pairs of pitches, and then synthesised all of them into a coherent mathematical description, which persists to the present as just intonation – the standard for comparison of consonance in the many other, less-than exact but more facile compromise tuning systems. |last=Barker |first=A. |year=2010 |title=Mathematical beauty made audible: Musical aesthetics in Ptolemy's Harmonics |journal=Classical Philology |volume=105 |issue=4 |pages=403–420 |doi=10.1086/657028 |s2cid=161714215 |last=Tolsa |first=C. |year=2015 |title=Philosophical presentation in Ptolemy's Harmonics: The Timaeus as a model for organization |journal=Greek, Roman, and Byzantine Studies |volume=55 |issue=3 |pages=688–705 |issn=2159-3159 |url=https://grbs.library.duke.edu/article/view/15395

Optics

Main article: Optics (Ptolemy)

The Optica (Koine Greek: 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, refraction, and colour. 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. |last=Smith |first=A. Mark |year=1996 |title=Ptolemy's Theory of Visual Perception: An English translation of the Optics |publisher=The American Philosophical Society |isbn=0-87169-862-5 |url=https://books.google.com/books?id=mhLVHR5QAQkC&pg=PP1 |access-date=27 June 2009 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. |first1=H.E. |last1=Ross |first2=G.M. |last2=Ross |year=1976 |title=Did Ptolemy understand the moon illusion? |journal=Perception |volume=5 |issue=4 |pages=377–395 |doi=10.1068/p050377 |pmid=794813 |s2cid=23948158 |first=A.I. |last=Sabra |year=1987 |section=Psychology versus mathematics: Ptolemy and Alhazen on the moon illusion |editor1=Grant, E. |editor2=Murdoch, J.E. |title=Mathematics and its Application to Science and Natural Philosophy in the Middle Ages |place=Cambridge, UK |publisher=Cambridge University Press |pages=217–247

The work is divided into three major sections. The first section (Book II) deals with direct vision from first principles and ends with a discussion of binocular vision. The second section (Books III-IV) treats reflection in plane, convex, concave, and compound mirrors. |last=Smith |first=A. M. |year=1982 |title=Ptolemy's search for a law of refraction: A case-study in the classical methodology of "saving the appearances" and its limitations |journal=Archive for History of Exact Sciences |volume=26 |issue=3 |pages=221–240 |doi=10.1007/BF00348501 |jstor=41133649 |s2cid=117259123 |issn=0003-9519 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. |first=C.B. |last=Boyer |author-link=Carl Benjamin Boyer |year=1959 |title=The Rainbow: From myth to mathematics However, according to Mark Smith, Ptolemy's table was based in part on real experiments. |last=Smith |first=Mark |year=2015 |title=From Sight to Light: The passage from ancient to modern optics |publisher=The University of Chicago Press |pages=116–118 |bibcode=2014fslp.book.....S

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. |last=Riley |first=M. |year=1995 |title=Ptolemy's use of his predecessors' data |journal=Transactions of the American Philological Association |volume=125 |jstor=i212542 |language=en 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. |first1=H.W. |last1=Ross |first2=C. |last2=Plug |year=1998 |section=The history of size constancy and size illusions |editor1-first=V. |editor1-last=Walsh |editor2-first=J. |editor2-last=Kulikowski |title=Perceptual Constancy: Why things look as they do |place=Cambridge, UK |publisher=Cambridge University Press |pages=499–528

Philosophy

Although mainly known for his contributions to astronomy and other scientific subjects, Ptolemy also engaged in epistemological and psychological discussions across his corpus. |last=Feke |first=J. |year=2018 |title=Ptolemy's Philosophy: Mathematics as a way of life |publisher=Princeton University Press |isbn=978-0-691-17958-2 |url=https://press.princeton.edu/books/hardcover/9780691179582/ptolemys-philosophy He wrote a short essay entitled On the Criterion and Hegemonikon (), which may have been one of his earliest works. Ptolemy deals specifically with how humans obtain scientific knowledge (i.e., the "criterion" of truth), as well as with the nature and structure of the human psyche or soul, particularly its ruling faculty (i.e., the hegemonikon). Ptolemy argues that, to arrive at the truth, one should use both reason and sense perception in ways that complement each other. On the Criterion is also noteworthy for being the only one of Ptolemy's works that is devoid of mathematics. |last=Schiefsky |first=M.J. |year=2014 |section=The epistemology of Ptolemy's On the Criterion |editor=Lee, M.-K. |title=Strategies of Argument: Essays in ancient ethics, epistemology, and logic |publisher=Oxford University Press |pages=301–331

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 Platonic and Aristotelian traditions, where theology or metaphysics occupied the highest honour. Despite being a minority position among ancient philosophers, Ptolemy's views were shared by other mathematicians such as Hero of Alexandria. |last=Feke |first=J. |year=2014 |title=Meta-mathematical rhetoric: Hero and Ptolemy against the philosophers |journal=Historia Mathematica |volume=41 |issue=3 |pages=261–276 |doi=10.1016/j.hm.2014.02.002 |doi-access=free

Named after Ptolemy

There are several characters and items named after Ptolemy, including:

The crater Ptolemaeus on the Moon
The 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 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

Notes

Footnotes

Citations

Bibliography

Works of Ptolemy

{{cite book |first=Claudius |last=Ptolemaios |author-link=Ptolemy |year=1519 |title=Quadripartitum |publisher=Ottaviano Scoto (1.) eredi & C. |location=Venezia |language=la |url=https://gutenberg.beic.it/webclient/DeliveryManager?pid=13189467
{{cite book |first=Claudius |last=Ptolemaios |author-link=Ptolemy |year=1541 |title=[Opere] |language=la |publisher=Heinrich Petri |location=Basel |url=https://gutenberg.beic.it/webclient/DeliveryManager?pid=4657866
{{cite book |first=Claudius |last=Ptolemaios |author-link=Ptolemy |year=1559 |title=In Claudii Ptolemaei Quadripartitum |language=la |volume= |publisher=Heinrich Petri |location=Basel, CH |url=https://gutenberg.beic.it/webclient/DeliveryManager?pid=12853586
{{cite book |first=Claudius |last=Ptolemaios |author-link=Ptolemy |title=Quadripartitum |language=la |year=1622 |publisher=Johann Bringer |location=Frankfurt am Main |url=https://gutenberg.beic.it/webclient/DeliveryManager?pid=4658973
{{cite book |first=Claudius |last=Ptolemaios |author-link=Ptolemy |year=1658 |title=Quadripartitum |language=la |publisher=Paolo Frambotto |location=Padova |url=https://gutenberg.beic.it/webclient/DeliveryManager?pid=13235070
{{cite book |first=Claudius |last=Ptolemaios |author-link=Ptolemy |year=1663 |title=De iudicandi facultate et animi principatu |publisher=Sebastian Cramoisy (1.) & Sebastian Mabre-Cramoisy |location=Paris |language=la |url=https://gutenberg.beic.it/webclient/DeliveryManager?pid=4659628
{{cite book |first=Claudius |last=Ptolemaios |author-link=Ptolemy |year=1663 |title=De iudicandi facultate et animi principatu |publisher=Adriaen Vlacq |location=Den Haag |language=la |url=https://gutenberg.beic.it/webclient/DeliveryManager?pid=4660219
{{cite book |first=Claudius |last=Ptolemaios |author-link=Ptolemy |year=1682 |title=Harmonicorum libri |publisher=Theatrum Sheldonianum |location=Oxford, UK |language=la |url=https://gutenberg.beic.it/webclient/DeliveryManager?pid=4657131
{{cite book |first=Claudius |last=Ptolemaios |author-link=Ptolemy |title=Planisphaerium |language=la |url=https://www.sciamvs.org/files/SCIAMVS_08_037-139_Sidoli_Berggren.pdf |via=sciamvs.org

References

{{cite journal |last = Bagrow |first=L. |date = 1 January 1945 |title = The origin of Ptolemy's Geographia |journal = Geografiska Annaler |volume = 27 |pages=318–387 |jstor = 520071 |issn = 1651-3215 |doi = 10.2307/520071
{{cite book |first=Claudius |last=Ptolemaios |author-link=Ptolemy |editor1=Berggren, J. Lennart |editor2=Jones, Alexander |year=2000 |title=Ptolemy's Geography: An annotated translation of the theoretical chapters |place=Princeton, NJ / Oxford, UK |publisher=Princeton University Press |isbn=0-691-01042-0
{{cite journal |last=Gingerich |first=O. |author-link=Owen Gingerich |year=1980 |title=Was Ptolemy a fraud? |journal=Quarterly Journal of the Royal Astronomical Society |volume=21 |page=253 |bibcode=1980QJRAS..21..253G |url=https://adsabs.harvard.edu/full/1980QJRAS..21..253G |via=The SAO/NASA Astrophysics Data System
{{cite journal |first=Bernard R. |last=Goldstein |author-link=Bernard R. Goldstein |date=24 February 1978 |title=Casting doubt on Ptolemy: The Crime of Claudius Ptolemy. Robert R. Newton. |journal=Science |volume=199 |issue=4331 |pages=872–873 |doi=10.1126/science.199.4331.872.a |pmid=17757580 |s2cid=239876775 |url=https://www.science.org/doi/10.1126/science.199.4331.872.a |url-access=subscription
{{cite book |first=Thomas, Sir |last=Heath |year=1921 |title=A History of Greek Mathematics |place=Oxford, UK |publisher=Clarendon Press
{{cite book |first=Claudius |last=Ptolemaios |author-link=Ptolemy |editor-last=Hübner |editor-first=Wolfgang |year=1998 |title=Claudius Ptolemaeus, Opera quae exstant omnia |language=la |trans-title=The complete existing works of Claudius Ptolemy |volume=III |at=Fascia 1: Αποτελεσματικα (Tetrabiblos) |publisher=De Gruyter |isbn=978-3-598-71746-8 |series=Bibliotheca scriptorum Graecorum et Romanorum Teubneriana
{{cite book |first=Claudius |last=Ptolemaios |author-link=Ptolemy |editor-last=Lejeune |editor-first=A. |year=1989 |title=L'Optique de Claude Ptolémée dans la version latine d'après l'arabe de l'émir Eugène de Sicile |language=fr, la |trans-title=The Optics of Claudius Ptolemy in the Latin version based on the Arabic of Emir Eugene of Sicily |series=Collection de travaux de l'Académie International d'Histoire des Sciences |volume=31 |place=Leiden |publisher=E.J.Brill
{{cite journal |last=Lewis |first=H.A.G. |year=1979 |title=Review of The Crime of Claudius Ptolemy, by R.R. Newton |journal=Imago Mundi |volume=31 |pages=105–107 |doi=10.1080/03085697908592494 |jstor=1150735
{{cite book |last=Neugebauer |first=Otto |year=1975 |title=A History of Ancient Mathematical Astronomy |volume=I-III |publisher=Springer Verlag |location=Berlin, DE / New York, NY
{{cite book |editor=Nobbe, C.F.A. |year=1843 |title=Claudii Ptolemaei Geographia |language=la |trans-title=Claudius Ptolemy's Geography |place=Leipzig |publisher=Carolus Tauchnitus
{{cite journal |first1=R.H.J. |last1=Peerlings |first2=F. |last2=Laurentius |first3=J. |last3=van den Bovenkamp |title=The watermarks in the Rome editions of Ptolemy's Cosmography and more |journal=Quaerendo |volume=47 |pages=307–327 |year=2017 |issue=3–4 |doi=10.1163/15700690-12341392
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.
{{cite book |first=Claudius |last=Ptolemaios |author-link=Ptolemy |year=1980 |orig-year=1930 |title=Die Harmonielehre des Klaudios Ptolemaios |editor=Düring, Ingemar |series=Göteborgs högskolas årsskrift |volume=36 |place=Göteborg / New York, NY |publisher=Elanders boktr. aktiebolag. (1930) / Garland Publishing (1980) |edition=reprint
{{cite book |first1=Claudius |last1=Ptolemaios |author1-link=Ptolemy |last2=Solomon |first2=Jon |year=2000 |title=Harmonics |translator=Solomon, Jon |series=Mnemosyne, Bibliotheca Classica Batava, Supplementum |volume=203 |place=Leiden / Boston, MA |publisher=Brill Publishers |isbn=90-04-11591-9 |id=0169–8958
{{cite journal |last=Smith |first=A.M. |year=1996 |title=Ptolemy's Theory of Visual Perception: An English translation of the Optics with introduction and commentary |type=book review |journal=Transactions of the American Philosophical Society |volume=86, Part 2 |place=Philadelphia, PA |publisher=The American Philosophical Society
{{cite book |first=Claudius |last=Ptolemaios |author-link=Ptolemy |editor-last=Stevenson |editor-first=Edward Luther |translator=E.L. Stevenson |year=1991 |orig-year=1932 |title=Claudius Ptolemy: The Geography |place=New York, NY |publisher=New York Public Library, 1932 / Dover, 1991 |edition=Reprint
{{cite book |first=Claudius |last=Ptolemaios |author-link=Ptolemy |editor1-first=Alfred |editor1-last=Stückelberger |editor2-first=Gerd |editor2-last=Graßhoff |year=2006 |title=Ptolemaios, Handbuch der Geographie, Griechisch-Deutsch |language=de |trans-title=Ptolemy, Geography Handbook, Greek-German |place=Basel, CH |publisher=Schwabe Verlag |isbn=978-3-7965-2148-5
{{cite encyclopedia | first = Gerald J. | last = Toomer | author-link = Gerald J. Toomer | year = 1970 | title = Ptolemy (Claudius Ptolemæus) | editor-last = Gillispie | editor-first = Charles | encyclopedia = Dictionary of Scientific Biography | volume = 11 | pages = 186–206 | location = New York, NY | publisher = Scribner & American Council of Learned Societies | isbn = 978-0-684-10114-9 | url = http://www.u.arizona.edu/~aversa/scholastic/Dictionary%20of%20Scientific%20Biography/Ptolemy%20(Toomer).pdf | access-date = 25 April 2011 | url-status = dead | archive-url = https://web.archive.org/web/20120314024102/http://www.u.arizona.edu/~aversa/scholastic/Dictionary%20of%20Scientific%20Biography/Ptolemy%20(Toomer).pdf | archive-date = 14 March 2012
Ptolemy's Almagest, Translated and annotated by G. J. Toomer, 1998. Princeton University Press
{{cite journal |first=Nicholas |last=Wade |author-link=Nicholas Wade |year=1977 |title=Scandal in the Heavens: Renowned Astronomer Accused of Fraud |journal=Science |volume=198 |issue=4318 |pages=707–709 |doi=10.1126/science.198.4318.707 |bibcode=1977Sci...198..707W |url=https://www.science.org/doi/10.1126/science.198.4318.707 |url-access=subscription

References

{{britannica. 482098. Ptolemy
Richter, Lukas. (2001). "Ptolemy". [[Oxford University Press]].
{{harvtxt. Neugebauer. 1975
(2025-01-31). "Ptolemy {{!}} Accomplishments, Biography, & Facts".
Holme, Audun. (2010-09-23). "Geometry: Our Cultural Heritage". Springer Science & Business Media.
Toomer, J.. (1998-11-08). "Ptolemy's Almagest". Princeton University Press.
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]] or the emperor [[Nero]].{{harvtxt. Toomer. 1970
{{rp. x In later [[Arabic]] sources, he was often known as "the [[Upper Egypt]]ian",J. F. Weidler (1741). ''Historia astronomiae'', p. 177. Wittenberg: Gottlieb.
Jones, A.. (2020). "Ptolemy's ''Science of the Stars in the Middle Ages''".
Charles Homer Haskins, ''Studies in the History of Mediaeval Science'', New York: Frederick Ungar Publishing, 1967, reprint of the Cambridge, Mass., 1927 edition
(2020). "Ptolemy's Science of the Stars in the Middle Ages".
Defaux, Olivier. (2017). "The Iberian peninsula in Ptolemy's geography: origins of the coordinates and textual history". PRO BUSINESS digital printing Deutschland GmbH.
north celestial pole]]The north celestial pole is the point in the sky lying at the common centre of the circles which the stars appear to people in the northern hemisphere to trace out during the course of a [[sidereal time. sidereal day]].

::callout[type=info title="Wikipedia Source"] This article was imported from Wikipedia and is available under the Creative Commons Attribution-ShareAlike 4.0 License. Content has been adapted to SurfDoc format. Original contributors can be found on the article history page. ::