Editing Ptolemy (section)

==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.<ref name=Jones-2020>{{cite book |last=Jones |first=A. |year=2020 |section=The ancient Ptolemy |title=Ptolemy's ''Science of the Stars in the Middle Ages'' |editor1=Juste, D. |editor2=van Dalen, B. |editor3=Hasse, D.N. |editor4=Burnett, C. |editor5=Turnhout |editor6=Brepols |series=Ptolemaeus Arabus et Latinus Studies |volume=1 |pages=13–34 |section-url=https://archive.nyu.edu/bitstream/2451/59914/3/Jones%202020%20The%20ancient%20Ptolemy.pdf |via=[[New York University]] / archive.nyu.edu}}</ref>

=== ''Mathēmatikē Syntaxis'' ===
{{main|Almagest}}[[File:Bodleian Library Pococke369 roll332 frame38.jpg|thumb|upright=1.1|Pages from the ''[[Almagest]]'' in Arabic translation showing astronomical tables.]]

Ptolemy's ''[[Almagest]]'' (originally {{Langx|grc|Μαθηματικὴ Σύνταξις|translit=Mathēmatikē Syntaxis}}, {{Lit|Mathematical Systematic Treatise}}) 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.<ref>
{{cite book
 |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
}}
</ref>

The earliest person who attempted to merge these two approaches was [[Hipparchus]], who produced [[geometric model]]s that not only reflected the arrangement of the planets and stars but could be used to calculate celestial motions.<ref name=Jones-1991>
{{cite journal
 |last=Jones |first=Alexander
 |year=1991
 |title=The adaptation of Babylonian methods in Greek numerical astronomy
 |journal=[[Isis (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
 }}
</ref>
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&nbsp;years; however, many astronomers have for centuries suspected that some of his models' parameters were adopted independently of observations.<ref>
{{cite web
 |url=http://www.dioi.org/cot.htm#mjpg
 |title=Dennis Rawlins
 |publisher=The International Journal of Scientific History
 |access-date=7 October 2009
}}
</ref>

Ptolemy presented his astronomical models alongside convenient tables, which could be used to compute the future or past position of the planets.<ref>
{{cite journal
 |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
}}
</ref>
The ''Almagest'' also contains a [[star catalogue]], which is a version of a catalogue created by Hipparchus. Its list of forty-eight [[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 in the northern hemisphere).<ref>
{{cite journal
 |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
}}
</ref>
For over a thousand years, the ''Almagest'' was the authoritative text on astronomy across Europe, the Middle East, and North Africa.<ref>
 S. C. McCluskey,
 1998,
 ''Astronomies and Cultures in Early Medieval Europe'',
 Cambridge: Cambridge Univ. Pr.
 pp. 20–21.
</ref>

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 {{tlit|grc|Hē Megistē Syntaxis}} ('The greatest treatise'), as the work was presumably known during [[late antiquity]].<ref>
{{cite journal
 |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
}}
</ref>
Because of its reputation, it was widely sought and translated twice into Latin [[Latin translations of the 12th century|in the 12th century]], once in Sicily and again in Spain.<ref>Charles Homer Haskins, ''Studies in the History of Mediaeval Science'', New York: Frederick Ungar Publishing, 1967, reprint of the Cambridge, Mass., 1927 edition</ref> 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.{{sfn|Wade|1977}}{{sfn|Lewis|1979}} 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&nbsp;pm.{{sfn|Wade|1977}}

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.{{sfn|Goldstein|1978}} 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".{{sfn|Wade|1977}} 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.{{sfn|Wade|1977}} In attempting to disprove Newton, Herbert Lewis also found himself agreeing that "Ptolemy was an outrageous fraud,"{{sfn|Lewis|1979}} and that "all those result capable of statistical analysis point beyond question towards fraud and against accidental error".{{sfn|Lewis|1979}}

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.{{sfn|Wade|1977}} [[Owen Gingerich]], while agreeing that the ''Almagest'' contains "some remarkably fishy numbers",{{sfn|Wade|1977}} including in the matter of the 30-hour displaced equinox, which he noted aligned perfectly with predictions made by Hipparchus 278 years earlier,{{sfn|Gingerich|1980}} rejected the qualification of fraud.{{sfn|Wade|1977}} Objections were also raised by [[Bernard R. Goldstein|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.{{sfn|Goldstein|1978}} Other authors have pointed out that instrument warping or atmospheric refraction may also explain some of Ptolemy's observations at a wrong time.<ref>
{{cite journal
 |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
}}
</ref><ref>
{{cite thesis
 |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.
}}
</ref>

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:

<blockquote>It also confirms that Ptolemy’s Star Catalogue was not based solely on data from Hipparchus’ Catalogue.<br/>

... 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.<ref>
{{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
}}
</ref>
</blockquote>

=== ''Handy Tables'' ===
{{Main articles|Handy Tables}}
The ''[[Handy Tables]]'' ({{Langx|el|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]] 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 ''[[Zij|zījes]]''.<ref>
 Juste, D. (2021).
 Ptolemy, ''Handy Tables''.
 ''Ptolemaeus Arabus et Latinus, Works''.
 [https://ptolemaeus.badw.de/work/153]
</ref>

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''.<ref>
{{cite journal
 |last=Jones |first=A.
 |year=2017
 |title=Ptolemy's Handy Tables
 |url=https://doi.org/10.1177/0021828617706254
 |journal=Journal for the History of Astronomy
 |volume=48 |issue=2 |pages=238–241
 |doi=10.1177/0021828617706254
 |bibcode=2017JHA....48..238J |s2cid=125658099
}}
</ref>

=== ''Planetary Hypotheses'' ===
[[File:Bartolomeu Velho 1568.jpg|thumb|upright=1.1|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'' ({{Langx|el|Ὑποθέσεις τῶν πλανωμένων}}, {{Lit|Hypotheses of the Planets}}) is a [[Cosmology|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 mechanics|celestial motion]].<ref>
{{cite journal
 |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
}}
</ref>
Ptolemy goes beyond the mathematical models of the ''Almagest'' to present a physical realization of the universe as a set of nested spheres,<ref>
{{cite web
 |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
}} — Cited page seems to present for viewing some alternate version of the now defunct [[Shockwave Flash]] video file format. The video file ''player'' software for the file has been "retired" and delibarately disabled / shut down / blocked / by [[Adobe Inc.|Adobe]]. The file is still present, embedded in the archived web page's source, and with only a little extra effort can be extracted from the copy saved in the Internet Archive, linked to in the citation.
</ref>
in which he used the [[epicycle]]s of his planetary model to compute the dimensions of the universe. He estimated the Sun was at an average distance of {{nobr|{{gaps|1|210}} Earth radii}} (now known to actually be {{nobr|{{gaps|~23|450}} radii),}} while the radius of the sphere of the fixed stars was {{nobr|{{gaps|20|000}} times}} the radius of the Earth.<ref>
{{cite journal
 |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
 }}
</ref>

The work is also notable for having descriptions on how to build instruments to depict the planets and their movements from a [[Geocentric model|geocentric]] perspective, much as an [[orrery]] would have done for a [[Heliocentrism|heliocentric]] one, presumably for didactic purposes.<ref>
{{cite journal
 |last=Hamm |first=E.
 |year=2016
 |title=Modeling the heavens: Sphairopoiia and Ptolemy's planetary hypotheses
 |url=https://doi.org/10.1162/POSC_a_00214
 |journal=[[Perspectives on Science]]
 |volume=24 |issue=4 |pages=416–424
 |doi=10.1162/POSC_a_00214 |s2cid=57560804
}}
</ref>

=== Other astronomical works ===
The ''Analemma'' is a short treatise where Ptolemy provides a method for specifying the location of the Sun in three pairs of locally oriented coordinate arcs as a function of the declination of the Sun, the terrestrial latitude, and the hour. The key to the approach is to represent the solid configuration in a plane diagram that Ptolemy calls the ''[[analemma]]''.<ref>{{cite book | chapter-url=https://www.brepolsonline.net/doi/pdf/10.1484/M.PALS-EB.5.120173 | doi=10.1484/M.PALS-EB.5.120173 | chapter=Mathematical Methods in Ptolemy's ''Analemma'' | title=Ptolemy's Science of the Stars in the Middle Ages | date=2020 | last1=Sidoli | first1=Nathan | pages=35–77 | isbn=978-2-503-58639-7 | s2cid=242599669 }}</ref>

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.<ref>
{{cite book
 |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
}}
</ref>

The ''[[Planisphaerium]]'' ({{Langx|el|Ἅπλωσις ἐπιφανείας σφαίρας}}, {{Lit|Flattening of the sphere}}) contains 16&nbsp;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.<ref>
{{cite book
 |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
}}
</ref>

Ptolemy also erected an inscription in a temple at [[Canopus, Egypt|Canopus]], around 146–147&nbsp;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.<ref>
{{cite journal
 |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
}}
</ref>

In 2023, archaeologists were able to read a manuscript which gives instructions for the construction of an astronomical tool called a ''[[meteoroscope]]'' ({{math|μετεωροσκόπιον}} or {{math|μετεωροσκοπεῖον}}). The text, which comes from an eighth-century manuscript which also contains Ptolemy's ''Analemma'', was identified on the basis of both its content and linguistic analysis as being by Ptolemy.<ref>
{{cite news
 |first=Jennifer |last=Nalewicki
 |date=7 April 2023
 |title=Hidden Ptolemy text, printed beneath a Latin manuscript, deciphered after 200&nbsp;years
 |website=Live Science
 |url=https://www.livescience.com/hidden-ptolemy-text-printed-beneath-a-latin-manuscript-deciphered-after-200-years
}}
</ref><ref>
{{Cite journal
 |first1=Victor    |last1=Gysembergh     |first2=Alexander |last2=Jones
 |first3=Emanuel   |last3=Zingg          |first4=Pascal    |last4=Cotte
 |first5=Salvatore |last5=Apicella
 |date=1 March 2023
 |title=Ptolemy's treatise on the meteoroscope recovered
 |journal=[[Archive for History of Exact Sciences]]
 |volume=77 |issue=2 |pages=221–240
 |doi=10.1007/s00407-022-00302-w
 |s2cid=257453722 |doi-access=free
}}</ref>

Ptolemy is also though to have produced his [[Table of Noteworthy Cities (Ptolemy)|Table of Noteworthy Cities]] as an aid to his [[Handy Tables|astronomical tables]].<ref>{{Cite thesis |last=Defaux |first=Olivier |title=The Iberian peninsula in Ptolemy's geography: origins of the coordinates and textual history |date=2017 |publisher=PRO BUSINESS digital printing Deutschland GmbH |place=Berlin |isbn=9783981638462}} pp.122-6</ref>