TheCatholic Church promoted his work, which included the only mathematically soundgeocentric model of theSolar System, and unlike mostGreek mathematicians, Ptolemy's writings (foremost theAlmagest) never ceased to be copied or commented upon, both inlate antiquity and in theMiddle 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 onepicycles is now seen as a very complex theoretical model built in order to explain a false tenet based on faith.
Ptolemy's date of birth and birthplace are both unknown. The 14th-century astronomerTheodore Meliteniotes wrote that Ptolemy's birthplace wasPtolemais Hermiou, a Greek city in theThebaid region of Egypt (now El Mansha,Sohag Governorate). This attestation is quite late, however, and there is no evidence to support it.[3][c]
It is known that Ptolemy lived in or around the city ofAlexandria, in theRoman province of Egypt underRoman rule.[5]He had a Latin name, Claudius, which is generally taken to imply he was aRoman citizen.[6]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.[7]
Ptolemy died in Alexandria.[8](p311) Ptolemy's year of death is not directly recorded by primary sources, and has to be inferred from the scale of his work.[9] Suggested years of death includec. 165,[10]c. 168,[8](p311)c. 170,[9] andc. 175.[11]
Engraving of a crowned Ptolemy being guided byUrania, byGregor Reisch (1508), fromMargarita Philosophica showing an early conflation of the mathematician with the royal house ofPtolemaic Egypt, with the same last name.
The nameClaudius is a Roman name, belonging to thegens Claudia; the peculiar multipart form of the whole nameClaudius Ptolemaeus is a Roman custom, characteristic of Roman citizens. This indicates that Ptolemy would have been aRoman citizen.[3] Gerald Toomer, the translator of Ptolemy'sAlmagest into English, suggests that citizenship was probably granted to one of Ptolemy's ancestors by either the emperorClaudius or the emperorNero.[14]
The 9th centuryPersianastronomerAbu Ma'shar al-Balkhi mistakenly presents Ptolemy as a member ofPtolemaic Egypt's royal lineage, stating that the descendants of the Alexandrine general and PharaohPtolemy I Soter were wise "and included Ptolemy the Wise, who composed the book of theAlmagest". 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 theAlmagest. The correct answer is not known."[15]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.[17]It is no longer doubted that the astronomer who wrote theAlmagest also wrote theTetrabiblos as its astrological counterpart.[18](p x) In laterArabic sources, he was often known as "theUpper Egyptian",[19][20](p 606) suggesting he may have had origins in southernEgypt.[20](pp 602, 606)Arabic astronomers,geographers, andphysicists referred to his name inArabic asBaṭlumyus (Arabic:بَطْلُمْيوس).[21]
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 theGeography and theTetrabiblos have significant references to astronomy.[29]
The earliest person who attempted to merge these two approaches wasHipparchus, who producedgeometric models that not only reflected the arrangement of the planets and stars but could be used to calculate celestial motions.[24]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.[31]
Ptolemy presented his astronomical models alongside convenient tables, which could be used to compute the future or past position of the planets.[32]TheAlmagest also contains astar catalogue, which is a version of a catalogue created by Hipparchus. Its list of forty-eightconstellations 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).[33]For over a thousand years, theAlmagest was the authoritative text on astronomy across Europe, the Middle East, and North Africa.[34]
TheAlmagest was preserved, like many extant Greek scientific works, in Arabic manuscripts; the modern title is thought to be an Arabic corruption of the Greek nameHē Megistē Syntaxis ('The greatest treatise'), as the work was presumably known duringlate antiquity.[35]Because of its reputation, it was widely sought and translated twice into Latinin the 12th century, once in Sicily and again in Spain.[36] Ptolemy's planetary models, like those of the majority of his predecessors, were geocentric and almost universally accepted until the reappearance ofheliocentric models during theScientific Revolution.
Under the scrutiny of modern scholarship, and the cross-checking of observations contained in theAlmagest against figures produced through backwards extrapolation, various patterns of errors have emerged within the work.[37][38] 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.[37]
The overall quality of Ptolemy's observations has been challenged by several modern scientists, but prominently byRobert R. Newton in his 1977 bookThe Crime of Claudius Ptolemy, which asserted that Ptolemy fabricated many of his observations to fit his theories.[39] 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".[37] 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.[37] In attempting to disprove Newton, Herbert Lewis also found himself agreeing that "Ptolemy was an outrageous fraud,"[38] and that "all those result capable of statistical analysis point beyond question towards fraud and against accidental error".[38]
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.[37]Owen Gingerich, while agreeing that theAlmagest contains "some remarkably fishy numbers",[37] including in the matter of the 30-hour displaced equinox, which he noted aligned perfectly with predictions made by Hipparchus 278 years earlier,[40] rejected the qualification of fraud.[37] Objections were also raised byBernard 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.[39] Other authors have pointed out that instrument warping or atmospheric refraction may also explain some of Ptolemy's observations at a wrong time.[41][42]
In 2022 the first Greek fragments of Hipparchus' lost star catalog were discovered in apalimpsest and they debunked accusations made by the French astronomerJean 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:
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.[43]
TheHandy Tables (Greek: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, andeclipses of the Sun and Moon, making it a useful tool for astronomers and astrologers. The tables themselves are known throughTheon of Alexandria's version. Although Ptolemy'sHandy Tables do not survive as such in Arabic or in Latin, they represent the prototype of most Arabic and Latin astronomical tables orzījes.[44]
Additionally, the introduction to theHandy Tables survived separately from the tables themselves (apparently part of a gathering of some of Ptolemy's shorter writings) under the titleArrangement and Calculation of the Handy Tables.[45]
A depiction of the non-Ptolemaic Universe with no epicycles, possibly from 500 years before Ptolemy, as described in thePlanetary Hypotheses byBartolomeu Velho (1568).
ThePlanetary Hypotheses (Greek:Ὑποθέσεις τῶν πλανωμένων,lit.'Hypotheses of the Planets') is acosmological work, probably one of the last written by Ptolemy, in two books dealing with the structure of the universe and the laws that governcelestial motion.[46]Ptolemy goes beyond the mathematical models of theAlmagest to present a physical realization of the universe as a set of nested spheres,[47]in which he used theepicycles of his planetary model to compute the dimensions of the universe. He estimated the Sun was at an average distance of1210 Earth radii (now known to actually be~23450 radii), while the radius of the sphere of the fixed stars was20000 times the radius of the Earth.[48]
The work is also notable for having descriptions on how to build instruments to depict the planets and their movements from ageocentric perspective, much as anorrery would have done for aheliocentric one, presumably for didactic purposes.[49]
TheAnalemma 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 theanalemma.[50]
In another work, thePhaseis (Risings of the Fixed Stars), Ptolemy gave aparapegma, a starcalendar oralmanac, based on the appearances and disappearances of stars over the course of the solar year.[51]
Ptolemy also erected an inscription in a temple atCanopus, around 146–147 AD, known as theCanobic 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.[53]
In 2023, archaeologists were able to read a manuscript which gives instructions for the construction of an astronomical tool called ameteoroscope (μετεωροσκόπιον orμετεωροσκοπεῖον). The text, which comes from an eighth-century manuscript which also contains Ptolemy'sAnalemma, was identified on the basis of both its content and linguistic analysis as being by Ptolemy.[54][55]
The first part of theGeography 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.[60]About6300 of these places and geographic features have assignedcoordinates so that they can be placed in agrid that spanned the globe.[29]Latitude was measured from theequator, as it is today, but Ptolemy preferred to express it asclimata, the length of the longest day rather thandegrees of arc: The length of themidsummer day increases from 12h to 24h as one goes from the equator to thepolar circle.[61]One of the places Ptolemy noted specific coordinates for was the now-loststone tower which marked the midpoint on the ancientSilk Road, and which scholars have been trying to locate ever since.[62]
In the third part of theGeography, Ptolemy gives instructions on how to create maps both of the whole inhabited world (oikoumenē) and of the Roman provinces, including the necessarytopographic lists, and captions for the maps. Hisoikoumenē spanned 180 degrees of longitude from the Blessed Islands in theAtlantic Ocean to the middle ofChina, and about 80 degrees of latitude fromShetland to anti-Meroe (east coast ofAfrica); 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.[57][58]
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.[63] This means that information contained in different parts of theGeography is likely to be of different dates, in addition to containing many scribal errors. However, although the regional andworld maps in surviving manuscripts date fromc. 1300 AD (after the text was rediscovered byMaximus Planudes), there are some scholars who think that such maps go back to Ptolemy himself.[60]
Ptolemy wrote an astrological treatise, in four parts, known by the Greek termTetrabiblos (lit.'Four Books') or by its Latin equivalentQuadripartitum.[64]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".[18](p x)As a source of reference, theTetrabiblos is said to have "enjoyed almost the authority of a Bible among the astrological writers of a thousand years or more".[18](p xii)It was first translated from Arabic into Latin byPlato of Tivoli (Tiburtinus) in 1138, while he was in Spain.[65]
Much of the content of theTetrabiblos 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 theAlmagest was the first, concerned with the influences of the celestial bodies in thesublunary sphere.[16][17] Thus explanations of a sort are provided for the astrological effects of theplanets, based upon their combined effects of heating, cooling, moistening, and drying.[66] Ptolemy dismisses other astrological practices, such as considering thenumerological significance of names, that he believed to be without sound basis, and leaves out popular topics, such aselectional astrology (interpreting astrological charts to determine courses of action) andmedical astrology, for similar reasons.[67]
The great respect in which later astrologers held theTetrabiblos derived from its nature as an exposition of theory, rather than as a manual.[67]
A collection of one hundredaphorisms about astrology called theCentiloquium, ascribed to Ptolemy, was widely reproduced and commented on by Arabic, Latin, and Hebrew scholars, and often bound together in medieval manuscripts after theTetrabiblos as a kind of summation.[29] It is now believed to be a much laterpseudepigraphical composition. The identity and date of the actual author of the work, referred to now asPseudo-Ptolemy, remains the subject of conjecture.[68]
Ptolemy'sHarmonics (Greek:Ἁρμονικόν) is a work in three books onmusic theory and the mathematics behind musical scales[69]
Harmonics begins with a definition of harmonic theory, with a long exposition on the relationship between reason and sense perception in corroborating theoretical assumptions. After criticizing the approaches of his predecessors, Ptolemy argues for basing musical intervals on mathematical ratios (as opposed to the ideas advocated by followers ofAristoxenus), backed up by empirical observation (in contrast to the excessively theoretical approach of thePythagoreans).[70][71]
Ptolemy introduces theharmonic canon (Greek name) ormonochord (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 discussPythagorean 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, theperfect 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 smallertetrachords (combinations of four pitch ratios which together make aperfect fourth) andoctaves.[72][73]Ptolemy reviewed standard (andancient, disused) musical tuning practice of his day, which he then compared to his own subdivisions of thetetrachord and theoctave, which he derived experimentally using amonochord / 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).[74]
Although Ptolemy'sHarmonics never had the influence of hisAlmagest orGeography, 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 samesingle 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 asjust intonation – the standard for comparison of consonance in the many other, less-than exact but more facilecompromise tuning systems.[75][76]
TheOptica (Koine Greek:Ὀπτικά), known as theOptics, is a work that survives only in a somewhat poor Latin version, which, in turn, was translated from a lost Arabic version byEugenius of Palermo (c. 1154). In it, Ptolemy writes about properties of sight (not light), includingreflection,refraction, andcolour. The work is a significant part of the earlyhistory of optics and influenced the more famous and superior 11th-centuryBook of Optics byIbn al-Haytham.[78] 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 orMoon illusion (the enlarged apparent size on the horizon) based on the difficulty of looking upwards.[79][80]
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) treatsreflection in plane, convex, concave, and compound mirrors.[81] The last section (Book V) deals withrefraction 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.[82]However, according to Mark Smith, Ptolemy's table was based in part on real experiments.[83]
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.[78][84]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.[85]
Although mainly known for his contributions to astronomy and other scientific subjects, Ptolemy also engaged inepistemological andpsychological discussions across his corpus.[86]He wrote a short essay entitledOn the Criterion and Hegemonikon (Greek: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 humanpsyche or soul, particularly its ruling faculty (i.e., thehegemonikon).[74] 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 ofmathematics.[87]
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 totheology ormetaphysics because the latter are conjectural while only the former can secure certain knowledge. This view is contrary to thePlatonic andAristotelian traditions, where theology or metaphysics occupied the highest honour.[86] Despite being a minority position among ancient philosophers, Ptolemy's views were shared by other mathematicians such asHero of Alexandria.[88]
^Since no contemporary depictions or descriptions of Ptolemy are known to have existed, later artists' impressions are unlikely to have reproduced his appearance accurately.
^"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 (c. 1360) andunsupported." — Toomer & Jones (2018)[4]
^"But what we really want to know is to what extent the Alexandrian mathematicians of the period from the 1st to the 5th centuriesCE 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 descriptionsexist. — V.J. Katz (1998, p. 184)[25]
^abPecker, Jean Claude; Dumont, Simone (2001). "From pre-Galilean astronomy to the Hubble Space Telescope and beyond". In Kaufman, Susan (ed.).Understanding the Heavens: Thirty centuries of astronomical ideas from ancient thinking to modern cosmology. Springer. pp. 309–372.doi:10.1007/978-3-662-04441-4_7.ISBN3-540-63198-4.
^abcJones, A. (2020)."The ancient Ptolemy"(PDF). In Juste, D.; van Dalen, B.; Hasse, D.N.; Burnett, C.; Turnhout; Brepols (eds.).Ptolemy'sScience of the Stars in the Middle Ages. Ptolemaeus Arabus et Latinus Studies. Vol. 1. pp. 13–34 – viaNew York University / archive.nyu.edu.
^Schiefsky, M. (2012). "The creation of second-order knowledge in ancient Greek science as a process in the globalization of knowledge".The Globalization of Knowledge in History. MPRL – Studies. Berlin: Max-Planck-Gesellschaft zur Förderung der Wissenschaften.ISBN978-3-945561-23-2.
^"Dennis Rawlins". The International Journal of Scientific History. Retrieved7 October 2009.
^Charles Homer Haskins,Studies in the History of Mediaeval Science, New York: Frederick Ungar Publishing, 1967, reprint of the Cambridge, Mass., 1927 edition
^Duke, Dennis."Ptolemy's cosmology".scs.fsu.edu/~dduke (academic pers. website).Florida State University. Archived fromthe original on 7 November 2009. — Cited page seems to present for viewing some alternate version of the now defunctShockwave Flash video file format. The video fileplayer software for the file has been "retired" and delibarately disabled / shut down / blocked / byAdobe. 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.
^Defaux, Olivier (2017).The Iberian peninsula in Ptolemy's geography: origins of the coordinates and textual history (Thesis). Berlin: PRO BUSINESS digital printing Deutschland GmbH.ISBN9783981638462. pp.122-6
^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 asidereal day.
^abMittenhuber, F. (2010). "The tradition of texts and maps in Ptolemy'sGeography".Ptolemy in Perspective: Use and criticism of his work from antiquity to the nineteenth century. Archimedes. Vol. 23. Dordrecht, NL: Springer Netherlands. pp. 95–119.doi:10.1007/978-90-481-2788-7_4.ISBN978-90-481-2788-7.
^Dean, Riaz (2022).The Stone Tower: Ptolemy, the silk road, and a 2,000 year-old riddle. Delhi, IN: Penguin Viking. pp. xi, 135, 148, 160.ISBN978-0670093625.
^Rutkin, H. Darrel (2010). "The use and abuse of Ptolemy'sTetrabiblos in Renaissance and early modern Europe".Jones (2010). p. 135.[16](p 135)
^abRobbins, Frank E., ed. (1940).Ptolemy Tetrabiblos. Loeb Classical Library. Cambridge, MA: Harvard University Press.ISBN0-674-99479-5.{{cite book}}:ISBN / Date incompatibility (help)
^Boudet, J.-P. (2014). "Astrology between rational science and divine inspiration: The pseudo-Ptolemy's centiloquium". In Rapisarda, S.; Niblaeus, E. (eds.).Dialogues among Books in Medieval Western Magic and Divination. Micrologus' library. Vol. 65. Sismel edizioni del Galluzzo. pp. 47–73.ISBN9788884505811. Retrieved19 August 2021.
^Hetherington, Norriss S. (8 April 2014).Encyclopedia of Cosmology. Routledge Revivals. Vol. Historical, Philosophical, and Scientific Foundations of Modern Cosmology. Routledge. p. 527.ISBN978-1-317-67766-6.
^Sabra, A.I. (1987). "Psychology versus mathematics: Ptolemy and Alhazen on the moon illusion". In Grant, E.; Murdoch, J.E. (eds.).Mathematics and its Application to Science and Natural Philosophy in the Middle Ages. Cambridge, UK: Cambridge University Press. pp. 217–247.
^Boyer, C.B. (1959).The Rainbow: From myth to mathematics.
^Smith, Mark (2015).From Sight to Light: The passage from ancient to modern optics. The University of Chicago Press. pp. 116–118.Bibcode:2014fslp.book.....S.
^Ross, H.W.; Plug, C. (1998). "The history of size constancy and size illusions". In Walsh, V.; Kulikowski, J. (eds.).Perceptual Constancy: Why things look as they do. Cambridge, UK: Cambridge University Press. pp. 499–528.
^Schiefsky, M.J. (2014). "The epistemology of Ptolemy'sOn the Criterion". In Lee, M.-K. (ed.).Strategies of Argument: Essays in ancient ethics, epistemology, and logic. Oxford University Press. pp. 301–331.
Heath, Thomas, Sir (1921).A History of Greek Mathematics. Oxford, UK: Clarendon Press.{{cite book}}: CS1 maint: multiple names: authors list (link)
Ptolemaios, Claudius (1998). Hübner, Wolfgang (ed.).Claudius Ptolemaeus, Opera quae exstant omnia [The complete existing works of Claudius Ptolemy]. Bibliotheca scriptorum Graecorum et Romanorum Teubneriana (in Latin). Vol. III. De Gruyter. Fascia 1:Αποτελεσματικα (Tetrabiblos).ISBN978-3-598-71746-8. — The most recent edition of the Greek text of Ptolemy's astrological work, based on earlier editions by F. Boll and E. Boer.
Ptolemaios, Claudius (1989). Lejeune, A. (ed.).L'Optique de Claude Ptolémée dans la version latine d'après l'arabe de l'émir Eugène de Sicile [TheOptics of Claudius Ptolemy in the Latin version based on the Arabic of Emir Eugene of Sicily]. Collection de travaux de l'Académie International d'Histoire des Sciences (in French and Latin). Vol. 31. Leiden: E.J.Brill. — Latin text with French translation
Neugebauer, Otto (1975).A History of Ancient Mathematical Astronomy. Vol. I–III. Berlin, DE / New York, NY: Springer Verlag.
Nobbe, C.F.A., ed. (1843).Claudii PtolemaeiGeographia [Claudius Ptolemy'sGeography] (in Latin). 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'sCosmography and more".Quaerendo.47 (3–4):307–327.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.
Ptolemaios, Claudius (1980) [1930]. Düring, Ingemar (ed.).Die Harmonielehre des Klaudios Ptolemaios. Göteborgs högskolas årsskrift. Vol. 36 (reprint ed.). Göteborg / New York, NY: Elanders boktr. aktiebolag. (1930) / Garland Publishing (1980).
Smith, A.M. (1996). "Ptolemy's Theory of Visual Perception: An English translation of theOptics with introduction and commentary".Transactions of the American Philosophical Society (book review). 86, Part 2. Philadelphia, PA: The American Philosophical Society.
Ptolemaios, Claudius (1991) [1932]. Stevenson, Edward Luther (ed.).Claudius Ptolemy:The Geography. Translated by E.L. Stevenson (Reprint ed.). New York, NY: New York Public Library, 1932 / Dover, 1991. — This is the only complete English translation of Ptolemy'sGeography, but it is marred by numerous mistakes; and placenames are given in Latinised forms, rather than in the Greek, as in the original.
Ptolemaios, Claudius (2006). Stückelberger, Alfred; Graßhoff, Gerd (eds.).Ptolemaios, Handbuch der Geographie, Griechisch-Deutsch [Ptolemy,Geography Handbook, Greek-German] (in German). Basel, CH: Schwabe Verlag.ISBN978-3-7965-2148-5. — Massive 2 vol,1018 pp. academic edition ofGeography by a team of a dozen scholars that takes account of all known manuscripts, with facing Greek and German text, with footnotes on manuscript variations, color maps, and a CD with the geographical data.
Geography, digitised codex made in Italy between 1460 and 1477, translated to Latin by Jacobus Angelus atSomni. Also known asCodex Valentinus, it is the oldest manuscript of the codices with maps of Ptolemy with the donis projections.
Ptolemaeus Arabus et Latinus (PAL) Project, dedicated to the edition and study of the Arabic and Latin versions of Ptolemy’s astronomical and astrological texts and related material.
