Ptolemy - Knowledge

917:, 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". 1483: 774: 80: 7663: 7625: 1718:, 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 1253: 2226:... "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 ... 7735: 1021: 7612: 2232:

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

7723: 7687: 7711: 1211:. 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. 7699: 7675: 7651: 1594: 1659:(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 936:, 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. 666:". 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 1667:, 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 670:. The correct answer is not known." 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. It is no longer doubted that the astronomer who wrote the 1637:

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

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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

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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

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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

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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

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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

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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

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and includes the earliest surviving table of refraction from air to water, for which the values (with the exception of the 60° angle of incidence) show signs of being obtained from an arithmetic progression. However, according to Mark Smith, Ptolemy's table was based in part on real experiments.

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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

1814:. 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 837:

that not only reflected the arrangement of the planets and stars but could be used to calculate celestial motions. Ptolemy, following Hipparchus, derived each of his geometrical models for the Sun, Moon, and the planets from selected astronomical observations done in the spanning of more than

527: 1722:, 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 508:. 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. 2198:"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 ( 461:. 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 1835:

and shape were determined by the visual angle subtended at the eye combined with perceived distance and orientation. This was one of the early statements of size-distance invariance as a cause of perceptual size and shape constancy, a view supported by the Stoics.

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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

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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

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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

981:) 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 1559:

did possess might be attributed to its nature as an exposition of the art of astrology, and as a compendium of astrological lore, rather than as a manual. It speaks in general terms, avoiding illustrations and details of practice.

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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). For over a thousand years, the

956:... 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. 1821:

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

1863:), 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 5372:

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.

3600:. 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. 1663:(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 1899:

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

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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" ...

1445:); 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. 1200:) 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. 3973:

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

885:, 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 5380: 749:

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

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Since no contemporary depictions or descriptions of Ptolemy are known to have existed, later artists' impressions are unlikely to have reproduced his appearance accurately.

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is said to have "enjoyed almost the authority of a Bible among the astrological writers of a thousand years or more". It was first translated from Arabic into Latin by

2828:"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 1680: 1573:, ascribed to Ptolemy, was widely reproduced and commented on by Arabic, Latin, and Hebrew scholars, and often bound together in medieval manuscripts after the 928:

contains "some remarkably fishy numbers", including in the matter of the 30-hour displaced equinox, which he noted aligned perfectly with predictions made by

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Boudet, J.-P. (2014). "Astrology between rational science and divine inspiration: The pseudo-Ptolemy's centiloquium". In Rapisarda, S.; Niblaeus, E. (eds.).

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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.

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Smith, A. M. (1982). "Ptolemy's search for a law of refraction: A case-study in the classical methodology of "saving the appearances" and its limitations".

5258:. Göteborgs högskolas årsskrift. Vol. 36 (reprint ed.). Göteborg / New York, NY: Elanders boktr. aktiebolag. (1930) / Garland Publishing (1980). 6381: 5002: 1540:, based upon their combined effects of heating, cooling, moistening, and drying. Ptolemy dismisses other astrological practices, such as considering the 5302: 3612: 838:

800 years; however, many astronomers have for centuries suspected that some of his models' parameters were adopted independently of observations.

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Ptolemy presented his astronomical models alongside convenient tables, which could be used to compute the future or past position of the planets. The

5873: 4139: 5831:"The work of Claudius Ptolemy, as the epitome of the Macedonian Legacy in History, and of the Hellenistic and Alexandrian Science and Civilization" 5088: 3816: 7870: 7485: 2718: 1216: 5403: 2690: 4028: 5776: 7085: 5654: 5146:]. Collection de travaux de l'Académie International d'Histoire des Sciences (in French and Latin). Vol. 31. Leiden: E.J.Brill. 3076:

Schiefsky, M. (2012). "The creation of second-order knowledge in ancient Greek science as a process in the globalization of knowledge".

2635: 2217:"But what we really want to know is to what extent the Alexandrian mathematicians of the period from the 1st to the 5th centuries 1952: 1214:

In 2023, archaeologists were able to read a manuscript which gives instructions for the construction of an astronomical tool called a

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survived separately from the tables themselves (apparently part of a gathering of some of Ptolemy's shorter writings) under the title

7563: 273: 1871:). Ptolemy argues that, to arrive at the truth, one should use both reason and sense perception in ways that complement each other. 1068:

work, probably one of the last written by Ptolemy, in two books dealing with the structure of the universe and the laws that govern

6866: 6402: 6144: 5720: 5327:, but it is marred by numerous mistakes; and placenames are given in Latinised forms, rather than in the Greek, as in the original. 4681:

Sabra, A.I. (1987). "Psychology versus mathematics: Ptolemy and Alhazen on the moon illusion". In Grant, E.; Murdoch, J.E. (eds.).

4571:. Routledge Revivals. Vol. Historical, Philosophical, and Scientific Foundations of Modern Cosmology. Routledge. p. 527. 7795: 6374: 6348: 648: 7830: 7410: 5699: 1359:

provides a catalogue of 8,000 localities he collected from Marinus and others, the biggest such database from antiquity. About

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The work is also notable for having descriptions on how to build instruments to depict the planets and their movements from a

7825: 7140: 5866: 5397: 5351: 5127:— The most recent edition of the Greek text of Ptolemy's astrological work, based on earlier editions by F. Boll and E. Boer. 5120: 4848: 4698: 4576: 4256: 4011: 3888: 3840: 3748: 3713: 3087: 2855: 2535: 2399: 2308: 2423: 1777:

is a work that survives only in a somewhat poor Latin version, which, in turn, was translated from a lost Arabic version by

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The overall quality of Claudius Ptolemy's observations has been challenged by several modern scientists, but prominently by

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do not survive as such in Arabic or in Latin, they represent the prototype of most Arabic and Latin astronomical tables or

5560: 3571: 2601:; Dumont, Simone (2001). "From pre-Galilean astronomy to the Hubble Space Telescope and beyond". In Kaufman, Susan (ed.). 7800: 7473: 6876: 6338: 6134: 1606: 1024:

A depiction of the non-Ptolemaic Universe with no epicycles, possibly from 500 years before Ptolemy, as described in the

166: 5675: 5273:. Mnemosyne, Bibliotheca Classica Batava, Supplementum. Vol. 203. Translated by Solomon, Jon. Leiden / Boston, MA: 7840: 7820: 7815: 7810: 7540: 6367: 5388: 5107:]. Bibliotheca scriptorum Graecorum et Romanorum Teubneriana (in Latin). Vol. III. De Gruyter. Fascia 1: 4605: 4058: 4819:

Ross, H.W.; Plug, C. (1998). "The history of size constancy and size illusions". In Walsh, V.; Kulikowski, J. (eds.).

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is likely to be of different dates, in addition to containing many scribal errors. However, although the regional and

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of the Sun and Moon, making it a useful tool for astronomers and astrologers. The tables themselves are known through

5890: 5523: 5282: 4983: 4613: 4415: 4222: 4117: 3064: 2999: 2893: 2618: 1695:/ harmonic canon. The volume ends with a more speculative exposition of the relationships between harmony, the soul ( 1080:

of his planetary model to compute the dimensions of the universe. He estimated the Sun was at an average distance of

5481:"The Arabic version of Ptolemy's planisphere or flattening the surface of the sphere: Text, translation, commentary" 1891:

because the latter are conjectural while only the former can secure certain knowledge. This view is contrary to the

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Peerlings, R.H.J.; Laurentius, F.; van den Bovenkamp, J. (2017). "The watermarks in the Rome editions of Ptolemy's

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into English, suggests that citizenship was probably granted to one of Ptolemy's ancestors by either the emperor

5762:"Claudius Ptolemaeus (Ptolemy): Representation, understanding, and mathematical labeling of the spherical Earth" 4838: 1843:

Although mainly known for his contributions to astronomy and other scientific subjects, Ptolemy also engaged in

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Database of the Arabic and Latin versions of Ptolemy’s astronomical and astrological texts and related material

3056: 1982: 7855: 7845: 6271: 5321:. Translated by E.L. Stevenson (Reprint ed.). New York, NY: New York Public Library, 1932 / Dover, 1991. 944: 7578: 7335: 7223: 6398: 4359: 2603:

Understanding the Heavens: Thirty centuries of astronomical ideas from ancient thinking to modern cosmology

2339: 2164: 1512:), roughly meaning "(books) on the Effects" or "Outcomes", or "Prognostics". As a source of reference, the 568: 170: 4435: 3765: 1544:

significance of names, that he believed to be without sound basis, and leaves out popular topics, such as

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Gysembergh, Victor; Jones, Alexander; Zingg, Emanuel; Cotte, Pascal; Apicella, Salvatore (1 March 2023).

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Studien über Claudius Ptolemaeus. Ein Beitrag zur Geschichte der griechischen Philosophie und Astrologie

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Murschel, A. (1995). "The structure and function of Ptolemy's physical hypotheses of planetary motion".

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

336: 6705: 5392:. Vol. 11. New York, NY: Scribner & American Council of Learned Societies. pp. 186–206. 2266: 34: 7449: 7420: 6780: 6635: 6068: 3740:

Geminos's Introduction to the Phenomena: A translation and study of a Hellenistic survey of astronomy

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has come to symbolize a very complex theoretical model built in order to explain a false assumption.

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Goldstein, Bernard R. (1997). "Saving the phenomena: The background to Ptolemy's planetary theory".

7583: 7317: 6860: 5663: 5566: 3689: 3579: 2065: 2037: 2009: 1944:, sometimes known as the Ptolemy Cluster, an open cluster of stars in the constellation of Scorpius 1301: 1076:

to present a physical realization of the universe as a set of nested spheres, in which he used the

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is a Roman custom, characteristic of Roman citizens. This indicates that Ptolemy would have been a

55: 2107: 2093: 2079: 2051: 2023: 1642:), backed up by empirical observation (in contrast to the excessively theoretical approach of the 901:

Under the scrutiny of modern scholarship, and the cross-checking of observations contained in the

7545: 7521: 7395: 7330: 7271: 7208: 7198: 6934: 6853: 6715: 6625: 6505: 6063: 5882: 5605:, digitised codex made in Italy between 1460 and 1477, translated to Latin by Jacobus Angelus at 4407: 3653: 3357:

Bruin, Franz; Bruin, Margaret (1976). "The equator ring, equinoxes, and atmospheric refraction".

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Claudius Ptolemy and self-promotion: A study on Ptolemy's intellectual milieu in Roman Alexandria

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of works by Ptolemy in .jpg and .tiff format. Online Galleries, History of Science Collections,

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Graßhoff, G.; Mittenhuber, F.; Rinner, E. (2017). "Of paths and places: The origin of Ptolemy's

2827: 7568: 7516: 7415: 7243: 7193: 7178: 7173: 6944: 6745: 6680: 6670: 6620: 6210: 6083: 6018: 5812: 5639: 5545: 4399: 2707:(in Arabic and Latin). editors & translators Yamamoto, K. & Burnett, Ch. Leiden. 4.1.4. 1981:, a project at University of California, Berkeley, aimed at modeling, simulating and designing 1726:– the standard for comparison of consonance in the many other, less-than exact but more facile 1454: 1247: 1232:, was identified on the basis of both its content and linguistic analysis as being by Ptolemy. 497: 162: 5136:

L'Optique de Claude Ptolémée dans la version latine d'après l'arabe de l'émir Eugène de Sicile

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Barker, A. (1994). "Ptolemy's Pythagoreans, Archytas, and Plato's conception of mathematics".

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Ptolemy in Perspective: Use and criticism of his work from antiquity to the nineteenth century

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software for the file has been "retired" and delibarately disabled / shut down / blocked / by

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Ptolemy in Perspective: Use and criticism of his work from antiquity to the nineteenth century

2300: 1482: 773: 7616: 7468: 7312: 7253: 7130: 7053: 7001: 6803: 6710: 6560: 6246: 6175: 5913: 5613:, it is the oldest manuscript of the codices with maps of Ptolemy with the donis projections. 5027: 3786: 3411: 1401: 890: 474: 190: 5581: 5514:

Ptolemy's Universe: The natural philosophical and ethical foundations of Ptolemy's astronomy

4596: 4246: 1683:) musical tuning practice of his day, which he then compared to his own subdivisions of the 7593: 7533: 7497: 7340: 7163: 7110: 7080: 7070: 6979: 6842: 6735: 6650: 6605: 6585: 6430: 6415: 6317: 6058: 6008: 5928: 5903: 5450: 5436: 5212:— Until Stückelberger (2006), this was the most recent edition of the complete Greek text. 5023: 5011: 4772: 4638: 4459: 3536: 3491: 3425: 3366: 3278:, New York: Frederick Ungar Publishing, 1967, reprint of the Cambridge, Mass., 1927 edition 3249: 3185: 3136: 1962: 1958: 1823: 1789: 1727: 1545: 1504:. Its original title is unknown, but may have been a term found in some Greek manuscripts, 1371: 933: 822: 380: 376: 178: 79: 3817:"Hidden Ptolemy text, printed beneath a Latin manuscript, deciphered after 200 years" 2324: 1167:, based on the appearances and disappearances of stars over the course of the solar year. 862:

was the authoritative text on astronomy across Europe, the Middle East, and North Africa.

8: 7765: 7760: 7727: 7573: 7492: 7480: 7461: 7425: 7345: 7263: 7248: 7238: 7188: 7183: 7125: 6994: 6886: 6750: 6740: 6640: 6610: 6550: 6525: 6450: 6440: 6425: 6088: 5993: 5943: 5918: 5797: 5633: 5624: 4926: 4749: 4491: 4323: 2437: 1778: 1296: 1241: 1228:). The text, which comes from an eighth-century manuscript which also contains Ptolemy's 1069: 986: 584: 367: 5830: 5724: 5454: 5015: 4776: 4463: 3540: 3495: 3429: 3370: 3253: 3189: 3140: 3082:. MPRL – Studies. Berlin, DE: Max-Planck-Gesellschaft zur Förderung der Wissenschaften. 2501: 1818:(the enlarged apparent size on the horizon) based on the difficulty of looking upwards. 1581:

composition. The identity and date of the actual author of the work, referred to now as

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In 2022 the first Greek fragments of Hipparchus' lost star catalog were discovered in a

7715: 7667: 7629: 7588: 7528: 7456: 7322: 7297: 7115: 7090: 7058: 6896: 6655: 6600: 6565: 6460: 6322: 6236: 5648: 5175: 5082: 5061: 4951: 4801: 4731: 4723: 4663: 4508: 4381: 4340: 4299: 4193: 4156: 3921: 3913: 3859: 3719: 3670: 3629: 3552: 3507: 3378: 3201: 3152: 2969: 2961: 2808: 2712: 2598: 2580: 2521: 2363: 2287: 1900: 1700: 1660: 1598: 932:

278 years earlier, rejected the qualification of fraud. Objections were also raised by

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Barker, A. (2010). "Mathematical beauty made audible: Musical aesthetics in Ptolemy's

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Goldstein, Bernard R. (1967). "The Arabic version of Ptolemy's planetary hypotheses".

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in plane, convex, concave, and compound mirrors. The last section (Book V) deals with

1415:, Ptolemy gives instructions on how to create maps both of the whole inhabited world ( 873:

manuscripts; the modern title is thought to be an Arabic corruption of the Greek name

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of Claudius Ptolemy in the Latin version based on the Arabic of Emir Eugene of Sicily

5116: 5065: 5053: 5036: 4979: 4943: 4844: 4735: 4715: 4655: 4609: 4572: 4547: 4512: 4411: 4385: 4344: 4291: 4252: 4218: 4174:

Riley, M. (1987). "Theoretical and practical astrology: Ptolemy and his colleagues".

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and there were several of this name among Alexander's army, one of whom made himself

543: 489:). This attestation is quite late, however, and there is no evidence to support it. 486: 478: 473:

Ptolemy's date of birth and birthplace are both unknown. The 14th-century astronomer

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Mathematics and its Application to Science and Natural Philosophy in the Middle Ages

4667: 3674: 3588:— Cited page seems to present for viewing some alternate version of the now defunct 2973: 2367: 2261: 7850: 7755: 7691: 7679: 7655: 7504: 7375: 7292: 7048: 7036: 6984: 6720: 6343: 6296: 6266: 6256: 6205: 6180: 5595: 5458: 5376: 5274: 5231: 5167: 5049: 5045: 4935: 4896: 4707: 4647: 4527: 4500: 4467: 4373: 4332: 4283: 4217:. Micrologus' library. Vol. 65. Sismel edizioni del Galluzzo. pp. 47–73. 4185: 3999: 3897: 3849: 3701: 3662: 3621: 3544: 3499: 3433: 3374: 3193: 3144: 2945: 2843: 2800: 2647: 2606: 2429:. In Juste, D.; van Dalen, B.; Hasse, D.N.; Burnett, C.; Turnhout; Brepols (eds.). 2355: 2296: 1756: 1743: 1533: 1465: 1114: 1029: 910: 237: 89: 5551: 3998:. Archimedes. Vol. 23. Dordrecht, NL: Springer Netherlands. pp. 95–119. 3945: 881:. Because of its reputation, it was widely sought and translated twice into Latin 7145: 7135: 7029: 6755: 6291: 6226: 6195: 6093: 6023: 5643: 5500: 5462: 4377: 3589: 2879: 2552: 2474: 2389: 2359: 1986: 1978: 1972: 1936: 1896: 1723: 1517: 1422: 1317: 1309: 870: 834: 734: 715: 659: 592: 572: 432: 332: 85: 5802: 5572: 5306:(book review). 86, Part 2. Philadelphia, PA: The American Philosophical Society. 5244:

New findings and discoveries in the 1507/8 Rome edition of Ptolemy's Cosmography

4471: 4436:"Mathematizing the soul: The development of Ptolemy's psychological theory from 4003: 3583: 3233: 2610: 2436:. Ptolemaeus Arabus et Latinus Studies. Vol. 1. pp. 13–34 – via 1468:), there are some scholars who think that such maps go back to Ptolemy himself. 7739: 7405: 7400: 7228: 7120: 7100: 6928: 6485: 6455: 6154: 6033: 5968: 5948: 5779:– at Paul Stoddard's Animated Virtual Planetarium, Northern Illinois University 4993: 4287: 3854: 3835: 3705: 3548: 3412:"New evidence for Hipparchus' star catalogue revealed by multispectral imaging" 3197: 3148: 2936: 2791: 2158: 1991: 1875:

is also noteworthy for being the only one of Ptolemy's works that is devoid of

1856: 1811: 1806: 1672: 1616: 1582: 1536:. Thus explanations of a sort are provided for the astrological effects of the 1494:

Ptolemy wrote an astrological treatise, in four parts, known by the Greek term

1430: 1389: 1348: 1271: 1204: 1177: 1172: 1041: 974: 921: 878: 846: 792: 553: 454: 391: 350: 320: 285: 267: 141: 5818: 5782: 5235: 5171: 4336: 3901: 3437: 2847: 1252: 821:, is the only surviving comprehensive ancient treatise on astronomy. Although 7749: 7365: 7233: 7203: 7024: 6832: 6775: 6276: 6261: 6241: 5695: 5679: 5620: 5432: 4947: 4901: 4884: 4719: 4551: 4295: 4152: 3974: 3909: 3503: 3445: 3261: 3171: 3029: 2957: 2786: 2735:

Heilen, Stephan (2010). "Ptolemy's doctrine of the terms and its reception".

2548: 2470: 1948: 1815: 1664: 1578: 1122: 854: 738: 599:. Almost all subsequent pharaohs of Egypt, with a few exceptions, were named 576: 535: 505: 371:, which is a thorough discussion on maps and the geographic knowledge of the 304: 145: 6359: 4636:

Ross, H.E.; Ross, G.M. (1976). "Did Ptolemy understand the moon illusion?".

1532:

was the first, concerned with the influences of the celestial bodies in the

1400:. One of the places Ptolemy noted specific coordinates for was the now-lost 504:. He had a Latin name, Claudius, which is generally taken to imply he was a 7703: 7307: 7095: 6770: 6530: 6520: 6124: 5973: 5761: 5629: 5425: 5057: 3479: 3394:

On the quality of solar and lunar observations and parameters in Ptolemy's

2931: 1844: 1643: 1628: 1569: 1397: 1333: 1305: 1256:

A printed map from the 15th century depicting Ptolemy's description of the

969: 886: 615: 501: 440: 137: 5851: 5741: 2084:(in Latin). Paris: Sebastian Cramoisy (1.) & Sebastian Mabre-Cramoisy. 1788:). In it, Ptolemy writes about properties of sight (not light), including 1417: 6921: 6809: 6515: 6500: 5963: 5908: 5158: 4870:

Strategies of Argument: Essays in ancient ethics, epistemology, and logic

4659: 4047:

The Stone Tower: Ptolemy, the silk road, and a 2,000 year-old riddle

3666: 2909: 1888: 1766: 1734: 1639: 1496: 1477: 726: 687: 678: 604: 542:

showing an early conflation of the mathematician with the royal house of

458: 421: 416: 4727: 3917: 3410:

Gysembergh, Victor; Williams, Peter J.; Zingg, Emanuel (November 2022).

1308:

known at the time. He relied on previous work by an earlier geographer,

1020: 375:. The third is the astrological treatise in which he attempted to adapt 6907: 6826: 6765: 6760: 6700: 6685: 6630: 6615: 6570: 6510: 6495: 6475: 6445: 6410: 6281: 6098: 6043: 6003: 5933: 5606: 5179: 4885:"Meta-mathematical rhetoric: Hero and Ptolemy against the philosophers" 4805: 4711: 4303: 4160: 3946:"Lines, damned lines and statistics: Unearthing structure in Ptolemy's 3649:"Modeling the heavens: Sphairopoiia and Ptolemy's planetary hypotheses" 3648: 3633: 3048: 2218: 2169: 1848: 1827: 1793: 1684: 1668: 1541: 1367: 1321: 940: 929: 850: 830: 662:

were wise "and included Ptolemy the Wise, who composed the book of the

493: 436: 316: 312: 308: 124: 7734: 4955: 4197: 3990:

Mittenhuber, F. (2010). "The tradition of texts and maps in Ptolemy's

3467: 2965: 1911:

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

1548:(interpreting astrological charts to determine courses of action) and 1429:

spanned 180 degrees of longitude from the Blessed Islands in the

658:, stating that the descendants of the Alexandrine general and Pharaoh 6660: 6645: 6595: 6490: 6480: 6465: 6435: 6185: 6038: 6028: 6013: 5958: 5953: 5898: 5845: 5819:

Codex Vaticanus graecus 1291 (Vat.gr.1291) in Vatican Digital Library

5222: 4598:

Ptolemy's Theory of Visual Perception: An English translation of the

4274: 2147: 1941: 1892: 1719: 1692: 1655: 1405: 1393: 1313: 1065: 829:

The earliest person that attempted to merge these two approaches was

279: 215: 211: 207: 148: 5621:

Hieronymi Cardani ... In Cl. Ptolemaei ... IIII De astrorum judiciis

5215: 4651: 4034:(Report). Orbis Terrarum. Vol. 9 (2003–2007). pp. 177–180. 3625: 877:(lit. "The greatest treatise"), as the work was presumably known in 6797: 6575: 6420: 6286: 6114: 5978: 5821:- Complete reproduction of the 9th century manuscript of Ptolemy's 4939: 4504: 4189: 4112:. Loeb Classical Library. Cambridge, MA: Harvard University Press. 3103: 2949: 2932:"The adaptation of Babylonian methods in Greek numerical astronomy" 2804: 1884: 1564: 1438: 1375: 1160: 1140: 1077: 982: 817: 779: 768: 672: 645: 634: 462: 449: 341: 324: 186: 5600: 2755:

Robbins, Frank E. (1940). "Introduction". In Robbins, F.E. (ed.).

2131:— medieval Arabic translations and an English translation of those 1396:

day increases from 12h to 24h as one goes from the equator to the

733:. He might have been a Roman citizen, but was ethnically either a 339:

science. The first was his astronomical treatise now known as the

7370: 6690: 6590: 6580: 6555: 6190: 6053: 5998: 5988: 4364: 2153: 1537: 1379: 1258: 1164: 588: 526: 482: 5700:"Cartographic Images of the World on the Eve of the Discoveries" 4317:

Crickmore, L. (2003). "A re-valuation of the ancient science of

3032:(1936). "The Unity and Diversity of the Mediterranean World", 435:

promoted his work, which included the only mathematically sound

6665: 6540: 6301: 6251: 6200: 6073: 5923: 2142: 1851:

discussions across his corpus. He wrote a short essay entitled

1797: 1738: 1688: 1676: 1442: 1332:

based on scientific principles had been made since the time of

1118: 707: 683: 531: 219: 182: 5670:, Supplementband 21,2. Teubner, Leipzig, pp. 49–244. 5647: 5437:"Scandal in the Heavens: Renowned Astronomer Accused of Fraud" 5242:

Peerlings, R.H.J., Laurentius F., van den Bovenkamp J.,(2018)

5191:. Vol. I–III. Berlin, DE / New York, NY: Springer Verlag. 4823:. Cambridge, UK: Cambridge University Press. pp. 499–528. 4769:

From Sight to Light: The passage from ancient to modern optics

4685:. Cambridge, UK: Cambridge University Press. pp. 217–247. 4214:

Dialogues among Books in Medieval Western Magic and Divination

3877: 3875: 3873: 1577:

as a kind of summation. It is now believed to be a much later

7041: 7019: 6675: 5323:— This is the only complete English translation of Ptolemy's 4790:

Riley, M. (1995). "Ptolemy's use of his predecessors' data".

3597: 1434: 1384: 691: 558: 271: 2789:(1992). "Animadversions on the origins of western science". 1408:, and which scholars have been trying to locate ever since. 943:

and they debunked accusations made by the French astronomer

3870: 1930: 1920: 1593: 1329: 869:

was preserved, like many extant Greek scientific works, in

638: 258: 252: 7698: 5632:

From the Rare Book and Special Collection Division at the

5623:

From the Rare Book and Special Collection Division at the

4086:

Rutkin, H. Darrel (2010). "The use and abuse of Ptolemy's

2881:

A Sourcebook for Ancient Greek: Grammar, Poetry, and Prose

2834:. In Rahman, Shahid; Street, Tony; Tahiri, Hassan (eds.). 1631:

and the mathematics behind musical scales in three books.

246: 3881: 3833: 3238:

and some geometrical mechanisms to the era of Copernicus"

1804:

and influenced the more famous and superior 11th-century

1671:(combinations of four pitch ratios which together make a 1382:, as it is today, but Ptolemy preferred to express it as 995: 5721:"Κλαυδιου Πτολεμιου: Γεωγραφικῆς Ύφηγήσεως (Geographie)" 4452:

Studies in History and Philosophy of Science Part A

4248:

Music, Experiment, and Mathematics in England, 1653–1705

3328: 3326: 2014:(in Latin). Venezia: Ottaviano Scoto (1.) eredi & C. 948:

had claimed. Scientists analyzing the charts concluded:

492:

It is known that Ptolemy lived in or around the city of

5723:(in German and English). Frank Haselein. Archived from 5567:

Extracts of Ptolemy on the country of the Seres (China)

5336:

Ptolemaios, Handbuch der Geographie, Griechisch-Deutsch

4966:(2000). Berggren, J. Lennart; Jones, Alexander (eds.). 4864:

Schiefsky, M.J. (2014). "The epistemology of Ptolemy's

3409: 2150:– Ptolemy Cluster, star cluster described by Ptolemaeus 453:) never ceased to be copied or commented upon, both in 5334:(2006). Stückelberger, Alfred; Graßhoff, Gerd (eds.). 4972:: An annotated translation of the theoretical chapters 4920:

Bagrow, L. (1 January 1945). "The origin of Ptolemy's

2530:. Springer Science & Business Media. p. 834. 1975:, the graphs whose distances obey Ptolemy's inequality 1421:) and of the Roman provinces, including the necessary 1366:

of these places and geographic features have assigned

1100:

while the radius of the sphere of the fixed stars was

7639: 4793:

Transactions of the American Philological Association

4771:. The University of Chicago Press. pp. 116–118. 4177:

Transactions of the American Philological Association

3338: 3323: 2750: 2748: 2746: 1072:. Ptolemy goes beyond the mathematical models of the 3313: 3311: 3309: 2161:– a dated list of kings used by ancient astronomers. 1867:

or soul, particularly its ruling faculty (i.e., the

249: 243: 5578:

The complete text of Heiberg's edition (PDF) Greek.

5003:

Quarterly Journal of the Royal Astronomical Society

4251:. London, UK / New York, NY: Routledge. p. 7. 3296: 3294: 3292: 3290: 3288: 3286: 3284: 2257: 2255: 2253: 2251: 1203:Ptolemy also erected an inscription in a temple at 358: 255: 240: 5511: 5303:Transactions of the American Philosophical Society 5018:– via The SAO/NASA Astrophysics Data System. 4840:Ptolemy's Philosophy: Mathematics as a way of life 4067: 3836:"Ptolemy's treatise on the meteoroscope recovered" 3737:Evans, James; Berggren, J. Lennart (5 June 2018). 3613:Transactions of the American Philosophical Society 2743: 2280: 783:in Arabic translation showing astronomical tables. 690:", suggesting he may have had origins in southern 5658:. Vol. 22 (11th ed.). pp. 618–626. 5265: 4140:Proceedings of the American Philosophical Society 3698:Ptolemy's Science of the Stars in the Middle Ages 3306: 3220:Astronomies and Cultures in Early Medieval Europe 3106:. The International Journal of Scientific History 424:meaning "Four Books", or by its Latin equivalent 7747: 5764:. Center for Spatially Integrated Social Science 4821:Perceptual Constancy: Why things look as they do 4133:Riley, M. (1988). "Science and tradition in the 3985: 3983: 3281: 3231: 2248: 1741:in his own musings on the harmony of the world ( 621:; the peculiar multipart form of the whole name 5105:The complete existing works of Claudius Ptolemy 4103: 4101: 3939: 3937: 3935: 1500:(lit. "Four Books") or by its Latin equivalent 1008:Arrangement and Calculation of the Handy Tables 849:, which is a version of a catalogue created by 607:in 30 BC, ending the Macedonian family's rule. 530:Engraving of a crowned Ptolemy being guided by 5638: 5478: 5346:] (in German). Basel, CH: Schwabe Verlag. 5210:] (in Latin). Leipzig: Carolus Tauchnitus. 4026: 2781: 2779: 2730: 2728: 2569: 2112:(in Latin). Oxford, UK: Theatrum Sheldonianum. 2056:(in Latin). Frankfurt am Main: Johann Bringer. 1800:. The work is a significant part of the early 6389: 6375: 5867: 5195: 5101:Claudius Ptolemaeus, Opera quae exstant omnia 4590: 4588: 3980: 3736: 3222:, Cambridge: Cambridge Univ. Pr. pp. 20–21. 2925: 2923: 2579:(Doctoral thesis). Universitat de Barcelona. 2449: 2447: 1520:(Tiburtinus) in 1138, while he was in Spain. 1266:Ptolemy's second most well-known work is his 629:. Gerald Toomer, the translator of Ptolemy's 5759: 5668:Neue Jahrbücher für Philologie und Pädagogik 5087:: CS1 maint: multiple names: authors list ( 4872:. Oxford University Press. pp. 301–331. 4832: 4830: 4564: 4429: 4427: 4098: 3932: 3172:"The enigma of Ptolemy's catalogue of stars" 2985: 2983: 2914:Episodes from the Early History of Astronomy 2836:The Unity of Science in the Arabic Tradition 2597: 2417: 2415: 2413: 2411: 2383: 2381: 2379: 2377: 1388:, the length of the longest day rather than 51:Roman astronomer and geographer (c. 100–170) 5881: 5784:Animation of Ptolemy's two Solar hypotheses 5189:A History of Ancient Mathematical Astronomy 4029:Hipparchus' table of climata and Ptolemy's 3989: 3769:Planispherium. Ptolemaeus Arabus et Latinus 3276:Studies in the History of Mediaeval Science 2776: 2725: 2702: 2557:Complete Dictionary of Scientific Biography 2547: 2527:A History of Ancient Mathematical Astronomy 2479:Complete Dictionary of Scientific Biography 2469: 1279: 1185: 1049: 800: 654:mistakenly presents Ptolemy as a member of 399: 386:of his day. This is sometimes known as the 15: 6382: 6368: 5874: 5860: 5828: 5330: 5310: 5249: 5186: 5130: 5095: 4962: 4585: 3356: 2920: 2842:/ Springer Netherlands. pp. 183–225. 2717:: CS1 maint: location missing publisher ( 2520: 2453: 2444: 2102: 2095:De iudicandi facultate et animi principatu 2088: 2081:De iudicandi facultate et animi principatu 2074: 2060: 2046: 2032: 2018: 2004: 1691:, which he derived experimentally using a 1320:. He also acknowledged ancient astronomer 757:have significant references to astronomy. 682:as its astrological counterpart. In later 78: 16: 5314:(1991) . Stevenson, Edward Luther (ed.). 5255:Die Harmonielehre des Klaudios Ptolemaios 5022: 4992: 4900: 4863: 4827: 4565:Hetherington, Norriss S. (8 April 2014). 4528:"Philosophical presentation in Ptolemy's 4424: 4360:"Greek musicologists in the Roman Empire" 4316: 4244: 4090:in Renaissance and early modern Europe". 3853: 3814: 3609: 3344: 3332: 3242:Repositorio Institucional CONICET Digital 3124: 3079:The Globalization of Knowledge in History 3075: 2992:A History of Mathematics: An introduction 2980: 2916:. New York, NY: Springer. pp. 62–65. 2877: 2408: 2374: 2207:unsupported." — Toomer & Jones (2018) 1404:which marked the midpoint on the ancient 1324:for having provided the elevation of the 521: 327:, three of which were important to later 5739: 5718: 5498: 4818: 4635: 3524: 3234:"Notes on the transmission of Ptolemy's 3169: 2183: 1951:used in the mathematics courses at both 1592: 1481: 1437:, and about 80 degrees of latitude from 1251: 1019: 772: 525: 24:This is an accepted version of this page 5777:Java simulation of the Ptolemaic System 5479:Sidoli, Nathan; Berggren, J.L. (2007). 4107: 3943: 3391: 2754: 2433:Science of the Stars in the Middle Ages 2337: 2301:10.1093/gmo/9781561592630.article.22510 2278: 1300:, a handbook on how to draw maps using 1207:, around 146–147 AD, known as the 1125:one, presumably for didactic purposes. 1013: 760: 14: 7748: 7411:Latin translations of the 12th century 5803:Flash animation of Ptolemy's universe. 5702:. The Newberry Library. Archived from 5694: 5673: 5375: 4919: 4484: 4357: 4271: 4210: 4085: 4073: 4049:. Delhi, IN: Penguin Viking. pp. 3687: 3023: 2825: 2785: 2734: 2686: 2633: 2116: 2042:(in Latin). Basel, CH: Heinrich Petri. 1906: 1425:lists, and captions for the maps. His 1002:Additionally, the introduction to the 896: 7871:Epigrammatists of the Greek Anthology 7141:Straightedge and compass construction 6363: 5855: 5678:. obs.nineplanets.org. Archived from 5542:Ptolemy's Tetrabiblos at LacusCurtius 5294:Ptolemy's Theory of Visual Perception 5291: 5151: 5072: 4789: 4766: 4754:The Rainbow: From myth to mathematics 4748: 4699:Archive for History of Exact Sciences 4695: 4680: 4594: 4525: 4173: 4132: 3889:Archive for History of Exact Sciences 3841:Archive for History of Exact Sciences 3784: 3763: 3477: 3317: 3232:Krisciunas, K.; Bistué, M.B. (2019). 3019:. Encyclopædia Britannica, Inc. 2006. 2929: 2908: 2499: 2421: 2387: 1585:, remains the subject of conjecture. 7106:Incircle and excircles of a triangle 5509: 5431: 5148:— Latin text with French translation 4882: 4836: 4433: 4398: 4044: 3815:Nalewicki, Jennifer (7 April 2023). 3791:and Heliodorus' observation reports" 3646: 3528:Journal for the History of Astronomy 3484:Journal for the History of Astronomy 3417:Journal for the History of Astronomy 3300: 3177:Journal for the History of Astronomy 3128:Journal for the History of Astronomy 2989: 2660: 2506:. Oxford: Clarendon Press. pp. 2394:. Archimedes. Springer Netherlands. 2098:(in Latin). Den Haag: Adriaen Vlacq. 2070:(in Latin). Padova: Paolo Frambotto. 1638:the ideas advocated by followers of 1464:(after the text was rediscovered by 906:observations were taken at 12:30pm. 686:sources, he was often known as "the 477:wrote that Ptolemy's birthplace was 5796:– at Rosemary Kennett's website at 5561:Ptolemy's Geography at LacusCurtius 5556:of J.M. Ashmand's 1822 translation. 5300:with introduction and commentary". 4540:Greek, Roman, and Byzantine Studies 4245:Wardhaugh, Benjamin (5 July 2017). 3690:"Mathematical Methods in Ptolemy's 3464:Ptolemaeus Arabus et Latinus, Works 2129:(in Latin) – via sciamvs.org. 2039:In Claudii Ptolemaei Quadripartitum 1457:in surviving manuscripts date from 719: 447:, Ptolemy's writings (foremost the 323:who wrote about a dozen scientific 48: 5471: 5428:, 1998. Princeton University Press 5389:Dictionary of Scientific Biography 4606:The American Philosophical Society 3592:video file format. The video file 3379:10.1111/j.1600-0498.1976.tb00923.x 2553:"Ptolemy (or Claudius Ptolemaeus)" 2475:"Ptolemy (or Claudius Ptolemaeus)" 2028:(in Latin). Basel: Heinrich Petri. 614:is a Roman name, belonging to the 120: 170 (aged 69–70) 49: 7882: 5563:(English translation, incomplete) 5534: 5518:. Chicago, IL: Open Court Press. 5246:, In Quaerendo 48: 139–162, 2018. 5152:Lewis, H.A.G. (1979). "Review of 2570:Tolsa Domènech, Cristian (2013). 2234:exist. — V.J. Katz (1998, p. 184) 1679:. Ptolemy reviewed standard (and 826:ability to make any predictions. 414:) but more commonly known as the 7733: 7721: 7709: 7697: 7685: 7673: 7661: 7649: 7623: 7610: 5742:"The life & work of Ptolemy" 5296:: An English translation of the 5253:(1980) . Düring, Ingemar (ed.). 5099:(1998). Hübner, Wolfgang (ed.). 3569: 3399:(Ph.D. thesis). Yale University. 1853:On the Criterion and Hegemonikon 1607:Ptolemy's intense diatonic scale 1370:so that they can be placed in a 810:Mathematical Systematic Treatise 729:, and can be shown to have used 485:region of Egypt (now El Mansha, 236: 167:Ptolemy's intense diatonic scale 5829:Papaspirou, Panagiotis (2014). 5386:. In Gillispie, Charles (ed.). 4876: 4857: 4812: 4783: 4760: 4742: 4689: 4674: 4629: 4558: 4519: 4478: 4392: 4351: 4310: 4265: 4238: 4204: 4167: 4126: 4108:Robbins, Frank E., ed. (1940). 4079: 4038: 4020: 3967: 3827: 3808: 3778: 3757: 3730: 3681: 3640: 3603: 3563: 3518: 3471: 3452: 3403: 3392:Britton, John Phillips (1967). 3385: 3350: 3268: 3225: 3212: 3163: 3118: 3096: 3069: 3042: 3017:Britannica Concise Encyclopedia 3008: 2994:. Addison Wesley. p. 184. 2902: 2871: 2840:Springer Science+Business Media 2819: 2773:, p. 177. Wittenberg: Gottlieb. 2763: 2696: 2680: 2663:"Egypt in the Ptolemaic Period" 2654: 2627: 2591: 2563: 2514: 2493: 2211: 1710:never had the influence of his 1138:diagram that Ptolemy calls the 989:'s version. Although Ptolemy's 960: 656:Ptolemaic Egypt's royal lineage 7796:2nd-century Greek philosophers 7443:A History of Greek Mathematics 6956:The Quadrature of the Parabola 5424:, Translated and annotated by 5381:"Ptolemy (Claudius Ptolemæus)" 5077:. Oxford, UK: Clarendon Press. 5075:A History of Greek Mathematics 5050:10.1126/science.199.4331.872.a 4974:. Princeton, NJ / Oxford, UK: 4843:. Princeton University Press. 3743:. Princeton University Press. 3057:University of California Press 2650:– via perseus.tufts.edu. 2605:. Springer. pp. 309–372. 2503:A History of Greek Mathematics 2463: 2331: 2272: 2192: 1969:, to non-cyclic quadrilaterals 1611:Ptolemy wrote a work entitled 1555:The great popularity that the 1235: 1128: 13: 1: 7831:Ancient Greek music theorists 6272:Inferior and superior planets 5154:The Crime of Claudius Ptolemy 5030:The Crime of Claudius Ptolemy 4027:Shcheglov, D.A. (2002–2007). 2242: 2199: 1861:Περὶ Κριτηρίου καὶ Ἡγεμονικοῡ 1838: 1782: 1458: 1441:to anti-Meroe (east coast of 1337: 1262:by Johannes Schnitzer (1482). 915:The Crime of Claudius Ptolemy 605:Egypt became a Roman province 512: 293: 116: 101: 7826:Ancient Greek mathematicians 7224:Intersecting secants theorem 5463:10.1126/science.198.4318.707 4536:as a model for organization" 4378:10.1515/APEIRON.1994.27.4.53 3458:Juste, D. (2021). Ptolemy, 2551:; Jones, Alexander (2018) . 2473:; Jones, Alexander (2018) . 2360:10.1515/APEIRON.1994.27.4.75 2325:UK public library membership 1563:A collection of one hundred 1471: 744: 731:Babylonian astronomical data 468: 280: 7: 7781:2nd-century Egyptian people 7219:Intersecting chords theorem 7086:Doctrine of proportionality 5805:(best in Internet Explorer) 5196:Nobbe, C.F.A., ed. (1843). 5134:(1989). Lejeune, A. (ed.). 5073:Heath, Thomas, Sir (1921). 5028:"Casting doubt on Ptolemy: 4472:10.1016/j.shpsa.2012.06.006 4004:10.1007/978-90-481-2788-7_4 2611:10.1007/978-3-662-04441-4_7 2135: 1737:, Ptolemy's ideas inspired 1567:about astrology called the 1523:Much of the content of the 1328:for a few cities. Although 595:, the first pharaoh of the 583:upper class at the time of 569:ancient Greek personal name 511:Ptolemy died in Alexandria 359: 10: 7887: 7801:2nd-century mathematicians 6915:On the Sphere and Cylinder 6868:On the Sizes and Distances 6349:Medieval Islamic astronomy 6146:On the Sizes and Distances 5835:Macedonian Studies Journal 5794:Epicycle and deferent demo 5760:Sprague, Ben (2001–2007). 5740:Houlding, Deborah (2003). 4976:Princeton University Press 4912: 4288:10.1163/156852894321052135 3855:10.1007/s00407-022-00302-w 3706:10.1484/M.PALS-EB.5.120173 3578:(academic pers. website). 3549:10.1177/002182869502600102 3198:10.1177/002182869202300303 3149:10.1177/002182869702800101 2667:Metropolitan Museum of Art 2500:Heath, Sir Thomas (1921). 1965:, and its generalization, 1754: 1604: 1475: 1289:Guide to Drawing the Earth 1245: 1239: 1182:Ἅπλωσις ἐπιφανείας σφαίρας 1153:Risings of the Fixed Stars 1117:perspective, much like an 1090:(now known to actually be 924:, while agreeing that the 853:. Its list of forty-eight 766: 579:. It was common among the 559: 546:, with the same last name. 272: 53: 7841:Ancient Roman geographers 7821:Ancient Greek geographers 7816:Ancient Greek astronomers 7811:Ancient Greek astrologers 7617:Ancient Greece portal 7606: 7556: 7434: 7421:Philosophy of mathematics 7391: 7384: 7358: 7336:Ptolemy's table of chords 7280: 7262: 7161: 7154: 7010: 6972: 6789: 6397: 6391:Ancient Greek mathematics 6339:Medieval European science 6331: 6310: 6219: 6168: 6107: 6069:Sosigenes the Peripatetic 5889: 5502:The Earliest Printed Maps 5236:10.1163/15700690-12341392 5187:Neugebauer, Otto (1975). 5172:10.1080/03085697908592494 4568:Encyclopedia of Cosmology 4337:10.1177/03057356030314004 3902:10.1007/s00407-017-0194-7 3438:10.1177/00218286221128289 3053:The Age of Reconnaissance 2930:Jones, Alexander (1991). 2848:10.1007/978-1-4020-8405-8 2705:De magnis coniunctionibus 2165:Ptolemy's table of chords 1860: 1750: 1620: 1411:In the third part of the 1316:of the Roman and ancient 1275: 1181: 1110:the radius of the Earth. 1059:Hypotheses of the Planets 1045: 978: 796: 395: 354: 225: 203: 196: 171:Ptolemy's table of chords 154: 132: 112: 97: 77: 72: 65: 7288:Aristarchus's inequality 6861:On Conoids and Spheroids 5719:Haselein, Frank (2007). 5644:Beazley, Charles Raymond 5510:Taub, Liba Chia (1993). 4902:10.1016/j.hm.2014.02.002 4868:". In Lee, M.-K. (ed.). 3580:Florida State University 3504:10.1177/0021828617706254 3480:"Ptolemy's Handy Tables" 3218:S.C. McCluskey, 1998, 2990:Katz, Victor J. (1998). 2176: 1998: 1588: 1374:that spanned the globe. 1302:geographical coordinates 1195:Flattening of the sphere 1046:Ὑποθέσεις τῶν πλανωμένων 706:referred to his name in 56:Ptolemy (disambiguation) 31:latest accepted revision 7866:Egyptian mathematicians 7791:2nd-century geographers 7776:2nd-century astronomers 7396:Ancient Greek astronomy 7209:Inscribed angle theorem 7199:Greek geometric algebra 6854:Measurement of a Circle 6064:Sosigenes of Alexandria 5883:Ancient Greek astronomy 5655:Encyclopædia Britannica 5640:Bunbury, Edward Herbert 5548:'s English translation) 5505:. British Museum Press. 5269:; Solomon, Jon (2000). 4595:Smith, A. Mark (1996). 4408:Oxford University Press 4400:West, Martin Litchfield 3688:Sidoli, Nathan (2020). 3654:Perspectives on Science 3274:Charles Homer Haskins, 3170:Swerdlow, N.M. (1992). 2826:Tahiri, Hassan (2008). 2388:Jones, A., ed. (2010). 2293:Oxford University Press 2279:Richter, Lukas (2001). 2267:Encyclopædia Britannica 1747:, Appendix to Book V). 1649:Ptolemy introduces the 1552:, for similar reasons. 1347:), Ptolemy improved on 815:), better known as the 498:Roman province of Egypt 303:AD) was an Alexandrian 84:Portrait of Ptolemy by 7630:Mathematics portal 7416:Non-Euclidean geometry 7371:Mouseion of Alexandria 7244:Tangent-secant theorem 7194:Geometric mean theorem 7179:Exterior angle theorem 7174:Angle bisector theorem 6878:On Sizes and Distances 6136:On Sizes and Distances 5813:University of Oklahoma 5809:High resolution images 5630:Almagestū Cl. Ptolemei 5546:Loeb Classical Library 5544:(Transcription of the 5358:— Massive 2 vol, 4998:"Was Ptolemy a fraud?" 2878:Tomarchio, J. (2022). 2769:J. F. Weidler (1741). 1701:harmony of the spheres 1602: 1491: 1378:was measured from the 1354:The first part of the 1268:Geographike Hyphegesis 1263: 1121:would have done for a 1033: 958: 823:Babylonian astronomers 784: 547: 540:Margarita Philosophica 522:Naming and nationality 481:, a Greek city in the 345:, originally entitled 289: 7318:Pappus's area theorem 7254:Theorem of the gnomon 7131:Quadratrix of Hippias 7054:Circles of Apollonius 7002:Problem of Apollonius 6980:Constructible numbers 6804:Archimedes Palimpsest 6247:Deferent and epicycle 6176:Antikythera mechanism 5674:Arnett, Bill (2008). 5569:(English translation) 5499:Campbell, T. (1987). 5292:Smith, A.M. (1996). " 5024:Goldstein, Bernard R. 3572:"Ptolemy's cosmology" 2884:. CUA Press. p. 2703:Ma'shar, Abu (2000). 2661:Hill, Marsha (2006). 2424:"The ancient Ptolemy" 2340:"The teaching of the 1596: 1485: 1255: 1246:Further information: 1147:In another work, the 1023: 950: 891:scientific revolution 776: 652:Abu Ma'shar al-Balkhi 529: 475:Theodore Meliteniotes 365:). The second is the 347:Mathematical Treatise 127:, Egypt, Roman Empire 7856:Egyptian astronomers 7846:Astrological writers 7534:prehistoric counting 7331:Ptolemy's inequality 7272:Apollonius's theorem 7111:Method of exhaustion 7081:Diophantine equation 7071:Circumscribed circle 6888:On the Moving Sphere 6318:Babylonian astronomy 6009:Hippocrates of Chios 5727:on 18 September 2008 5706:on 27 September 2011 5662:Franz Boll (1894), " 5368:academic edition of 5332:Ptolemaios, Claudius 5312:Ptolemaios, Claudius 5267:Ptolemaios, Claudius 5251:Ptolemaios, Claudius 5132:Ptolemaios, Claudius 5097:Ptolemaios, Claudius 5026:(24 February 1978). 4964:Ptolemaios, Claudius 4889:Historia Mathematica 4767:Smith, Mark (2015). 3944:Isaksen, L. (2011). 3667:10.1162/POSC_a_00214 2771:Historia astronomiae 2644:A Homeric Dictionary 2338:Pingree, D. (1994). 2118:Ptolemaios, Claudius 2104:Ptolemaios, Claudius 2090:Ptolemaios, Claudius 2076:Ptolemaios, Claudius 2062:Ptolemaios, Claudius 2048:Ptolemaios, Claudius 2034:Ptolemaios, Claudius 2020:Ptolemaios, Claudius 2006:Ptolemaios, Claudius 1967:Ptolemy's inequality 1963:cyclic quadrilateral 1955:campuses in the U.S. 1699:), and the planets ( 1546:electional astrology 1392:: The length of the 1326:north celestial pole 1038:Planetary Hypotheses 1026:Planetary Hypotheses 1015:Planetary Hypotheses 789:Mathēmatikē Syntaxis 762:Mathēmatikē Syntaxis 571:. It occurs once in 550:Ptolemy's Greek name 445:Greek mathematicians 377:horoscopic astrology 361:Mathēmatikḗ Syntaxis 175:Ptolemy's inequality 54:For other uses, see 7620: • 7426:Neusis construction 7346:Spiral of Theodorus 7239:Pythagorean theorem 7184:Euclidean algorithm 7126:Lune of Hippocrates 6995:Squaring the circle 6751:Theon of Alexandria 6426:Aristaeus the Elder 6089:Theon of Alexandria 5798:Syracuse University 5634:Library of Congress 5625:Library of Congress 5455:1977Sci...198..707W 5205:Claudius Ptolemy's 5156:, by R.R. Newton". 5032:. Robert R. Newton" 5016:1980QJRAS..21..253G 4927:Geografiska Annaler 4777:2014fslp.book.....S 4492:Classical Philology 4464:2012SHPSA..43..585F 4404:Ancient Greek Music 4358:Barker, A. (1994). 4324:Psychology of Music 4110:Ptolemy Tetrabiblos 4045:Dean, Riaz (2022). 3789:Canobic Inscription 3586:on 7 November 2009. 3541:1995JHA....26...33M 3496:2017JHA....48..238J 3430:2022JHA....53..383G 3371:1976Cent...20...89B 3254:2019JAHH...22..492K 3190:1992JHA....23..173S 3141:1997JHA....28....1G 2757:Ptolemy Tetrabiblos 2634:Autenrieth, Georg. 2599:Pecker, Jean Claude 2559:. Encyclopedia.com. 2522:Neugebauer, Otto E. 2438:New York University 1907:Named after Ptolemy 1779:Eugenius of Palermo 1706:Although Ptolemy's 1462: 1300 AD 1276:Γεωγραφικὴ Ὑφήγησις 1248:Ptolemy's world map 1242:Geography (Ptolemy) 1209:Canobic Inscription 987:Theon of Alexandria 897:Modern reassessment 883:in the 12th century 875:Hē Megistē Syntaxis 797:Μαθηματικὴ Σύνταξις 623:Claudius Ptolemaeus 585:Alexander the Great 355:Μαθηματικὴ Σύνταξις 290:Claudius Ptolemaeus 163:Ptolemy's world map 73:Κλαύδιος Πτολεμαῖος 21:Page version status 7836:Ancient occultists 7786:2nd-century Romans 7771:1st-century Romans 7313:Menelaus's theorem 7303:Irrational numbers 7116:Parallel postulate 7091:Euclidean geometry 7059:Apollonian circles 6601:Isidore of Miletus 6323:Egyptian astronomy 6237:Circle of latitude 5676:"Ptolemy, the Man" 5422:Ptolemy's Almagest 5342:Geography Handbook 5316:Claudius Ptolemy: 5198:Claudii Ptolemaei 4712:10.1007/BF00348501 4526:Tolsa, C. (2015). 3785:Jones, A. (2005). 3764:Juste, D. (2021). 3700:. pp. 35–77. 3576:scs.fsu.edu/~dduke 3478:Jones, A. (2017). 2481:. Encyclopedia.com 2440:/ archive.nyu.edu. 2422:Jones, A. (2020). 2344:in late antiquity" 2288:Grove Music Online 2109:Harmonicorum libri 1961:on distances in a 1953:St. John's College 1901:Hero of Alexandria 1661:Pythagorean tuning 1603: 1599:Pythagorean tuning 1597:A diagram showing 1492: 1264: 1155:), Ptolemy gave a 1034: 889:models during the 785: 696:Arabic astronomers 548: 443:, and unlike most 384:natural philosophy 159:Ptolemaic universe 27: 7861:Egyptian calendar 7806:2nd-century poets 7637: 7636: 7602: 7601: 7354: 7353: 7341:Ptolemy's theorem 7214:Intercept theorem 7064:Apollonian gasket 6990:Doubling the cube 6963:The Sand Reckoner 6357: 6356: 6232:Celestial spheres 5449:(4318): 707–709. 5399:978-0-684-10114-9 5377:Toomer, Gerald J. 5353:978-3-7965-2148-5 5122:978-3-598-71746-8 5044:(4331): 872–873. 4883:Feke, J. (2014). 4850:978-0-691-17958-2 4837:Feke, J. (2018). 4578:978-1-317-67766-6 4434:Feke, J. (2012). 4258:978-1-351-55708-5 4053:, 135, 148, 160. 4013:978-90-481-2788-7 3750:978-0-691-18715-0 3715:978-2-503-58639-7 3647:Hamm, E. (2016). 3089:978-3-945561-23-2 3049:John Horace Parry 2857:978-1-4020-8404-1 2537:978-3-540-06995-9 2401:978-90-481-2787-0 2323:(subscription or 2310:978-1-56159-263-0 1959:Ptolemy's theorem 1802:history of optics 1728:compromise tuning 1579:pseudepigraphical 1550:medical astrology 1433:to the middle of 1304:for parts of the 979:Πρόχειροι κανόνες 934:Bernard Goldstein 913:in his 1977 book 725:Ptolemy wrote in 597:Ptolemaic Kingdom 487:Sohag Governorate 479:Ptolemais Hermiou 373:Greco-Roman world 229: 228: 198:Scientific career 179:Ptolemy's theorem 39:19 September 2024 18: 7878: 7738: 7737: 7726: 7725: 7724: 7714: 7713: 7712: 7702: 7701: 7690: 7689: 7688: 7678: 7677: 7676: 7666: 7665: 7654: 7653: 7652: 7645: 7628: 7627: 7615: 7614: 7613: 7389: 7388: 7376:Platonic Academy 7323:Problem II.8 of 7293:Crossbar theorem 7249:Thales's theorem 7189:Euclid's theorem 7159: 7158: 7076:Commensurability 7037:Axiomatic system 6985:Angle trisection 6950: 6940: 6902: 6892: 6882: 6872: 6848: 6838: 6821: 6384: 6377: 6370: 6361: 6360: 6344:Indian astronomy 6297:Sublunary sphere 6267:Hipparchic cycle 6206:Mural instrument 6181:Armillary sphere 6160: 6150: 6140: 6130: 6120: 5876: 5869: 5862: 5853: 5852: 5842: 5785: 5773: 5771: 5769: 5756: 5754: 5752: 5736: 5734: 5732: 5715: 5713: 5711: 5691: 5689: 5687: 5659: 5651: 5611:codex valentinus 5609:. Also known as 5593: 5589: 5529: 5517: 5506: 5495: 5485: 5466: 5418: 5416: 5414: 5409:on 14 March 2012 5408: 5402:. Archived from 5385: 5367: 5365: 5364: 5357: 5322: 5307: 5288: 5275:Brill Publishers 5260: 5239: 5230:(3–4): 307–327. 5211: 5192: 5183: 5147: 5126: 5110: 5092: 5086: 5078: 5069: 5019: 4989: 4959: 4907: 4906: 4904: 4880: 4874: 4873: 4866:On the Criterion 4861: 4855: 4854: 4834: 4825: 4824: 4816: 4810: 4809: 4787: 4781: 4780: 4764: 4758: 4757: 4746: 4740: 4739: 4693: 4687: 4686: 4678: 4672: 4671: 4633: 4627: 4626: 4624: 4622: 4592: 4583: 4582: 4562: 4556: 4555: 4523: 4517: 4516: 4482: 4476: 4475: 4438:On the Kritêrion 4431: 4422: 4421: 4396: 4390: 4389: 4355: 4349: 4348: 4314: 4308: 4307: 4269: 4263: 4262: 4242: 4236: 4235: 4233: 4231: 4208: 4202: 4201: 4171: 4165: 4164: 4130: 4124: 4123: 4105: 4096: 4095: 4083: 4077: 4071: 4065: 4064: 4052: 4042: 4036: 4035: 4024: 4018: 4017: 3987: 3978: 3971: 3965: 3964: 3954: 3941: 3930: 3929: 3879: 3868: 3867: 3857: 3831: 3825: 3824: 3812: 3806: 3805: 3795: 3782: 3776: 3775: 3761: 3755: 3754: 3734: 3728: 3727: 3685: 3679: 3678: 3644: 3638: 3637: 3607: 3601: 3587: 3582:. Archived from 3567: 3561: 3560: 3522: 3516: 3515: 3475: 3469: 3456: 3450: 3449: 3407: 3401: 3400: 3389: 3383: 3382: 3354: 3348: 3342: 3336: 3330: 3321: 3315: 3304: 3298: 3279: 3272: 3266: 3265: 3229: 3223: 3216: 3210: 3209: 3167: 3161: 3160: 3122: 3116: 3115: 3113: 3111: 3104:"Dennis Rawlins" 3100: 3094: 3093: 3073: 3067: 3046: 3040: 3027: 3021: 3020: 3012: 3006: 3005: 2987: 2978: 2977: 2927: 2918: 2917: 2906: 2900: 2899: 2887: 2875: 2869: 2868: 2866: 2864: 2838:. Vol. 11. 2823: 2817: 2816: 2783: 2774: 2767: 2761: 2760: 2752: 2741: 2740: 2732: 2723: 2722: 2716: 2708: 2700: 2694: 2684: 2678: 2677: 2675: 2673: 2658: 2652: 2651: 2648:Tufts University 2639: 2631: 2625: 2624: 2595: 2589: 2588: 2578: 2567: 2561: 2560: 2541: 2518: 2512: 2511: 2509: 2497: 2491: 2490: 2488: 2486: 2467: 2461: 2454:Neugebauer (1975 2451: 2442: 2441: 2428: 2419: 2406: 2405: 2385: 2372: 2371: 2335: 2329: 2328: 2321: 2319: 2317: 2284: 2276: 2270: 2259: 2236: 2235: 2215: 2209: 2208: 2204: 2201: 2196: 2190: 2187: 2130: 2128: 2113: 2099: 2085: 2071: 2057: 2043: 2029: 2015: 1987:embedded systems 1973:Ptolemaic graphs 1873:On the Criterion 1862: 1787: 1784: 1773:), known as the 1772: 1757:Optics (Ptolemy) 1681:ancient, disused 1653:(Greek name) or 1622: 1534:sublunary sphere 1466:Maximus Planudes 1463: 1460: 1365: 1364: 1346: 1342: 1339: 1312:, as well as on 1294:), known as the 1293: 1290: 1287: 1284: 1281: 1277: 1227: 1223: 1199: 1196: 1193: 1190: 1187: 1183: 1109: 1107: 1106: 1099: 1097: 1096: 1089: 1087: 1086: 1070:celestial motion 1063: 1060: 1057: 1054: 1051: 1047: 1030:Bartolomeu Velho 980: 911:Robert R. Newton 845:also contains a 835:geometric models 814: 811: 808: 805: 802: 798: 721: 644:The 9th century 562: 561: 517: 514: 413: 410: 407: 404: 401: 397: 364: 356: 337:Western European 302: 298: 295: 283: 277: 276: 265: 264: 261: 260: 257: 254: 251: 248: 245: 242: 232:Claudius Ptolemy 121: 118: 103: 90:Pedro Berruguete 82: 63: 62: 7886: 7885: 7881: 7880: 7879: 7877: 7876: 7875: 7746: 7745: 7744: 7732: 7722: 7720: 7710: 7708: 7696: 7686: 7684: 7674: 7672: 7660: 7650: 7648: 7640: 7638: 7633: 7622: 7611: 7609: 7598: 7564:Arabian/Islamic 7552: 7541:numeral systems 7430: 7380: 7350: 7298:Heron's formula 7276: 7258: 7150: 7146:Triangle center 7136:Regular polygon 7013:and definitions 7012: 7006: 6968: 6948: 6938: 6900: 6890: 6880: 6870: 6846: 6836: 6819: 6785: 6756:Theon of Smyrna 6401: 6393: 6388: 6358: 6353: 6327: 6306: 6292:Spherical Earth 6227:Callippic cycle 6215: 6196:Equatorial ring 6164: 6158: 6148: 6138: 6128: 6118: 6103: 6094:Theon of Smyrna 5885: 5880: 5850: 5783: 5767: 5765: 5750: 5748: 5730: 5728: 5709: 5707: 5685: 5683: 5649:"Ptolemy" 5616: 5591: 5587: 5537: 5532: 5526: 5483: 5474: 5472:Further reading 5469: 5412: 5410: 5406: 5400: 5383: 5362: 5360: 5359: 5354: 5285: 5123: 5108: 5080: 5079: 4986: 4915: 4910: 4881: 4877: 4862: 4858: 4851: 4835: 4828: 4817: 4813: 4788: 4784: 4765: 4761: 4747: 4743: 4694: 4690: 4679: 4675: 4652:10.1068/p050377 4634: 4630: 4620: 4618: 4616: 4593: 4586: 4579: 4563: 4559: 4524: 4520: 4483: 4479: 4432: 4425: 4418: 4397: 4393: 4356: 4352: 4315: 4311: 4270: 4266: 4259: 4243: 4239: 4229: 4227: 4225: 4209: 4205: 4172: 4168: 4131: 4127: 4120: 4106: 4099: 4084: 4080: 4072: 4068: 4061: 4050: 4043: 4039: 4025: 4021: 4014: 3988: 3981: 3972: 3968: 3952: 3942: 3933: 3880: 3871: 3832: 3828: 3813: 3809: 3793: 3783: 3779: 3762: 3758: 3751: 3735: 3731: 3716: 3686: 3682: 3645: 3641: 3626:10.2307/1006040 3608: 3604: 3590:Shockwave Flash 3568: 3564: 3523: 3519: 3476: 3472: 3457: 3453: 3408: 3404: 3390: 3386: 3355: 3351: 3343: 3339: 3331: 3324: 3316: 3307: 3299: 3282: 3273: 3269: 3230: 3226: 3217: 3213: 3168: 3164: 3123: 3119: 3109: 3107: 3102: 3101: 3097: 3090: 3074: 3070: 3047: 3043: 3028: 3024: 3014: 3013: 3009: 3002: 2988: 2981: 2928: 2921: 2907: 2903: 2896: 2885: 2876: 2872: 2862: 2860: 2858: 2824: 2820: 2784: 2777: 2768: 2764: 2753: 2744: 2733: 2726: 2710: 2709: 2701: 2697: 2685: 2681: 2671: 2669: 2659: 2655: 2637: 2632: 2628: 2621: 2596: 2592: 2576: 2568: 2564: 2538: 2519: 2515: 2507: 2498: 2494: 2484: 2482: 2468: 2464: 2452: 2445: 2426: 2420: 2409: 2402: 2386: 2375: 2336: 2332: 2322: 2315: 2313: 2311: 2277: 2273: 2260: 2249: 2245: 2240: 2239: 2233: 2216: 2212: 2206: 2202: 2197: 2193: 2188: 2184: 2179: 2174: 2159:Ptolemy's Canon 2138: 2126: 2025:[Opere] 2001: 1979:Ptolemy Project 1937:4001 Ptolemaeus 1909: 1845:epistemological 1841: 1785: 1770: 1759: 1753: 1744:Harmonice Mundi 1724:just intonation 1623:, known as the 1609: 1591: 1518:Plato of Tivoli 1480: 1474: 1461: 1362: 1360: 1349:map projections 1344: 1340: 1310:Marinus of Tyre 1291: 1288: 1285: 1282: 1250: 1244: 1238: 1226:μετεωροσκοπεῖον 1225: 1221: 1197: 1194: 1191: 1188: 1131: 1104: 1102: 1101: 1094: 1092: 1091: 1084: 1082: 1081: 1061: 1058: 1055: 1052: 1018: 965: 953: 899: 833:, who produced 812: 809: 806: 803: 777:Pages from the 771: 765: 747: 676:also wrote the 660:Ptolemy I Soter 637:or the emperor 593:Ptolemy I Soter 573:Greek mythology 544:Ptolemaic Egypt 524: 515: 471: 433:Catholic Church 411: 408: 405: 402: 300: 296: 239: 235: 189: 185: 181: 177: 173: 169: 165: 161: 128: 122: 119: 108: 105: 93: 86:Justus van Gent 68: 59: 52: 47: 46: 45: 44: 43: 42: 26: 12: 11: 5: 7884: 7874: 7873: 7868: 7863: 7858: 7853: 7848: 7843: 7838: 7833: 7828: 7823: 7818: 7813: 7808: 7803: 7798: 7793: 7788: 7783: 7778: 7773: 7768: 7763: 7758: 7743: 7742: 7730: 7718: 7706: 7694: 7682: 7670: 7658: 7635: 7634: 7607: 7604: 7603: 7600: 7599: 7597: 7596: 7591: 7586: 7581: 7576: 7571: 7566: 7560: 7558: 7557:Other cultures 7554: 7553: 7551: 7550: 7549: 7548: 7538: 7537: 7536: 7526: 7525: 7524: 7514: 7513: 7512: 7502: 7501: 7500: 7490: 7489: 7488: 7478: 7477: 7476: 7466: 7465: 7464: 7454: 7453: 7452: 7438: 7436: 7432: 7431: 7429: 7428: 7423: 7418: 7413: 7408: 7406:Greek numerals 7403: 7401:Attic numerals 7398: 7392: 7386: 7382: 7381: 7379: 7378: 7373: 7368: 7362: 7360: 7356: 7355: 7352: 7351: 7349: 7348: 7343: 7338: 7333: 7328: 7320: 7315: 7310: 7305: 7300: 7295: 7290: 7284: 7282: 7278: 7277: 7275: 7274: 7268: 7266: 7260: 7259: 7257: 7256: 7251: 7246: 7241: 7236: 7231: 7229:Law of cosines 7226: 7221: 7216: 7211: 7206: 7201: 7196: 7191: 7186: 7181: 7176: 7170: 7168: 7156: 7152: 7151: 7149: 7148: 7143: 7138: 7133: 7128: 7123: 7121:Platonic solid 7118: 7113: 7108: 7103: 7101:Greek numerals 7098: 7093: 7088: 7083: 7078: 7073: 7068: 7067: 7066: 7061: 7051: 7046: 7045: 7044: 7034: 7033: 7032: 7027: 7016: 7014: 7008: 7007: 7005: 7004: 6999: 6998: 6997: 6992: 6987: 6976: 6974: 6970: 6969: 6967: 6966: 6959: 6952: 6942: 6932: 6929:Planisphaerium 6925: 6918: 6911: 6904: 6894: 6884: 6874: 6864: 6857: 6850: 6840: 6830: 6823: 6813: 6806: 6801: 6793: 6791: 6787: 6786: 6784: 6783: 6778: 6773: 6768: 6763: 6758: 6753: 6748: 6743: 6738: 6733: 6728: 6723: 6718: 6713: 6708: 6703: 6698: 6693: 6688: 6683: 6678: 6673: 6668: 6663: 6658: 6653: 6648: 6643: 6638: 6633: 6628: 6623: 6618: 6613: 6608: 6603: 6598: 6593: 6588: 6583: 6578: 6573: 6568: 6563: 6558: 6553: 6548: 6543: 6538: 6533: 6528: 6523: 6518: 6513: 6508: 6503: 6498: 6493: 6488: 6483: 6478: 6473: 6468: 6463: 6458: 6453: 6448: 6443: 6438: 6433: 6428: 6423: 6418: 6413: 6407: 6405: 6399:Mathematicians 6395: 6394: 6387: 6386: 6379: 6372: 6364: 6355: 6354: 6352: 6351: 6346: 6341: 6335: 6333: 6329: 6328: 6326: 6325: 6320: 6314: 6312: 6308: 6307: 6305: 6304: 6299: 6294: 6289: 6284: 6279: 6274: 6269: 6264: 6259: 6254: 6249: 6244: 6239: 6234: 6229: 6223: 6221: 6217: 6216: 6214: 6213: 6208: 6203: 6198: 6193: 6188: 6183: 6178: 6172: 6170: 6166: 6165: 6163: 6162: 6156:On the Heavens 6152: 6142: 6132: 6129:(Eratosthenes) 6122: 6111: 6109: 6105: 6104: 6102: 6101: 6096: 6091: 6086: 6081: 6076: 6071: 6066: 6061: 6056: 6051: 6046: 6041: 6036: 6034:Philip of Opus 6031: 6026: 6021: 6016: 6011: 6006: 6001: 5996: 5991: 5986: 5981: 5976: 5971: 5966: 5961: 5956: 5951: 5946: 5941: 5936: 5931: 5926: 5921: 5916: 5911: 5906: 5901: 5895: 5893: 5887: 5886: 5879: 5878: 5871: 5864: 5856: 5849: 5848: 5843: 5826: 5816: 5806: 5800: 5791: 5780: 5774: 5757: 5737: 5716: 5696:Danzer, Gerald 5692: 5682:on 29 May 2005 5671: 5660: 5636: 5627: 5617: 5615: 5614: 5598: 5579: 5570: 5564: 5558: 5549: 5538: 5536: 5535:External links 5533: 5531: 5530: 5524: 5507: 5496: 5475: 5473: 5470: 5468: 5467: 5433:Wade, Nicholas 5429: 5419: 5398: 5373: 5352: 5344:, Greek-German 5328: 5308: 5289: 5283: 5263: 5247: 5240: 5213: 5193: 5184: 5149: 5128: 5121: 5109:Αποτελεσματικα 5093: 5070: 5020: 4990: 4984: 4960: 4940:10.2307/520071 4916: 4914: 4911: 4909: 4908: 4895:(3): 261–276. 4875: 4856: 4849: 4826: 4811: 4782: 4759: 4741: 4706:(3): 221–240. 4688: 4673: 4646:(4): 377–395. 4628: 4614: 4584: 4577: 4557: 4546:(3): 688–705. 4518: 4505:10.1086/657028 4499:(4): 403–420. 4477: 4458:(4): 585–594. 4423: 4416: 4406:. Oxford, UK: 4391: 4350: 4331:(4): 391–403. 4309: 4282:(2): 113–135. 4264: 4257: 4237: 4223: 4203: 4190:10.2307/283969 4166: 4125: 4118: 4097: 4094:. p. 135. 4078: 4066: 4060:978-0670093625 4059: 4037: 4019: 4012: 3979: 3966: 3931: 3896:(6): 483–508. 3869: 3848:(2): 221–240. 3826: 3807: 3777: 3756: 3749: 3729: 3714: 3680: 3661:(4): 416–424. 3639: 3602: 3570:Duke, Dennis. 3562: 3517: 3490:(2): 238–241. 3470: 3451: 3424:(4): 383–393. 3402: 3384: 3349: 3345:Gingerich 1980 3337: 3333:Goldstein 1978 3322: 3305: 3280: 3267: 3224: 3211: 3184:(3): 173–183. 3162: 3117: 3095: 3088: 3068: 3041: 3039:, p. 406–463 . 3022: 3007: 3000: 2979: 2950:10.1086/355836 2944:(3): 440–453. 2919: 2901: 2894: 2870: 2856: 2818: 2805:10.1086/356291 2799:(4): 596–607. 2775: 2762: 2742: 2724: 2695: 2679: 2653: 2626: 2619: 2590: 2562: 2549:Toomer, Gerald 2546: 2545: 2536: 2513: 2492: 2471:Toomer, Gerald 2462: 2443: 2407: 2400: 2373: 2330: 2309: 2271: 2246: 2244: 2241: 2238: 2237: 2230: 2229: 2225: 2224: 2210: 2191: 2181: 2180: 2178: 2175: 2173: 2172: 2167: 2162: 2156: 2151: 2145: 2139: 2137: 2134: 2133: 2132: 2123:Planisphaerium 2114: 2100: 2086: 2072: 2067:Quadripartitum 2058: 2053:Quadripartitum 2044: 2030: 2016: 2011:Quadripartitum 2000: 1997: 1996: 1995: 1992:Ptolemy Slocum 1989: 1976: 1970: 1956: 1945: 1939: 1933: 1923: 1908: 1905: 1840: 1837: 1812:Ibn al-Haytham 1807:Book of Optics 1755:Main article: 1752: 1749: 1673:perfect fourth 1651:harmonic canon 1590: 1587: 1583:Pseudo-Ptolemy 1506:Apotelesmatiká 1502:Quadripartitum 1488:Quadripartitum 1486:A copy of the 1476:Main article: 1473: 1470: 1431:Atlantic Ocean 1390:degrees of arc 1318:Persian Empire 1240:Main article: 1237: 1234: 1222:μετεωροσκόπιον 1173:Planisphaerium 1130: 1127: 1017: 1012: 964: 959: 922:Owen Gingerich 898: 895: 879:Late Antiquity 855:constellations 847:star catalogue 767:Main article: 764: 759: 746: 743: 737:or at least a 688:Upper Egyptian 523: 520: 470: 467: 455:late antiquity 409:On the Effects 396:Αποτελεσματικά 388:Apotelesmatika 321:music theorist 227: 226: 223: 222: 205: 201: 200: 194: 193: 156: 155:Known for 152: 151: 142:Greco-Egyptian 134: 130: 129: 123: 114: 110: 109: 106: 99: 95: 94: 83: 75: 74: 70: 69: 66: 50: 28: 22: 19: 17: 9: 6: 4: 3: 2: 7883: 7872: 7869: 7867: 7864: 7862: 7859: 7857: 7854: 7852: 7849: 7847: 7844: 7842: 7839: 7837: 7834: 7832: 7829: 7827: 7824: 7822: 7819: 7817: 7814: 7812: 7809: 7807: 7804: 7802: 7799: 7797: 7794: 7792: 7789: 7787: 7784: 7782: 7779: 7777: 7774: 7772: 7769: 7767: 7764: 7762: 7759: 7757: 7754: 7753: 7751: 7741: 7736: 7731: 7729: 7719: 7717: 7707: 7705: 7700: 7695: 7693: 7683: 7681: 7671: 7669: 7664: 7659: 7657: 7647: 7646: 7643: 7632: 7631: 7626: 7619: 7618: 7605: 7595: 7592: 7590: 7587: 7585: 7582: 7580: 7577: 7575: 7572: 7570: 7567: 7565: 7562: 7561: 7559: 7555: 7547: 7544: 7543: 7542: 7539: 7535: 7532: 7531: 7530: 7527: 7523: 7520: 7519: 7518: 7515: 7511: 7508: 7507: 7506: 7503: 7499: 7496: 7495: 7494: 7491: 7487: 7484: 7483: 7482: 7479: 7475: 7472: 7471: 7470: 7467: 7463: 7460: 7459: 7458: 7455: 7451: 7447: 7446: 7445: 7444: 7440: 7439: 7437: 7433: 7427: 7424: 7422: 7419: 7417: 7414: 7412: 7409: 7407: 7404: 7402: 7399: 7397: 7394: 7393: 7390: 7387: 7383: 7377: 7374: 7372: 7369: 7367: 7364: 7363: 7361: 7357: 7347: 7344: 7342: 7339: 7337: 7334: 7332: 7329: 7327: 7326: 7321: 7319: 7316: 7314: 7311: 7309: 7306: 7304: 7301: 7299: 7296: 7294: 7291: 7289: 7286: 7285: 7283: 7279: 7273: 7270: 7269: 7267: 7265: 7261: 7255: 7252: 7250: 7247: 7245: 7242: 7240: 7237: 7235: 7234:Pons asinorum 7232: 7230: 7227: 7225: 7222: 7220: 7217: 7215: 7212: 7210: 7207: 7205: 7204:Hinge theorem 7202: 7200: 7197: 7195: 7192: 7190: 7187: 7185: 7182: 7180: 7177: 7175: 7172: 7171: 7169: 7167: 7166: 7160: 7157: 7153: 7147: 7144: 7142: 7139: 7137: 7134: 7132: 7129: 7127: 7124: 7122: 7119: 7117: 7114: 7112: 7109: 7107: 7104: 7102: 7099: 7097: 7094: 7092: 7089: 7087: 7084: 7082: 7079: 7077: 7074: 7072: 7069: 7065: 7062: 7060: 7057: 7056: 7055: 7052: 7050: 7047: 7043: 7040: 7039: 7038: 7035: 7031: 7028: 7026: 7023: 7022: 7021: 7018: 7017: 7015: 7009: 7003: 7000: 6996: 6993: 6991: 6988: 6986: 6983: 6982: 6981: 6978: 6977: 6975: 6971: 6965: 6964: 6960: 6958: 6957: 6953: 6951: 6947: 6943: 6941: 6937: 6933: 6931: 6930: 6926: 6924: 6923: 6919: 6917: 6916: 6912: 6910: 6909: 6905: 6903: 6899: 6895: 6893: 6889: 6885: 6883: 6879: 6875: 6873: 6871:(Aristarchus) 6869: 6865: 6863: 6862: 6858: 6856: 6855: 6851: 6849: 6845: 6841: 6839: 6835: 6831: 6829: 6828: 6824: 6822: 6818: 6814: 6812: 6811: 6807: 6805: 6802: 6800: 6799: 6795: 6794: 6792: 6788: 6782: 6779: 6777: 6776:Zeno of Sidon 6774: 6772: 6769: 6767: 6764: 6762: 6759: 6757: 6754: 6752: 6749: 6747: 6744: 6742: 6739: 6737: 6734: 6732: 6729: 6727: 6724: 6722: 6719: 6717: 6714: 6712: 6709: 6707: 6704: 6702: 6699: 6697: 6694: 6692: 6689: 6687: 6684: 6682: 6679: 6677: 6674: 6672: 6669: 6667: 6664: 6662: 6659: 6657: 6654: 6652: 6649: 6647: 6644: 6642: 6639: 6637: 6634: 6632: 6629: 6627: 6624: 6622: 6619: 6617: 6614: 6612: 6609: 6607: 6604: 6602: 6599: 6597: 6594: 6592: 6589: 6587: 6584: 6582: 6579: 6577: 6574: 6572: 6569: 6567: 6564: 6562: 6559: 6557: 6554: 6552: 6549: 6547: 6544: 6542: 6539: 6537: 6534: 6532: 6529: 6527: 6524: 6522: 6519: 6517: 6514: 6512: 6509: 6507: 6504: 6502: 6499: 6497: 6494: 6492: 6489: 6487: 6484: 6482: 6479: 6477: 6474: 6472: 6469: 6467: 6464: 6462: 6459: 6457: 6454: 6452: 6449: 6447: 6444: 6442: 6439: 6437: 6434: 6432: 6429: 6427: 6424: 6422: 6419: 6417: 6414: 6412: 6409: 6408: 6406: 6404: 6400: 6396: 6392: 6385: 6380: 6378: 6373: 6371: 6366: 6365: 6362: 6350: 6347: 6345: 6342: 6340: 6337: 6336: 6334: 6330: 6324: 6321: 6319: 6316: 6315: 6313: 6309: 6303: 6300: 6298: 6295: 6293: 6290: 6288: 6285: 6283: 6280: 6278: 6277:Metonic cycle 6275: 6273: 6270: 6268: 6265: 6263: 6262:Heliocentrism 6260: 6258: 6255: 6253: 6250: 6248: 6245: 6243: 6242:Counter-Earth 6240: 6238: 6235: 6233: 6230: 6228: 6225: 6224: 6222: 6218: 6212: 6209: 6207: 6204: 6202: 6199: 6197: 6194: 6192: 6189: 6187: 6184: 6182: 6179: 6177: 6174: 6173: 6171: 6167: 6161: 6157: 6153: 6151: 6149:(Aristarchus) 6147: 6143: 6141: 6137: 6133: 6131: 6127: 6123: 6121: 6117: 6113: 6112: 6110: 6106: 6100: 6097: 6095: 6092: 6090: 6087: 6085: 6082: 6080: 6077: 6075: 6072: 6070: 6067: 6065: 6062: 6060: 6057: 6055: 6052: 6050: 6047: 6045: 6042: 6040: 6037: 6035: 6032: 6030: 6027: 6025: 6022: 6020: 6017: 6015: 6012: 6010: 6007: 6005: 6002: 6000: 5997: 5995: 5992: 5990: 5987: 5985: 5982: 5980: 5977: 5975: 5972: 5970: 5967: 5965: 5962: 5960: 5957: 5955: 5952: 5950: 5947: 5945: 5942: 5940: 5937: 5935: 5932: 5930: 5927: 5925: 5922: 5920: 5917: 5915: 5912: 5910: 5907: 5905: 5902: 5900: 5897: 5896: 5894: 5892: 5888: 5884: 5877: 5872: 5870: 5865: 5863: 5858: 5857: 5854: 5847: 5844: 5840: 5836: 5832: 5827: 5824: 5820: 5817: 5814: 5810: 5807: 5804: 5801: 5799: 5795: 5792: 5790: 5786: 5781: 5778: 5775: 5763: 5758: 5747: 5743: 5738: 5726: 5722: 5717: 5705: 5701: 5697: 5693: 5681: 5677: 5672: 5669: 5665: 5661: 5657: 5656: 5650: 5645: 5641: 5637: 5635: 5631: 5628: 5626: 5622: 5619: 5618: 5612: 5608: 5604: 5603: 5599: 5597: 5590:with preface 5586: 5584: 5580: 5577: 5575: 5571: 5568: 5565: 5562: 5559: 5557: 5555: 5550: 5547: 5543: 5540: 5539: 5527: 5525:0-8126-9229-2 5521: 5516: 5515: 5508: 5504: 5503: 5497: 5493: 5489: 5482: 5477: 5476: 5464: 5460: 5456: 5452: 5448: 5444: 5443: 5438: 5434: 5430: 5427: 5423: 5420: 5405: 5401: 5395: 5391: 5390: 5382: 5378: 5374: 5371: 5355: 5349: 5345: 5341: 5337: 5333: 5329: 5326: 5320: 5318:The Geography 5317: 5313: 5309: 5305: 5304: 5299: 5295: 5290: 5286: 5284:90-04-11591-9 5280: 5276: 5272: 5268: 5264: 5262: 5259: 5256: 5252: 5248: 5245: 5241: 5237: 5233: 5229: 5225: 5224: 5219: 5214: 5209: 5206: 5202: 5199: 5194: 5190: 5185: 5181: 5177: 5173: 5169: 5165: 5161: 5160: 5155: 5150: 5145: 5141: 5137: 5133: 5129: 5124: 5118: 5114: 5106: 5102: 5098: 5094: 5090: 5084: 5076: 5071: 5067: 5063: 5059: 5055: 5051: 5047: 5043: 5039: 5038: 5033: 5031: 5025: 5021: 5017: 5013: 5009: 5005: 5004: 4999: 4995: 4994:Gingerich, O. 4991: 4987: 4985:0-691-01042-0 4981: 4977: 4973: 4969: 4965: 4961: 4957: 4953: 4949: 4945: 4941: 4937: 4933: 4929: 4928: 4923: 4918: 4917: 4903: 4898: 4894: 4890: 4886: 4879: 4871: 4867: 4860: 4852: 4846: 4842: 4841: 4833: 4831: 4822: 4815: 4807: 4803: 4799: 4795: 4794: 4786: 4778: 4774: 4770: 4763: 4755: 4751: 4745: 4737: 4733: 4729: 4725: 4721: 4717: 4713: 4709: 4705: 4701: 4700: 4692: 4684: 4677: 4669: 4665: 4661: 4657: 4653: 4649: 4645: 4641: 4640: 4632: 4617: 4615:0-87169-862-5 4611: 4607: 4603: 4602: 4599: 4591: 4589: 4580: 4574: 4570: 4569: 4561: 4553: 4549: 4545: 4541: 4537: 4535: 4531: 4522: 4514: 4510: 4506: 4502: 4498: 4494: 4493: 4488: 4481: 4473: 4469: 4465: 4461: 4457: 4453: 4449: 4447: 4443: 4439: 4430: 4428: 4419: 4417:0-19-814975-1 4413: 4409: 4405: 4401: 4395: 4387: 4383: 4379: 4375: 4371: 4367: 4366: 4361: 4354: 4346: 4342: 4338: 4334: 4330: 4326: 4325: 4320: 4313: 4305: 4301: 4297: 4293: 4289: 4285: 4281: 4277: 4276: 4268: 4260: 4254: 4250: 4249: 4241: 4226: 4224:9788884505811 4220: 4216: 4215: 4207: 4199: 4195: 4191: 4187: 4183: 4179: 4178: 4170: 4162: 4158: 4154: 4150: 4146: 4142: 4141: 4136: 4129: 4121: 4119:0-674-99479-5 4115: 4111: 4104: 4102: 4093: 4089: 4082: 4075: 4070: 4062: 4056: 4048: 4041: 4033: 4032: 4023: 4015: 4009: 4005: 4001: 3997: 3993: 3986: 3984: 3976: 3970: 3963:(4): 254–260. 3962: 3958: 3951: 3949: 3940: 3938: 3936: 3927: 3923: 3919: 3915: 3911: 3907: 3903: 3899: 3895: 3891: 3890: 3885: 3878: 3876: 3874: 3865: 3861: 3856: 3851: 3847: 3843: 3842: 3837: 3830: 3822: 3818: 3811: 3803: 3799: 3792: 3790: 3781: 3773: 3772: 3768: 3760: 3752: 3746: 3742: 3741: 3733: 3725: 3721: 3717: 3711: 3707: 3703: 3699: 3695: 3693: 3684: 3676: 3672: 3668: 3664: 3660: 3656: 3655: 3650: 3643: 3635: 3631: 3627: 3623: 3619: 3615: 3614: 3606: 3599: 3595: 3591: 3585: 3581: 3577: 3573: 3566: 3558: 3554: 3550: 3546: 3542: 3538: 3534: 3530: 3529: 3521: 3513: 3509: 3505: 3501: 3497: 3493: 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2738: 2737:(Jones, 2010) 2731: 2729: 2720: 2714: 2706: 2699: 2692: 2688: 2683: 2668: 2664: 2657: 2649: 2645: 2641: 2630: 2622: 2620:3-540-63198-4 2616: 2612: 2608: 2604: 2600: 2594: 2586: 2582: 2575: 2574: 2566: 2558: 2554: 2550: 2544: 2543: 2539: 2533: 2529: 2528: 2523: 2517: 2505: 2504: 2496: 2480: 2476: 2472: 2466: 2459: 2455: 2450: 2448: 2439: 2435: 2432: 2425: 2418: 2416: 2414: 2412: 2403: 2397: 2393: 2392: 2384: 2382: 2380: 2378: 2369: 2365: 2361: 2357: 2353: 2349: 2345: 2343: 2334: 2326: 2312: 2306: 2302: 2298: 2294: 2290: 2289: 2283: 2275: 2269: 2268: 2263: 2258: 2256: 2254: 2252: 2247: 2228: 2227: 2223: 2222: 2220: 2214: 2195: 2186: 2182: 2171: 2168: 2166: 2163: 2160: 2157: 2155: 2152: 2149: 2146: 2144: 2141: 2140: 2125: 2124: 2119: 2115: 2111: 2110: 2105: 2101: 2097: 2096: 2091: 2087: 2083: 2082: 2077: 2073: 2069: 2068: 2063: 2059: 2055: 2054: 2049: 2045: 2041: 2040: 2035: 2031: 2027: 2026: 2021: 2017: 2013: 2012: 2007: 2003: 2002: 1993: 1990: 1988: 1985:, real-time, 1984: 1980: 1977: 1974: 1971: 1968: 1964: 1960: 1957: 1954: 1950: 1949:Ptolemy stone 1946: 1943: 1940: 1938: 1935:The asteroid 1934: 1932: 1928: 1924: 1922: 1918: 1914: 1913: 1912: 1904: 1902: 1898: 1894: 1890: 1886: 1880: 1878: 1874: 1870: 1866: 1858: 1854: 1850: 1849:psychological 1846: 1836: 1832: 1829: 1825: 1819: 1817: 1816:Moon illusion 1813: 1809: 1808: 1803: 1799: 1795: 1791: 1780: 1776: 1768: 1764: 1758: 1748: 1746: 1745: 1740: 1736: 1731: 1729: 1725: 1721: 1720:single string 1717: 1713: 1709: 1704: 1702: 1698: 1694: 1690: 1686: 1682: 1678: 1674: 1670: 1666: 1665:perfect fifth 1662: 1658: 1657: 1652: 1647: 1645: 1641: 1636: 1632: 1630: 1626: 1618: 1614: 1608: 1600: 1595: 1586: 1584: 1580: 1576: 1572: 1571: 1566: 1561: 1558: 1553: 1551: 1547: 1543: 1542:numerological 1539: 1535: 1531: 1526: 1521: 1519: 1515: 1511: 1507: 1503: 1499: 1498: 1489: 1484: 1479: 1469: 1467: 1456: 1452: 1446: 1444: 1440: 1436: 1432: 1428: 1424: 1420: 1419: 1414: 1409: 1407: 1403: 1399: 1395: 1391: 1387: 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Retrieved 4213: 4206: 4181: 4175: 4169: 4147:(1): 67–84. 4144: 4138: 4134: 4128: 4109: 4092:Jones (2010) 4091: 4087: 4081: 4069: 4046: 4040: 4030: 4022: 3995: 3991: 3975:sidereal day 3969: 3960: 3957:E-Perimetron 3956: 3947: 3893: 3887: 3883: 3845: 3839: 3829: 3821:Live Science 3820: 3810: 3801: 3797: 3788: 3780: 3770: 3766: 3759: 3739: 3732: 3697: 3691: 3683: 3658: 3652: 3642: 3617: 3611: 3605: 3593: 3584:the original 3575: 3565: 3535:(1): 33–61. 3532: 3526: 3520: 3487: 3483: 3473: 3463: 3460:Handy Tables 3459: 3454: 3421: 3415: 3405: 3397: 3393: 3387: 3362: 3358: 3352: 3340: 3275: 3270: 3245: 3241: 3235: 3227: 3219: 3214: 3181: 3175: 3165: 3132: 3126: 3120: 3108:. Retrieved 3098: 3078: 3071: 3052: 3044: 3036: 3033: 3025: 3016: 3010: 2991: 2941: 2935: 2913: 2904: 2880: 2873: 2861:. Retrieved 2835: 2829: 2821: 2796: 2790: 2770: 2765: 2756: 2736: 2704: 2698: 2687:Toomer (1970 2682: 2670:. Retrieved 2666: 2656: 2643: 2629: 2602: 2593: 2572: 2565: 2556: 2526: 2516: 2502: 2495: 2483:. 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Retrieved 2286: 2274: 2265: 2213: 2194: 2185: 2122: 2117: 2108: 2103: 2094: 2089: 2080: 2075: 2066: 2061: 2052: 2047: 2038: 2033: 2024: 2019: 2010: 2005: 1910: 1897:Aristotelian 1881: 1872: 1868: 1864: 1852: 1842: 1833: 1820: 1805: 1774: 1762: 1760: 1742: 1732: 1715: 1711: 1707: 1705: 1696: 1654: 1650: 1648: 1644:Pythagoreans 1634: 1633: 1629:music theory 1624: 1612: 1610: 1574: 1570:Centiloquium 1568: 1562: 1556: 1554: 1529: 1524: 1522: 1513: 1509: 1505: 1501: 1495: 1493: 1487: 1450: 1447: 1426: 1416: 1412: 1410: 1398:polar circle 1383: 1355: 1353: 1334:Eratosthenes 1295: 1267: 1265: 1257: 1229: 1217:meteoroscope 1215: 1213: 1208: 1202: 1171: 1169: 1156: 1152: 1148: 1146: 1139: 1134: 1132: 1123:heliocentric 1112: 1073: 1066:cosmological 1037: 1035: 1025: 1014: 1007: 1004:Handy Tables 1003: 1001: 994: 991:Handy Tables 990: 970:Handy Tables 968: 966: 962:Handy Tables 961: 955: 951: 938: 925: 919: 914: 908: 902: 900: 887:heliocentric 874: 866: 864: 859: 842: 840: 828: 816: 788: 786: 778: 761: 754: 750: 748: 724: 711: 677: 671: 667: 663: 643: 630: 622: 616: 611: 609: 577:Homeric form 564: 551: 549: 539: 510: 491: 472: 448: 441:Solar System 430: 425: 415: 387: 381:Aristotelian 366: 360: 346: 340: 231: 230: 197: 140:; ethnicity: 60: 38: 29:This is the 23: 7716:Outer space 7668:Mathematics 7517:mathematics 7325:Arithmetica 6922:Ostomachion 6891:(Autolycus) 6810:Arithmetica 6586:Hippocrates 6516:Dinostratus 6501:Dicaearchus 6431:Aristarchus 6257:Geocentrism 6169:Instruments 6159:(Aristotle) 5964:Cleostratus 5929:Aristarchus 5909:Anaximander 5891:Astronomers 5768:26 November 5751:24 November 5731:24 November 5710:26 November 5686:24 November 5596:archive.org 5554:Tetrabiblos 5220:and more". 5218:Cosmography 5166:: 105–107. 5159:Imago Mundi 5113:Tetrabiblos 4934:: 318–387. 4750:Boyer, C.B. 4442:Hêgemonikon 4184:: 235–256. 4135:Tetrabiblos 4088:Tetrabiblos 4074:Bagrow 1945 3787:"Ptolemy's 3620:(4): 9–12. 3135:(1): 1–12. 3055:, p. 10. 3015:"Ptolemy". 2203: 1360 1925:The crater 1915:The crater 1889:metaphysics 1877:mathematics 1869:hegemonikon 1786: 1154 1767:Koine Greek 1735:Renaissance 1733:During the 1669:tetrachords 1640:Aristoxenus 1575:Tetrabiblos 1557:Tetrabiblos 1525:Tetrabiblos 1514:Tetrabiblos 1497:Tetrabiblos 1478:Tetrabiblos 1423:topographic 1402:stone tower 1368:coordinates 1306:Roman world 1236:Cartography 1129:Other works 1088:Earth radii 755:Tetrabiblos 727:Koine Greek 720:بَطْلُمْيوس 700:geographers 679:Tetrabiblos 591:in 323 BC: 459:Middle Ages 457:and in the 422:Koine Greek 420:, from the 417:Tetrábiblos 133:Citizenship 7766:170 deaths 7761:100 births 7750:Categories 7569:Babylonian 7469:arithmetic 7435:History of 7264:Apollonius 6949:(Menelaus) 6908:On Spirals 6827:Catoptrics 6766:Xenocrates 6761:Thymaridas 6746:Theodosius 6731:Theaetetus 6711:Simplicius 6701:Pythagoras 6686:Posidonius 6671:Philonides 6631:Nicomachus 6626:Metrodorus 6616:Menaechmus 6571:Hipparchus 6561:Heliodorus 6511:Diophantus 6496:Democritus 6476:Chrysippus 6446:Archimedes 6441:Apollonius 6411:Anaxagoras 6403:(timeline) 6332:Influenced 6311:Influences 6282:Octaeteris 6211:Triquetrum 6099:Timocharis 6084:Theodosius 6044:Posidonius 6004:Hipparchus 5994:Heraclides 5934:Aristyllus 5919:Apollonius 5914:Andronicus 5815:Libraries. 5592:(in Latin) 5588:(in Greek) 5576:books 1–13 5200:Geographia 4968:Ptolemy's 4922:Geographia 4639:Perception 3948:Geographia 3318:Lewis 1979 3248:(3): 492. 2787:Bernal, M. 2689:, p. 2638:Πτολεμαῖος 2485:21 January 2456:, p. 2431:Ptolemy's 2291:. Oxford: 2243:References 2170:Zhang Heng 1983:concurrent 1927:Ptolemaeus 1917:Ptolemaeus 1839:Philosophy 1828:refraction 1824:reflection 1794:refraction 1790:reflection 1730:systems. 1685:tetrachord 1613:Harmonikon 1605:See also: 1455:world maps 1343: – c. 1341: 276 1322:Hipparchus 1314:gazetteers 1115:geocentric 941:palimpsest 930:Hipparchus 851:Hipparchus 831:Hipparchus 787:Ptolemy's 741:Egyptian. 739:Hellenized 704:physicists 649:astronomer 581:Macedonian 575:and is of 565:Ptolemaîos 560:Πτολεμαῖος 554:Ptolemaeus 516: 168 502:Roman rule 494:Alexandria 437:geocentric 317:geographer 313:astrologer 309:astronomer 301: 170 299: – c. 297: 100 281:Ptolemaios 274:Πτολεμαῖος 146:Hellenized 125:Alexandria 7692:Astronomy 7680:Geography 7656:Biography 7030:Inscribed 6790:Treatises 6781:Zenodorus 6741:Theodorus 6716:Sosigenes 6661:Philolaus 6646:Oenopides 6641:Nicoteles 6636:Nicomedes 6596:Hypsicles 6491:Ctesibius 6481:Cleomedes 6466:Callippus 6451:Autolycus 6436:Aristotle 6416:Anthemius 6186:Astrolabe 6119:(Ptolemy) 6039:Philolaus 6029:Oenopides 6014:Hypsicles 5959:Cleomedes 5954:Callippus 5944:Autolycus 5899:Aglaonice 5602:Geography 5585:books 1–6 5370:Geography 5340:Ptolemy, 5325:Geography 5271:Harmonics 5223:Quaerendo 5207:Geography 5083:cite book 5066:239876775 4970:Geography 4948:1651-3215 4736:117259123 4720:0003-9519 4552:2159-3159 4530:Harmonics 4513:161714215 4487:Harmonics 4446:Harmonics 4386:170415282 4345:123117827 4319:Harmonics 4296:0031-8868 4275:Phronesis 4230:19 August 4153:0003-049X 4031:Geography 3992:Geography 3926:133641503 3910:0003-9519 3884:Geography 3864:257453722 3767:Ptolemy, 3724:242599669 3557:116006562 3512:125658099 3446:0021-8286 3365:(2): 89. 3359:Centaurus 3301:Wade 1977 3262:1440-2807 3206:116612700 3157:118875902 3110:7 October 3051:(1981). 2958:0021-1753 2910:Aaboe, A. 2813:143901637 2713:cite book 2585:191297168 2327:required) 2282:"Ptolemy" 2148:Messier 7 1942:Messier 7 1716:Geography 1708:Harmonics 1693:monochord 1656:monochord 1635:Harmonics 1625:Harmonics 1621:Ἁρμονικόν 1565:aphorisms 1472:Astrology 1451:Geography 1427:oikoumenē 1418:oikoumenē 1413:Geography 1406:Silk Road 1394:midsummer 1356:Geography 1297:Geography 1159:, a star 1157:parapegma 1078:epicycles 751:Geography 745:Astronomy 712:Baṭlumyus 610:The name 601:Ptolemies 567:), is an 496:, in the 469:Biography 463:epicycles 368:Geography 329:Byzantine 325:treatises 216:Astrology 212:Geography 208:Astronomy 136:possibly 7594:Japanese 7579:Egyptian 7522:timeline 7510:timeline 7498:timeline 7493:geometry 7486:timeline 7481:calculus 7474:timeline 7462:timeline 7165:Elements 7011:Concepts 6973:Problems 6946:Spherics 6936:Spherics 6901:(Euclid) 6847:(Euclid) 6844:Elements 6837:(Euclid) 6798:Almagest 6706:Serenus 6681:Porphyry 6621:Menelaus 6576:Hippasus 6551:Eutocius 6526:Domninus 6421:Archytas 6287:Solstice 6220:Concepts 6116:Almagest 6059:Seleucus 6019:Menelaus 5979:Euctemon 5698:(1988). 5646:(1911). 5583:Almagest 5574:Almagest 5435:(1977). 5413:25 April 5379:(1970). 5058:17757580 4996:(1980). 4752:(1959). 4728:41133649 4668:23948158 4402:(1992). 3918:45211928 3804:: 53–97. 3692:Analemma 3675:57560804 3396:Almagest 3236:Almagest 2974:92988054 2912:(2001). 2830:Almagest 2524:(2004). 2368:68478868 2342:Almagest 2136:See also 2106:(1682). 2092:(1663). 2078:(1663). 2064:(1658). 2050:(1622). 2036:(1559). 2022:(1541). 2008:(1519). 1893:Platonic 1885:theology 1712:Almagest 1687:and the 1530:Almagest 1439:Shetland 1376:Latitude 1230:Analemma 1161:calendar 1141:analemma 1135:Analemma 1074:Almagest 983:eclipses 945:Delambre 926:Almagest 903:Almagest 867:Almagest 860:Almagest 843:Almagest 818:Almagest 780:Almagest 769:Almagest 753:and the 673:Almagest 668:Almagest 664:Almagest 635:Claudius 631:Almagest 612:Claudius 450:Almagest 342:Almagest 191:Quadrant 187:Evection 149:Egyptian 35:reviewed 7851:Claudii 7756:Ptolemy 7740:Science 7642:Portals 7574:Chinese 7529:numbers 7457:algebra 7385:Related 7359:Centers 7155:Results 7025:Central 6696:Ptolemy 6691:Proclus 6656:Perseus 6611:Marinus 6591:Hypatia 6581:Hippias 6556:Geminus 6546:Eudoxus 6536:Eudemus 6506:Diocles 6191:Dioptra 6054:Pytheas 6049:Ptolemy 5999:Hicetas 5989:Geminus 5984:Eudoxus 5939:Attalus 5904:Agrippa 5789:YouTube 5552:Entire 5488:SciAMVS 5451:Bibcode 5442:Science 5180:1150735 5037:Science 5012:Bibcode 5010:: 253. 4913:Sources 4806:i212542 4773:Bibcode 4621:27 June 4534:Timaeus 4460:Bibcode 4444:to the 4365:Apeiron 4304:4182463 4161:3143825 3798:SciAMVS 3771:, Works 3634:1006040 3537:Bibcode 3492:Bibcode 3426:Bibcode 3367:Bibcode 3250:Bibcode 3186:Bibcode 3137:Bibcode 2863:9 March 2672:4 April 2348:Apeiron 2264:at the 2262:Ptolemy 2154:Pei Xiu 1994:, actor 1919:on the 1775:Optics, 1677:octaves 1538:planets 1385:climata 1380:equator 1283: 1259:Ecumene 1205:Canopus 1189: 1165:almanac 1149:Phaseis 1098:radii), 1064:) is a 1053: 1032:(1568). 804: 646:Persian 619:Claudia 589:pharaoh 483:Thebaid 403: 379:to the 333:Islamic 107:Unknown 67:Ptolemy 7589:Indian 7366:Cyrene 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