Ptolemy - Knowledge

925:, 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". 1491: 782: 88: 7671: 7633: 1726:, 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 1261: 2234:... "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 ... 7743: 1029: 7620: 2240:

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

7731: 7695: 7719: 1219:. 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. 7707: 7683: 7659: 1602: 1667:(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 944:, 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. 674:". 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 1675:, 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 678:. 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 1645:

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

1822:. 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 845:

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

535: 1730:, 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 516:. 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. 2206:"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 ( 469:. 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 1843:

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

989:) 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 1567:

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

964:... 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. 1829:

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

1871:), 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 5380:

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.

3608:. 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. 1671:(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 1907:

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" ...

1453:); 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. 1208:) 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. 3981:

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

893:, 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 5388: 757:

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

2836:"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 1688: 1581:, ascribed to Ptolemy, was widely reproduced and commented on by Arabic, Latin, and Hebrew scholars, and often bound together in medieval manuscripts after the 936:

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".

5266:. Göteborgs högskolas årsskrift. Vol. 36 (reprint ed.). Göteborg / New York, NY: Elanders boktr. aktiebolag. (1930) / Garland Publishing (1980). 6389: 5010: 1548:, based upon their combined effects of heating, cooling, moistening, and drying. Ptolemy dismisses other astrological practices, such as considering the 5310: 3620: 846:

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

5881: 4147: 5839:"The work of Claudius Ptolemy, as the epitome of the Macedonian Legacy in History, and of the Hellenistic and Alexandrian Science and Civilization" 5096: 3824: 7878: 7493: 2726: 1224: 5411: 2698: 4036: 5784: 7093: 5662: 5154:]. Collection de travaux de l'Académie International d'Histoire des Sciences (in French and Latin). Vol. 31. Leiden: E.J.Brill. 3084:

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

2643: 2225:"But what we really want to know is to what extent the Alexandrian mathematicians of the period from the 1st to the 5th centuries 1960: 1222:

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

7571: 281: 1879:). Ptolemy argues that, to arrive at the truth, one should use both reason and sense perception in ways that complement each other. 1076:

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

6874: 6410: 6152: 5728: 5335:, but it is marred by numerous mistakes; and placenames are given in Latinised forms, rather than in the Greek, as in the original. 4689:

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

4579:. Routledge Revivals. Vol. Historical, Philosophical, and Scientific Foundations of Modern Cosmology. Routledge. p. 527. 7803: 6382: 6356: 656: 7838: 7418: 5707: 1367:

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

7833: 7148: 5874: 5405: 5359: 5135:— The most recent edition of the Greek text of Ptolemy's astrological work, based on earlier editions by F. Boll and E. Boer. 5128: 4856: 4706: 4584: 4264: 4019: 3896: 3848: 3756: 3721: 3095: 2863: 2543: 2407: 2316: 2431: 1785:

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

5568: 3579: 2609:; Dumont, Simone (2001). "From pre-Galilean astronomy to the Hubble Space Telescope and beyond". In Kaufman, Susan (ed.). 7808: 7481: 6884: 6346: 6142: 1614: 1032:

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

174: 17: 5683: 5281:. Mnemosyne, Bibliotheca Classica Batava, Supplementum. Vol. 203. Translated by Solomon, Jon. Leiden / Boston, MA: 7848: 7828: 7823: 7818: 7548: 6375: 5396: 5115:]. Bibliotheca scriptorum Graecorum et Romanorum Teubneriana (in Latin). Vol. III. De Gruyter. Fascia 1: 4613: 4066: 4827:

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

5898: 5531: 5290: 4991: 4621: 4423: 4230: 4125: 3072: 3007: 2901: 2626: 1703:/ harmonic canon. The volume ends with a more speculative exposition of the relationships between harmony, the soul ( 1088:

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

5489:"The Arabic version of Ptolemy's planisphere or flattening the surface of the sphere: Text, translation, commentary" 1899:

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

5770:"Claudius Ptolemaeus (Ptolemy): Representation, understanding, and mathematical labeling of the spherical Earth" 4846: 1851:

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

3064: 1990: 7863: 7853: 6279: 5329:. Translated by E.L. Stevenson (Reprint ed.). New York, NY: New York Public Library, 1932 / Dover, 1991. 952: 7586: 7343: 7231: 6406: 4367: 2611:

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

2347: 2172: 1520:), roughly meaning "(books) on the Effects" or "Outcomes", or "Prognostics". As a source of reference, the 576: 178: 4443: 3773: 1552:

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.

344: 6713: 5400:. Vol. 11. New York, NY: Scribner & American Council of Learned Societies. pp. 186–206. 2274: 7457: 7428: 6788: 6643: 6076: 3748:

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".

7591: 7325: 6868: 5671: 5574: 3697: 3587: 2073: 2045: 2017: 1952:, sometimes known as the Ptolemy Cluster, an open cluster of stars in the constellation of Scorpius 1309: 1084:

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

63: 2115: 2101: 2087: 2059: 2031: 1650:), backed up by empirical observation (in contrast to the excessively theoretical approach of the 909:

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

7553: 7529: 7403: 7338: 7279: 7216: 7206: 6942: 6861: 6723: 6633: 6513: 6071: 5890: 5613:, digitised codex made in Italy between 1460 and 1477, translated to Latin by Jacobus Angelus at 4415: 3661: 3365:

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

2835: 7576: 7524: 7423: 7251: 7201: 7186: 7181: 6952: 6753: 6688: 6678: 6628: 6218: 6091: 6026: 5820: 5647: 5553: 4407: 2715:(in Arabic and Latin). editors & translators Yamamoto, K. & Burnett, Ch. Leiden. 4.1.4. 1989:, a project at University of California, Berkeley, aimed at modeling, simulating and designing 1734:– the standard for comparison of consonance in the many other, less-than exact but more facile 1462: 1255: 1240:, was identified on the basis of both its content and linguistic analysis as being by Ptolemy. 505: 170: 5144:

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

2308: 1490: 781: 7624: 7476: 7320: 7261: 7138: 7061: 7009: 6811: 6718: 6568: 6254: 6183: 5921: 5621:, it is the oldest manuscript of the codices with maps of Ptolemy with the donis projections. 5035: 3794: 3419: 1409: 898: 482: 198: 5589: 5522:

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

4604: 4254: 1691:) musical tuning practice of his day, which he then compared to his own subdivisions of the 7601: 7541: 7505: 7348: 7171: 7118: 7088: 7078: 6987: 6850: 6743: 6658: 6613: 6593: 6438: 6423: 6325: 6066: 6016: 5936: 5911: 5458: 5444: 5220:— Until Stückelberger (2006), this was the most recent edition of the complete Greek text. 5031: 5019: 4780: 4646: 4467: 3544: 3499: 3433: 3374: 3286:, New York: Frederick Ungar Publishing, 1967, reprint of the Cambridge, Mass., 1927 edition 3257: 3193: 3144: 1970: 1966: 1831: 1797: 1735: 1553: 1512:. Its original title is unknown, but may have been a term found in some Greek manuscripts, 1379: 941: 830: 388: 384: 186: 87: 3825:"Hidden Ptolemy text, printed beneath a Latin manuscript, deciphered after 200 years" 2332: 1175:, based on the appearances and disappearances of stars over the course of the solar year. 870:

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

8: 7773: 7768: 7735: 7581: 7500: 7488: 7469: 7433: 7353: 7271: 7256: 7246: 7196: 7191: 7133: 7002: 6894: 6758: 6748: 6648: 6618: 6558: 6533: 6458: 6448: 6433: 6096: 6001: 5951: 5926: 5805: 5641: 5632: 4934: 4757: 4499: 4331: 2445: 1786: 1304: 1249: 1236:). The text, which comes from an eighth-century manuscript which also contains Ptolemy's 1077: 994: 592: 375: 5838: 5732: 5462: 5023: 4784: 4471: 3548: 3503: 3437: 3378: 3261: 3197: 3148: 3090:. MPRL – Studies. Berlin, DE: Max-Planck-Gesellschaft zur Förderung der Wissenschaften. 2509: 1826:(the enlarged apparent size on the horizon) based on the difficulty of looking upwards. 1589:

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

7723: 7675: 7637: 7596: 7536: 7464: 7330: 7305: 7123: 7098: 7066: 6904: 6663: 6608: 6573: 6468: 6330: 6244: 5656: 5183: 5090: 5069: 4959: 4809: 4739: 4731: 4671: 4516: 4389: 4348: 4307: 4201: 4164: 3929: 3921: 3867: 3727: 3678: 3637: 3560: 3515: 3386: 3209: 3160: 2977: 2969: 2816: 2720: 2606: 2588: 2529: 2371: 2295: 1908: 1708: 1668: 1606: 940:

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

1423:, Ptolemy gives instructions on how to create maps both of the whole inhabited world ( 881:

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

7670: 7632: 7310: 7221: 7071: 6997: 6970: 6733: 6553: 6543: 6478: 6398: 6239: 6086: 5991: 5946: 5527: 5520: 5449: 5401: 5355: 5286: 5152:

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

5124: 5073: 5061: 5044: 4987: 4951: 4852: 4743: 4723: 4663: 4617: 4580: 4555: 4520: 4419: 4393: 4352: 4299: 4260: 4226: 4182:

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

551: 497:). This attestation is quite late, however, and there is no evidence to support it. 494: 486: 481:

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

4675: 3682: 3596:— Cited page seems to present for viewing some alternate version of the now defunct 2981: 2375: 2269: 7858: 7763: 7699: 7687: 7663: 7512: 7383: 7300: 7056: 7044: 6992: 6728: 6351: 6304: 6274: 6264: 6213: 6188: 5603: 5466: 5384: 5282: 5239: 5175: 5057: 5053: 4943: 4904: 4715: 4655: 4535: 4508: 4475: 4381: 4340: 4291: 4225:. Micrologus' library. Vol. 65. Sismel edizioni del Galluzzo. pp. 47–73. 4193: 4007: 3905: 3857: 3709: 3670: 3629: 3552: 3507: 3441: 3382: 3201: 3152: 2953: 2851: 2808: 2655: 2614: 2437:. In Juste, D.; van Dalen, B.; Hasse, D.N.; Burnett, C.; Turnhout; Brepols (eds.). 2363: 2304: 1764: 1751: 1541: 1473: 1122: 1037: 918: 245: 97: 5559: 4006:. Archimedes. Vol. 23. Dordrecht, NL: Springer Netherlands. pp. 95–119. 3953: 889:. Because of its reputation, it was widely sought and translated twice into Latin 7153: 7143: 7037: 6763: 6299: 6234: 6203: 6101: 6031: 5651: 5508: 5470: 4385: 3597: 2887: 2560: 2482: 2397: 2367: 1994: 1986: 1980: 1944: 1904: 1731: 1525: 1430: 1325: 1317: 878: 842: 742: 723: 667: 600: 580: 440: 340: 93: 5810: 5580: 5314:(book review). 86, Part 2. Philadelphia, PA: The American Philosophical Society. 5252:

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

4479: 4444:"Mathematizing the soul: The development of Ptolemy's psychological theory from 4011: 3591: 3241: 2618: 2444:. Ptolemaeus Arabus et Latinus Studies. Vol. 1. pp. 13–34 – via 1476:), there are some scholars who think that such maps go back to Ptolemy himself. 7747: 7413: 7408: 7236: 7128: 7108: 6936: 6493: 6463: 6162: 6041: 5976: 5956: 5787:– at Paul Stoddard's Animated Virtual Planetarium, Northern Illinois University 5001: 4295: 3862: 3843: 3713: 3556: 3420:"New evidence for Hipparchus' star catalogue revealed by multispectral imaging" 3205: 3156: 2944: 2799: 2166: 1999: 1883:

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

1864: 1819: 1814: 1680: 1624: 1590: 1544:. Thus explanations of a sort are provided for the astrological effects of the 1502:

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

1438: 1397: 1356: 1279: 1212: 1185: 1180: 1049: 982: 929: 886: 854: 800: 561: 462: 399: 358: 328: 293: 275: 149: 5826: 5790: 5243: 5179: 4344: 3909: 3445: 2855: 1260: 829:, is the only surviving comprehensive ancient treatise on astronomy. Although 7757: 7373: 7241: 7211: 7032: 6840: 6783: 6284: 6269: 6249: 5703: 5687: 5628: 5440: 4955: 4909: 4892: 4727: 4559: 4303: 4160: 3982: 3917: 3511: 3453: 3269: 3179: 3037: 2965: 2794: 2743:

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

2556: 2478: 1956: 1823: 1672: 1586: 1130: 862: 746: 607:. Almost all subsequent pharaohs of Egypt, with a few exceptions, were named 584: 543: 513: 379:, which is a thorough discussion on maps and the geographic knowledge of the 312: 153: 6367: 4644:

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

1540:

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

1408:. One of the places Ptolemy noted specific coordinates for was the now-lost 512:. He had a Latin name, Claudius, which is generally taken to imply he was a 7711: 7315: 7103: 6778: 6538: 6528: 6132: 5981: 5769: 5637: 5433: 5065: 3487: 3402:

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

2939: 1852: 1651: 1636: 1577: 1405: 1341: 1313: 1264:

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

977: 894: 623: 509: 448: 145: 5859: 5749: 2092:(in Latin). Paris: Sebastian Cramoisy (1.) & Sebastian Mabre-Cramoisy. 1796:). In it, Ptolemy writes about properties of sight (not light), including 1425: 6929: 6817: 6523: 6508: 5971: 5916: 5166: 4878:

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

4667: 4055:

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

3674: 2917: 1896: 1774: 1742: 1647: 1504: 1485: 734: 695: 686: 612: 550:

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

466: 429: 424: 4735: 3925: 3418:

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

1316:

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

1028: 383:. The third is the astrological treatise in which he attempted to adapt 6915: 6834: 6773: 6768: 6708: 6693: 6638: 6623: 6578: 6518: 6503: 6483: 6453: 6418: 6289: 6106: 6051: 6011: 5941: 5614: 5187: 4893:"Meta-mathematical rhetoric: Hero and Ptolemy against the philosophers" 4813: 4719: 4311: 4168: 3954:"Lines, damned lines and statistics: Unearthing structure in Ptolemy's 3657:"Modeling the heavens: Sphairopoiia and Ptolemy's planetary hypotheses" 3656: 3641: 3056: 2226: 2177: 1856: 1835: 1801: 1692: 1676: 1549: 1375: 1329: 948: 937: 858: 838: 670:

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

501: 444: 324: 320: 316: 132: 7742: 4963: 4205: 3998:

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

3475: 2973: 1919:

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

1556:(interpreting astrological charts to determine courses of action) and 1437:

spanned 180 degrees of longitude from the Blessed Islands in the

666:, stating that the descendants of the Alexandrine general and Pharaoh 6668: 6653: 6603: 6498: 6488: 6473: 6443: 6193: 6046: 6036: 6021: 5966: 5961: 5906: 5853: 5827:

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

5230: 4606:

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

4282: 2155: 1949: 1900: 1727: 1700: 1663: 1413: 1401: 1321: 1073: 837:

The earliest person that attempted to merge these two approaches was

287: 223: 219: 215: 156: 5629:

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

5223: 4659: 4042:(Report). Orbis Terrarum. Vol. 9 (2003–2007). pp. 177–180. 3633: 885:(lit. "The greatest treatise"), as the work was presumably known in 6805: 6583: 6428: 6294: 6122: 5986: 5829:- Complete reproduction of the 9th century manuscript of Ptolemy's 4947: 4512: 4197: 4120:. Loeb Classical Library. Cambridge, MA: Harvard University Press. 3111: 2957: 2940:"The adaptation of Babylonian methods in Greek numerical astronomy" 2812: 1892: 1572: 1446: 1383: 1168: 1148: 1085: 990: 825: 787: 776: 680: 653: 642: 470: 457: 349: 332: 194: 5608: 2763:

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

2139:— medieval Arabic translations and an English translation of those 1404:

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

741:. He might have been a Roman citizen, but was ethnically either a 347:

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

7378: 6698: 6598: 6588: 6563: 6198: 6061: 6006: 5996: 4372: 2161: 1545: 1387: 1266: 1172: 596: 534: 490: 5708:"Cartographic Images of the World on the Eve of the Discoveries" 4325:

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

3040:(1936). "The Unity and Diversity of the Mediterranean World", 443:

promoted his work, which included the only mathematically sound

6673: 6548: 6309: 6259: 6208: 6081: 5931: 2150: 1859:

discussions across his corpus. He wrote a short essay entitled

1805: 1746: 1696: 1684: 1450: 1340:

based on scientific principles had been made since the time of

1126: 715: 691: 539: 227: 190: 5678:, Supplementband 21,2. Teubner, Leipzig, pp. 49–244. 5655: 5445:"Scandal in the Heavens: Renowned Astronomer Accused of Fraud" 5250:

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

5199:. Vol. I–III. Berlin, DE / New York, NY: Springer Verlag. 4831:. Cambridge, UK: Cambridge University Press. pp. 499–528. 4777:

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

4693:. Cambridge, UK: Cambridge University Press. pp. 217–247. 4222:

Dialogues among Books in Medieval Western Magic and Divination

3885: 3883: 3881: 1585:

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

7049: 7027: 6683: 5331:— This is the only complete English translation of Ptolemy's 4798:

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

3605: 1442: 1392: 699: 566: 279: 2797:(1992). "Animadversions on the origins of western science". 1416:, and which scholars have been trying to locate ever since. 951:

and they debunked accusations made by the French astronomer

3878: 1938: 1928: 1601: 1337: 877:

was preserved, like many extant Greek scientific works, in

646: 266: 260: 7706: 5640:

From the Rare Book and Special Collection Division at the

5631:

From the Rare Book and Special Collection Division at the

4094:

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

2889:

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

2842:. In Rahman, Shahid; Street, Tony; Tahiri, Hassan (eds.). 1639:

and the mathematics behind musical scales in three books.

254: 3889: 3841: 3246:

and some geometrical mechanisms to the era of Copernicus"

1812:

and influenced the more famous and superior 11th-century

1679:(combinations of four pitch ratios which together make a 1390:, as it is today, but Ptolemy preferred to express it as 1003: 5729:"Κλαυδιου Πτολεμιου: Γεωγραφικῆς Ύφηγήσεως (Geographie)" 4460:

Studies in History and Philosophy of Science Part A

4256:

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

3336: 3334: 2022:(in Latin). Venezia: Ottaviano Scoto (1.) eredi & C. 956:

had claimed. Scientists analyzing the charts concluded:

500:

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

5731:(in German and English). Frank Haselein. Archived from 5575:

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

5344:

Ptolemaios, Handbuch der Geographie, Griechisch-Deutsch

4974:(2000). Berggren, J. Lennart; Jones, Alexander (eds.). 4872:

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

3417: 2158:– Ptolemy Cluster, star cluster described by Ptolemaeus 461:) never ceased to be copied or commented upon, both in 5342:(2006). Stückelberger, Alfred; Graßhoff, Gerd (eds.). 4980:: An annotated translation of the theoretical chapters 4928:

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

2538:. Springer Science & Business Media. p. 834. 1983:, the graphs whose distances obey Ptolemy's inequality 1429:) and of the Roman provinces, including the necessary 1374:

of these places and geographic features have assigned

1108:

while the radius of the sphere of the fixed stars was

7647: 4801:

Transactions of the American Philological Association

4779:. The University of Chicago Press. pp. 116–118. 4185:

Transactions of the American Philological Association

3346: 3331: 2758: 2756: 2754: 1080:. Ptolemy goes beyond the mathematical models of the 3321: 3319: 3317: 2169:– a dated list of kings used by ancient astronomers. 1875:

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

257: 251: 5586:

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

5011:

Quarterly Journal of the Royal Astronomical Society

4259:. London, UK / New York, NY: Routledge. p. 7. 3304: 3302: 3300: 3298: 3296: 3294: 3292: 2265: 2263: 2261: 2259: 1211:Ptolemy also erected an inscription in a temple at 366: 263: 248: 5519: 5311:Transactions of the American Philosophical Society 5026:– via The SAO/NASA Astrophysics Data System. 4848:Ptolemy's Philosophy: Mathematics as a way of life 4075: 3844:"Ptolemy's treatise on the meteoroscope recovered" 3745:Evans, James; Berggren, J. Lennart (5 June 2018). 3621:Transactions of the American Philosophical Society 2751: 2288: 791:in Arabic translation showing astronomical tables. 698:", suggesting he may have had origins in southern 5666:. Vol. 22 (11th ed.). pp. 618–626. 5273: 4148:Proceedings of the American Philosophical Society 3706:Ptolemy's Science of the Stars in the Middle Ages 3314: 3228:Astronomies and Cultures in Early Medieval Europe 3114:. The International Journal of Scientific History 432:meaning "Four Books", or by its Latin equivalent 7755: 5772:. Center for Spatially Integrated Social Science 4829:Perceptual Constancy: Why things look as they do 4141:Riley, M. (1988). "Science and tradition in the 3993: 3991: 3289: 3239: 2256: 1749:in his own musings on the harmony of the world ( 629:; the peculiar multipart form of the whole name 5113:The complete existing works of Claudius Ptolemy 4111: 4109: 3947: 3945: 3943: 1508:(lit. "Four Books") or by its Latin equivalent 1016:Arrangement and Calculation of the Handy Tables 857:, which is a version of a catalogue created by 615:in 30 BC, ending the Macedonian family's rule. 538:Engraving of a crowned Ptolemy being guided by 5646: 5486: 5354:] (in German). Basel, CH: Schwabe Verlag. 5218:] (in Latin). Leipzig: Carolus Tauchnitus. 4034: 2789: 2787: 2738: 2736: 2577: 2120:(in Latin). Oxford, UK: Theatrum Sheldonianum. 2064:(in Latin). Frankfurt am Main: Johann Bringer. 1808:. The work is a significant part of the early 6397: 6383: 5875: 5203: 5109:Claudius Ptolemaeus, Opera quae exstant omnia 4598: 4596: 3988: 3744: 3230:, Cambridge: Cambridge Univ. Pr. pp. 20–21. 2933: 2931: 2587:(Doctoral thesis). Universitat de Barcelona. 2457: 2455: 1528:(Tiburtinus) in 1138, while he was in Spain. 1274:Ptolemy's second most well-known work is his 637:. Gerald Toomer, the translator of Ptolemy's 5767: 5676:Neue Jahrbücher für Philologie und Pädagogik 5095:: CS1 maint: multiple names: authors list ( 4880:. Oxford University Press. pp. 301–331. 4840: 4838: 4572: 4437: 4435: 4106: 3940: 3180:"The enigma of Ptolemy's catalogue of stars" 2993: 2991: 2922:Episodes from the Early History of Astronomy 2844:The Unity of Science in the Arabic Tradition 2605: 2425: 2423: 2421: 2419: 2391: 2389: 2387: 2385: 1396:, the length of the longest day rather than 59:Roman astronomer and geographer (c. 100–170) 5889: 5792:Animation of Ptolemy's two Solar hypotheses 5197:A History of Ancient Mathematical Astronomy 4037:Hipparchus' table of climata and Ptolemy's 3997: 3777:Planispherium. Ptolemaeus Arabus et Latinus 3284:Studies in the History of Mediaeval Science 2784: 2733: 2710: 2565:Complete Dictionary of Scientific Biography 2555: 2535:A History of Ancient Mathematical Astronomy 2487:Complete Dictionary of Scientific Biography 2477: 1287: 1193: 1057: 808: 662:mistakenly presents Ptolemy as a member of 407: 394:of his day. This is sometimes known as the 23: 6390: 6376: 5882: 5868: 5836: 5338: 5318: 5257: 5194: 5138: 5103: 4970: 4593: 3364: 2928: 2850:/ Springer Netherlands. pp. 183–225. 2725:: CS1 maint: location missing publisher ( 2528: 2461: 2452: 2110: 2103:De iudicandi facultate et animi principatu 2096: 2089:De iudicandi facultate et animi principatu 2082: 2068: 2054: 2040: 2026: 2012: 1699:, which he derived experimentally using a 1328:. He also acknowledged ancient astronomer 765:have significant references to astronomy. 690:as its astrological counterpart. In later 86: 24: 5322:(1991) . Stevenson, Edward Luther (ed.). 5263:Die Harmonielehre des Klaudios Ptolemaios 5030: 5000: 4908: 4871: 4835: 4573:Hetherington, Norriss S. (8 April 2014). 4536:"Philosophical presentation in Ptolemy's 4432: 4368:"Greek musicologists in the Roman Empire" 4324: 4252: 4098:in Renaissance and early modern Europe". 3861: 3822: 3617: 3352: 3340: 3250:Repositorio Institucional CONICET Digital 3132: 3087:The Globalization of Knowledge in History 3083: 3000:A History of Mathematics: An introduction 2988: 2924:. New York, NY: Springer. pp. 62–65. 2885: 2416: 2382: 2215:unsupported." — Toomer & Jones (2018) 1412:which marked the midpoint on the ancient 1332:for having provided the elevation of the 529: 335:, three of which were important to later 5747: 5726: 5506: 4826: 4643: 3532: 3242:"Notes on the transmission of Ptolemy's 3177: 2191: 1959:used in the mathematics courses at both 1600: 1489: 1445:, and about 80 degrees of latitude from 1259: 1027: 780: 533: 32:This is an accepted version of this page 5785:Java simulation of the Ptolemaic System 5487:Sidoli, Nathan; Berggren, J.L. (2007). 4115: 3951: 3399: 2762: 2441:Science of the Stars in the Middle Ages 2345: 2309:10.1093/gmo/9781561592630.article.22510 2286: 1308:, a handbook on how to draw maps using 1215:, around 146–147 AD, known as the 1133:one, presumably for didactic purposes. 1021: 768: 14: 7756: 7419:Latin translations of the 12th century 5811:Flash animation of Ptolemy's universe. 5710:. The Newberry Library. Archived from 5702: 5681: 5383: 4927: 4492: 4365: 4279: 4218: 4093: 4081: 4057:. Delhi, IN: Penguin Viking. pp. 3695: 3031: 2833: 2793: 2742: 2694: 2641: 2124: 2050:(in Latin). Basel, CH: Heinrich Petri. 1914: 1433:lists, and captions for the maps. His 1010:Additionally, the introduction to the 904: 7879:Epigrammatists of the Greek Anthology 7149:Straightedge and compass construction 6371: 5863: 5686:. obs.nineplanets.org. Archived from 5550:Ptolemy's Tetrabiblos at LacusCurtius 5302:Ptolemy's Theory of Visual Perception 5299: 5159: 5080: 4797: 4774: 4762:The Rainbow: From myth to mathematics 4756: 4707:Archive for History of Exact Sciences 4703: 4688: 4602: 4533: 4181: 4140: 3897:Archive for History of Exact Sciences 3849:Archive for History of Exact Sciences 3792: 3771: 3485: 3325: 3240:Krisciunas, K.; Bistué, M.B. (2019). 3027:. Encyclopædia Britannica, Inc. 2006. 2937: 2916: 2507: 2429: 2395: 1593:, remains the subject of conjecture. 7114:Incircle and excircles of a triangle 5517: 5439: 5156:— Latin text with French translation 4890: 4844: 4441: 4406: 4052: 3823:Nalewicki, Jennifer (7 April 2023). 3799:and Heliodorus' observation reports" 3654: 3536:Journal for the History of Astronomy 3492:Journal for the History of Astronomy 3425:Journal for the History of Astronomy 3308: 3185:Journal for the History of Astronomy 3136:Journal for the History of Astronomy 2997: 2668: 2514:. Oxford: Clarendon Press. pp. 2402:. Archimedes. Springer Netherlands. 2106:(in Latin). Den Haag: Adriaen Vlacq. 2078:(in Latin). Padova: Paolo Frambotto. 1646:the ideas advocated by followers of 1472:(after the text was rediscovered by 914:observations were taken at 12:30pm. 694:sources, he was often known as "the 485:wrote that Ptolemy's birthplace was 5804:– at Rosemary Kennett's website at 5569:Ptolemy's Geography at LacusCurtius 5564:of J.M. Ashmand's 1822 translation. 5308:with introduction and commentary". 4548:Greek, Roman, and Byzantine Studies 4253:Wardhaugh, Benjamin (5 July 2017). 3698:"Mathematical Methods in Ptolemy's 3472:Ptolemaeus Arabus et Latinus, Works 2137:(in Latin) – via sciamvs.org. 2047:In Claudii Ptolemaei Quadripartitum 1465:in surviving manuscripts date from 727: 455:, Ptolemy's writings (foremost the 331:who wrote about a dozen scientific 56: 5479: 5436:, 1998. Princeton University Press 5397:Dictionary of Scientific Biography 4614:The American Philosophical Society 3600:video file format. The video file 3387:10.1111/j.1600-0498.1976.tb00923.x 2561:"Ptolemy (or Claudius Ptolemaeus)" 2483:"Ptolemy (or Claudius Ptolemaeus)" 2036:(in Latin). Basel: Heinrich Petri. 622:is a Roman name, belonging to the 128: 170 (aged 69–70) 57: 7890: 5571:(English translation, incomplete) 5542: 5526:. Chicago, IL: Open Court Press. 5254:, In Quaerendo 48: 139–162, 2018. 5160:Lewis, H.A.G. (1979). "Review of 2578:Tolsa Domènech, Cristian (2013). 2242:exist. — V.J. Katz (1998, p. 184) 1687:. Ptolemy reviewed standard (and 834:ability to make any predictions. 422:) but more commonly known as the 7741: 7729: 7717: 7705: 7693: 7681: 7669: 7657: 7631: 7618: 5750:"The life & work of Ptolemy" 5304:: An English translation of the 5261:(1980) . Düring, Ingemar (ed.). 5107:(1998). Hübner, Wolfgang (ed.). 3577: 3407:(Ph.D. thesis). Yale University. 1861:On the Criterion and Hegemonikon 1615:Ptolemy's intense diatonic scale 1378:so that they can be placed in a 818:Mathematical Systematic Treatise 737:, and can be shown to have used 493:region of Egypt (now El Mansha, 244: 175:Ptolemy's intense diatonic scale 5837:Papaspirou, Panagiotis (2014). 5394:. In Gillispie, Charles (ed.). 4884: 4865: 4820: 4791: 4768: 4750: 4697: 4682: 4637: 4566: 4527: 4486: 4400: 4359: 4318: 4273: 4246: 4212: 4175: 4134: 4116:Robbins, Frank E., ed. (1940). 4087: 4046: 4028: 3975: 3835: 3816: 3786: 3765: 3738: 3689: 3648: 3611: 3571: 3526: 3479: 3460: 3411: 3400:Britton, John Phillips (1967). 3393: 3358: 3276: 3233: 3220: 3171: 3126: 3104: 3077: 3050: 3025:Britannica Concise Encyclopedia 3016: 3002:. Addison Wesley. p. 184. 2910: 2879: 2848:Springer Science+Business Media 2827: 2781:, p. 177. Wittenberg: Gottlieb. 2771: 2704: 2688: 2671:"Egypt in the Ptolemaic Period" 2662: 2635: 2599: 2571: 2522: 2501: 2219: 1718:never had the influence of his 1146:diagram that Ptolemy calls the 997:'s version. Although Ptolemy's 968: 664:Ptolemaic Egypt's royal lineage 7804:2nd-century Greek philosophers 7451:A History of Greek Mathematics 6964:The Quadrature of the Parabola 5432:, Translated and annotated by 5389:"Ptolemy (Claudius Ptolemæus)" 5085:. Oxford, UK: Clarendon Press. 5083:A History of Greek Mathematics 5058:10.1126/science.199.4331.872.a 4982:. Princeton, NJ / Oxford, UK: 4851:. Princeton University Press. 3751:. Princeton University Press. 3065:University of California Press 2658:– via perseus.tufts.edu. 2613:. Springer. pp. 309–372. 2511:A History of Greek Mathematics 2471: 2339: 2280: 2200: 1977:, to non-cyclic quadrilaterals 1619:Ptolemy wrote a work entitled 1563:The great popularity that the 1243: 1136: 13: 1: 7839:Ancient Greek music theorists 6280:Inferior and superior planets 5162:The Crime of Claudius Ptolemy 5038:The Crime of Claudius Ptolemy 4035:Shcheglov, D.A. (2002–2007). 2250: 2207: 1869:Περὶ Κριτηρίου καὶ Ἡγεμονικοῡ 1846: 1790: 1466: 1449:to anti-Meroe (east coast of 1345: 1270:by Johannes Schnitzer (1482). 923:The Crime of Claudius Ptolemy 613:Egypt became a Roman province 520: 301: 124: 109: 7834:Ancient Greek mathematicians 7232:Intersecting secants theorem 5471:10.1126/science.198.4318.707 4544:as a model for organization" 4386:10.1515/APEIRON.1994.27.4.53 3466:Juste, D. (2021). Ptolemy, 2559:; Jones, Alexander (2018) . 2481:; Jones, Alexander (2018) . 2368:10.1515/APEIRON.1994.27.4.75 2333:UK public library membership 1571:A collection of one hundred 1479: 752: 739:Babylonian astronomical data 476: 288: 7: 7789:2nd-century Egyptian people 7227:Intersecting chords theorem 7094:Doctrine of proportionality 5813:(best in Internet Explorer) 5204:Nobbe, C.F.A., ed. (1843). 5142:(1989). Lejeune, A. (ed.). 5081:Heath, Thomas, Sir (1921). 5036:"Casting doubt on Ptolemy: 4480:10.1016/j.shpsa.2012.06.006 4012:10.1007/978-90-481-2788-7_4 2619:10.1007/978-3-662-04441-4_7 2143: 1745:, Ptolemy's ideas inspired 1575:about astrology called the 1531:Much of the content of the 1336:for a few cities. Although 603:, the first pharaoh of the 591:upper class at the time of 577:ancient Greek personal name 519:Ptolemy died in Alexandria 367: 10: 7895: 7809:2nd-century mathematicians 6923:On the Sphere and Cylinder 6876:On the Sizes and Distances 6357:Medieval Islamic astronomy 6154:On the Sizes and Distances 5843:Macedonian Studies Journal 5802:Epicycle and deferent demo 5768:Sprague, Ben (2001–2007). 5748:Houlding, Deborah (2003). 4984:Princeton University Press 4920: 4296:10.1163/156852894321052135 3863:10.1007/s00407-022-00302-w 3714:10.1484/M.PALS-EB.5.120173 3586:(academic pers. website). 3557:10.1177/002182869502600102 3206:10.1177/002182869202300303 3157:10.1177/002182869702800101 2675:Metropolitan Museum of Art 2508:Heath, Sir Thomas (1921). 1973:, and its generalization, 1762: 1612: 1483: 1297:Guide to Drawing the Earth 1253: 1247: 1190:Ἅπλωσις ἐπιφανείας σφαίρας 1161:Risings of the Fixed Stars 1125:perspective, much like an 1098:(now known to actually be 932:, while agreeing that the 861:. Its list of forty-eight 774: 587:. It was common among the 567: 554:, with the same last name. 280: 61: 7849:Ancient Roman geographers 7829:Ancient Greek geographers 7824:Ancient Greek astronomers 7819:Ancient Greek astrologers 7625:Ancient Greece portal 7614: 7564: 7442: 7429:Philosophy of mathematics 7399: 7392: 7366: 7344:Ptolemy's table of chords 7288: 7270: 7169: 7162: 7018: 6980: 6797: 6405: 6399:Ancient Greek mathematics 6347:Medieval European science 6339: 6318: 6227: 6176: 6115: 6077:Sosigenes the Peripatetic 5897: 5510:The Earliest Printed Maps 5244:10.1163/15700690-12341392 5195:Neugebauer, Otto (1975). 5180:10.1080/03085697908592494 4576:Encyclopedia of Cosmology 4345:10.1177/03057356030314004 3910:10.1007/s00407-017-0194-7 3446:10.1177/00218286221128289 3061:The Age of Reconnaissance 2938:Jones, Alexander (1991). 2856:10.1007/978-1-4020-8405-8 2713:De magnis coniunctionibus 2173:Ptolemy's table of chords 1868: 1758: 1628: 1419:In the third part of the 1324:of the Roman and ancient 1283: 1189: 1118:the radius of the Earth. 1067:Hypotheses of the Planets 1053: 986: 804: 403: 362: 233: 211: 204: 179:Ptolemy's table of chords 162: 140: 120: 105: 85: 80: 73: 7296:Aristarchus's inequality 6869:On Conoids and Spheroids 5727:Haselein, Frank (2007). 5652:Beazley, Charles Raymond 5518:Taub, Liba Chia (1993). 4910:10.1016/j.hm.2014.02.002 4876:". In Lee, M.-K. (ed.). 3588:Florida State University 3512:10.1177/0021828617706254 3488:"Ptolemy's Handy Tables" 3226:S.C. McCluskey, 1998, 2998:Katz, Victor J. (1998). 2184: 2006: 1596: 1382:that spanned the globe. 1310:geographical coordinates 1203:Flattening of the sphere 1054:Ὑποθέσεις τῶν πλανωμένων 714:referred to his name in 64:Ptolemy (disambiguation) 39:latest accepted revision 7874:Egyptian mathematicians 7799:2nd-century geographers 7784:2nd-century astronomers 7404:Ancient Greek astronomy 7217:Inscribed angle theorem 7207:Greek geometric algebra 6862:Measurement of a Circle 6072:Sosigenes of Alexandria 5891:Ancient Greek astronomy 5663:Encyclopædia Britannica 5648:Bunbury, Edward Herbert 5556:'s English translation) 5513:. British Museum Press. 5277:; Solomon, Jon (2000). 4603:Smith, A. Mark (1996). 4416:Oxford University Press 4408:West, Martin Litchfield 3696:Sidoli, Nathan (2020). 3662:Perspectives on Science 3282:Charles Homer Haskins, 3178:Swerdlow, N.M. (1992). 2834:Tahiri, Hassan (2008). 2396:Jones, A., ed. (2010). 2301:Oxford University Press 2287:Richter, Lukas (2001). 2275:Encyclopædia Britannica 1755:, Appendix to Book V). 1657:Ptolemy introduces the 1560:, for similar reasons. 1355:), Ptolemy improved on 823:), better known as the 506:Roman province of Egypt 311:AD) was an Alexandrian 92:Portrait of Ptolemy by 7638:Mathematics portal 7424:Non-Euclidean geometry 7379:Mouseion of Alexandria 7252:Tangent-secant theorem 7202:Geometric mean theorem 7187:Exterior angle theorem 7182:Angle bisector theorem 6886:On Sizes and Distances 6144:On Sizes and Distances 5821:University of Oklahoma 5817:High resolution images 5638:Almagestū Cl. Ptolemei 5554:Loeb Classical Library 5552:(Transcription of the 5366:— Massive 2 vol, 5006:"Was Ptolemy a fraud?" 2886:Tomarchio, J. (2022). 2777:J. F. Weidler (1741). 1709:harmony of the spheres 1610: 1499: 1386:was measured from the 1362:The first part of the 1276:Geographike Hyphegesis 1271: 1129:would have done for a 1041: 966: 831:Babylonian astronomers 792: 555: 548:Margarita Philosophica 530:Naming and nationality 489:, a Greek city in the 353:, originally entitled 297: 7326:Pappus's area theorem 7262:Theorem of the gnomon 7139:Quadratrix of Hippias 7062:Circles of Apollonius 7010:Problem of Apollonius 6988:Constructible numbers 6812:Archimedes Palimpsest 6255:Deferent and epicycle 6184:Antikythera mechanism 5682:Arnett, Bill (2008). 5577:(English translation) 5507:Campbell, T. (1987). 5300:Smith, A.M. (1996). " 5032:Goldstein, Bernard R. 3580:"Ptolemy's cosmology" 2892:. CUA Press. p. 2711:Ma'shar, Abu (2000). 2669:Hill, Marsha (2006). 2432:"The ancient Ptolemy" 2348:"The teaching of the 1604: 1493: 1263: 1254:Further information: 1155:In another work, the 1031: 958: 899:scientific revolution 784: 660:Abu Ma'shar al-Balkhi 537: 483:Theodore Meliteniotes 373:). The second is the 355:Mathematical Treatise 135:, Egypt, Roman Empire 7864:Egyptian astronomers 7854:Astrological writers 7542:prehistoric counting 7339:Ptolemy's inequality 7280:Apollonius's theorem 7119:Method of exhaustion 7089:Diophantine equation 7079:Circumscribed circle 6896:On the Moving Sphere 6326:Babylonian astronomy 6017:Hippocrates of Chios 5735:on 18 September 2008 5714:on 27 September 2011 5670:Franz Boll (1894), " 5376:academic edition of 5340:Ptolemaios, Claudius 5320:Ptolemaios, Claudius 5275:Ptolemaios, Claudius 5259:Ptolemaios, Claudius 5140:Ptolemaios, Claudius 5105:Ptolemaios, Claudius 5034:(24 February 1978). 4972:Ptolemaios, Claudius 4897:Historia Mathematica 4775:Smith, Mark (2015). 3952:Isaksen, L. (2011). 3675:10.1162/POSC_a_00214 2779:Historia astronomiae 2652:A Homeric Dictionary 2346:Pingree, D. (1994). 2126:Ptolemaios, Claudius 2112:Ptolemaios, Claudius 2098:Ptolemaios, Claudius 2084:Ptolemaios, Claudius 2070:Ptolemaios, Claudius 2056:Ptolemaios, Claudius 2042:Ptolemaios, Claudius 2028:Ptolemaios, Claudius 2014:Ptolemaios, Claudius 1975:Ptolemy's inequality 1971:cyclic quadrilateral 1963:campuses in the U.S. 1707:), and the planets ( 1554:electional astrology 1400:: The length of the 1334:north celestial pole 1046:Planetary Hypotheses 1034:Planetary Hypotheses 1023:Planetary Hypotheses 797:Mathēmatikē Syntaxis 770:Mathēmatikē Syntaxis 579:. It occurs once in 558:Ptolemy's Greek name 453:Greek mathematicians 385:horoscopic astrology 369:Mathēmatikḗ Syntaxis 183:Ptolemy's inequality 62:For other uses, see 7628: • 7434:Neusis construction 7354:Spiral of Theodorus 7247:Pythagorean theorem 7192:Euclidean algorithm 7134:Lune of Hippocrates 7003:Squaring the circle 6759:Theon of Alexandria 6434:Aristaeus the Elder 6097:Theon of Alexandria 5806:Syracuse University 5642:Library of Congress 5633:Library of Congress 5463:1977Sci...198..707W 5213:Claudius Ptolemy's 5164:, by R.R. Newton". 5040:. Robert R. Newton" 5024:1980QJRAS..21..253G 4935:Geografiska Annaler 4785:2014fslp.book.....S 4500:Classical Philology 4472:2012SHPSA..43..585F 4412:Ancient Greek Music 4366:Barker, A. (1994). 4332:Psychology of Music 4118:Ptolemy Tetrabiblos 4053:Dean, Riaz (2022). 3797:Canobic Inscription 3594:on 7 November 2009. 3549:1995JHA....26...33M 3504:2017JHA....48..238J 3438:2022JHA....53..383G 3379:1976Cent...20...89B 3262:2019JAHH...22..492K 3198:1992JHA....23..173S 3149:1997JHA....28....1G 2765:Ptolemy Tetrabiblos 2642:Autenrieth, Georg. 2607:Pecker, Jean Claude 2567:. Encyclopedia.com. 2530:Neugebauer, Otto E. 2446:New York University 1915:Named after Ptolemy 1787:Eugenius of Palermo 1714:Although Ptolemy's 1470: 1300 AD 1284:Γεωγραφικὴ Ὑφήγησις 1256:Ptolemy's world map 1250:Geography (Ptolemy) 1217:Canobic Inscription 995:Theon of Alexandria 905:Modern reassessment 891:in the 12th century 883:Hē Megistē Syntaxis 805:Μαθηματικὴ Σύνταξις 631:Claudius Ptolemaeus 593:Alexander the Great 363:Μαθηματικὴ Σύνταξις 298:Claudius Ptolemaeus 171:Ptolemy's world map 81:Κλαύδιος Πτολεμαῖος 29:Page version status 18:Claudius Ptolemaeus 7844:Ancient occultists 7794:2nd-century Romans 7779:1st-century Romans 7321:Menelaus's theorem 7311:Irrational numbers 7124:Parallel postulate 7099:Euclidean geometry 7067:Apollonian circles 6609:Isidore of Miletus 6331:Egyptian astronomy 6245:Circle of latitude 5684:"Ptolemy, the Man" 5430:Ptolemy's Almagest 5350:Geography Handbook 5324:Claudius Ptolemy: 5206:Claudii Ptolemaei 4720:10.1007/BF00348501 4534:Tolsa, C. (2015). 3793:Jones, A. (2005). 3772:Juste, D. (2021). 3708:. pp. 35–77. 3584:scs.fsu.edu/~dduke 3486:Jones, A. (2017). 2489:. Encyclopedia.com 2448:/ archive.nyu.edu. 2430:Jones, A. (2020). 2352:in late antiquity" 2296:Grove Music Online 2117:Harmonicorum libri 1969:on distances in a 1961:St. John's College 1909:Hero of Alexandria 1669:Pythagorean tuning 1611: 1607:Pythagorean tuning 1605:A diagram showing 1500: 1272: 1163:), Ptolemy gave a 1042: 897:models during the 793: 704:Arabic astronomers 556: 451:, and unlike most 392:natural philosophy 167:Ptolemaic universe 35: 7869:Egyptian calendar 7814:2nd-century poets 7645: 7644: 7610: 7609: 7362: 7361: 7349:Ptolemy's theorem 7222:Intercept theorem 7072:Apollonian gasket 6998:Doubling the cube 6971:The Sand Reckoner 6365: 6364: 6240:Celestial spheres 5457:(4318): 707–709. 5407:978-0-684-10114-9 5385:Toomer, Gerald J. 5361:978-3-7965-2148-5 5130:978-3-598-71746-8 5052:(4331): 872–873. 4891:Feke, J. (2014). 4858:978-0-691-17958-2 4845:Feke, J. (2018). 4586:978-1-317-67766-6 4442:Feke, J. (2012). 4266:978-1-351-55708-5 4061:, 135, 148, 160. 4021:978-90-481-2788-7 3758:978-0-691-18715-0 3723:978-2-503-58639-7 3655:Hamm, E. (2016). 3097:978-3-945561-23-2 3057:John Horace Parry 2865:978-1-4020-8404-1 2545:978-3-540-06995-9 2409:978-90-481-2787-0 2331:(subscription or 2318:978-1-56159-263-0 1967:Ptolemy's theorem 1810:history of optics 1736:compromise tuning 1587:pseudepigraphical 1558:medical astrology 1441:to the middle of 1312:for parts of the 987:Πρόχειροι κανόνες 942:Bernard Goldstein 921:in his 1977 book 733:Ptolemy wrote in 605:Ptolemaic Kingdom 495:Sohag Governorate 487:Ptolemais Hermiou 381:Greco-Roman world 237: 236: 206:Scientific career 187:Ptolemy's theorem 47:19 September 2024 26: 16:(Redirected from 7886: 7746: 7745: 7734: 7733: 7732: 7722: 7721: 7720: 7710: 7709: 7698: 7697: 7696: 7686: 7685: 7684: 7674: 7673: 7662: 7661: 7660: 7653: 7636: 7635: 7623: 7622: 7621: 7397: 7396: 7384:Platonic Academy 7331:Problem II.8 of 7301:Crossbar theorem 7257:Thales's theorem 7197:Euclid's theorem 7167: 7166: 7084:Commensurability 7045:Axiomatic system 6993:Angle trisection 6958: 6948: 6910: 6900: 6890: 6880: 6856: 6846: 6829: 6392: 6385: 6378: 6369: 6368: 6352:Indian astronomy 6305:Sublunary sphere 6275:Hipparchic cycle 6214:Mural instrument 6189:Armillary sphere 6168: 6158: 6148: 6138: 6128: 5884: 5877: 5870: 5861: 5860: 5850: 5793: 5781: 5779: 5777: 5764: 5762: 5760: 5744: 5742: 5740: 5723: 5721: 5719: 5699: 5697: 5695: 5667: 5659: 5619:codex valentinus 5617:. Also known as 5601: 5597: 5537: 5525: 5514: 5503: 5493: 5474: 5426: 5424: 5422: 5417:on 14 March 2012 5416: 5410:. Archived from 5393: 5375: 5373: 5372: 5365: 5330: 5315: 5296: 5283:Brill Publishers 5268: 5247: 5238:(3–4): 307–327. 5219: 5200: 5191: 5155: 5134: 5118: 5100: 5094: 5086: 5077: 5027: 4997: 4967: 4915: 4914: 4912: 4888: 4882: 4881: 4874:On the Criterion 4869: 4863: 4862: 4842: 4833: 4832: 4824: 4818: 4817: 4795: 4789: 4788: 4772: 4766: 4765: 4754: 4748: 4747: 4701: 4695: 4694: 4686: 4680: 4679: 4641: 4635: 4634: 4632: 4630: 4600: 4591: 4590: 4570: 4564: 4563: 4531: 4525: 4524: 4490: 4484: 4483: 4446:On the Kritêrion 4439: 4430: 4429: 4404: 4398: 4397: 4363: 4357: 4356: 4322: 4316: 4315: 4277: 4271: 4270: 4250: 4244: 4243: 4241: 4239: 4216: 4210: 4209: 4179: 4173: 4172: 4138: 4132: 4131: 4113: 4104: 4103: 4091: 4085: 4079: 4073: 4072: 4060: 4050: 4044: 4043: 4032: 4026: 4025: 3995: 3986: 3979: 3973: 3972: 3962: 3949: 3938: 3937: 3887: 3876: 3875: 3865: 3839: 3833: 3832: 3820: 3814: 3813: 3803: 3790: 3784: 3783: 3769: 3763: 3762: 3742: 3736: 3735: 3693: 3687: 3686: 3652: 3646: 3645: 3615: 3609: 3595: 3590:. Archived from 3575: 3569: 3568: 3530: 3524: 3523: 3483: 3477: 3464: 3458: 3457: 3415: 3409: 3408: 3397: 3391: 3390: 3362: 3356: 3350: 3344: 3338: 3329: 3323: 3312: 3306: 3287: 3280: 3274: 3273: 3237: 3231: 3224: 3218: 3217: 3175: 3169: 3168: 3130: 3124: 3123: 3121: 3119: 3112:"Dennis Rawlins" 3108: 3102: 3101: 3081: 3075: 3054: 3048: 3035: 3029: 3028: 3020: 3014: 3013: 2995: 2986: 2985: 2935: 2926: 2925: 2914: 2908: 2907: 2895: 2883: 2877: 2876: 2874: 2872: 2846:. Vol. 11. 2831: 2825: 2824: 2791: 2782: 2775: 2769: 2768: 2760: 2749: 2748: 2740: 2731: 2730: 2724: 2716: 2708: 2702: 2692: 2686: 2685: 2683: 2681: 2666: 2660: 2659: 2656:Tufts University 2647: 2639: 2633: 2632: 2603: 2597: 2596: 2586: 2575: 2569: 2568: 2549: 2526: 2520: 2519: 2517: 2505: 2499: 2498: 2496: 2494: 2475: 2469: 2462:Neugebauer (1975 2459: 2450: 2449: 2436: 2427: 2414: 2413: 2393: 2380: 2379: 2343: 2337: 2336: 2329: 2327: 2325: 2292: 2284: 2278: 2267: 2244: 2243: 2223: 2217: 2216: 2212: 2209: 2204: 2198: 2195: 2138: 2136: 2121: 2107: 2093: 2079: 2065: 2051: 2037: 2023: 1995:embedded systems 1981:Ptolemaic graphs 1881:On the Criterion 1870: 1795: 1792: 1781:), known as the 1780: 1765:Optics (Ptolemy) 1689:ancient, disused 1661:(Greek name) or 1630: 1542:sublunary sphere 1474:Maximus Planudes 1471: 1468: 1373: 1372: 1354: 1350: 1347: 1320:, as well as on 1302:), known as the 1301: 1298: 1295: 1292: 1289: 1285: 1235: 1231: 1207: 1204: 1201: 1198: 1195: 1191: 1117: 1115: 1114: 1107: 1105: 1104: 1097: 1095: 1094: 1078:celestial motion 1071: 1068: 1065: 1062: 1059: 1055: 1038:Bartolomeu Velho 988: 919:Robert R. Newton 853:also contains a 843:geometric models 822: 819: 816: 813: 810: 806: 729: 652:The 9th century 570: 569: 525: 522: 421: 418: 415: 412: 409: 405: 372: 364: 345:Western European 310: 306: 303: 291: 285: 284: 273: 272: 269: 268: 265: 262: 259: 256: 253: 250: 240:Claudius Ptolemy 129: 126: 111: 98:Pedro Berruguete 90: 71: 70: 21: 7894: 7893: 7889: 7888: 7887: 7885: 7884: 7883: 7754: 7753: 7752: 7740: 7730: 7728: 7718: 7716: 7704: 7694: 7692: 7682: 7680: 7668: 7658: 7656: 7648: 7646: 7641: 7630: 7619: 7617: 7606: 7572:Arabian/Islamic 7560: 7549:numeral systems 7438: 7388: 7358: 7306:Heron's formula 7284: 7266: 7158: 7154:Triangle center 7144:Regular polygon 7021:and definitions 7020: 7014: 6976: 6956: 6946: 6908: 6898: 6888: 6878: 6854: 6844: 6827: 6793: 6764:Theon of Smyrna 6409: 6401: 6396: 6366: 6361: 6335: 6314: 6300:Spherical Earth 6235:Callippic cycle 6223: 6204:Equatorial ring 6172: 6166: 6156: 6146: 6136: 6126: 6111: 6102:Theon of Smyrna 5893: 5888: 5858: 5791: 5775: 5773: 5758: 5756: 5738: 5736: 5717: 5715: 5693: 5691: 5657:"Ptolemy" 5624: 5599: 5595: 5545: 5540: 5534: 5491: 5482: 5480:Further reading 5477: 5420: 5418: 5414: 5408: 5391: 5370: 5368: 5367: 5362: 5293: 5131: 5116: 5088: 5087: 4994: 4923: 4918: 4889: 4885: 4870: 4866: 4859: 4843: 4836: 4825: 4821: 4796: 4792: 4773: 4769: 4755: 4751: 4702: 4698: 4687: 4683: 4660:10.1068/p050377 4642: 4638: 4628: 4626: 4624: 4601: 4594: 4587: 4571: 4567: 4532: 4528: 4491: 4487: 4440: 4433: 4426: 4405: 4401: 4364: 4360: 4323: 4319: 4278: 4274: 4267: 4251: 4247: 4237: 4235: 4233: 4217: 4213: 4180: 4176: 4139: 4135: 4128: 4114: 4107: 4092: 4088: 4080: 4076: 4069: 4058: 4051: 4047: 4033: 4029: 4022: 3996: 3989: 3980: 3976: 3960: 3950: 3941: 3888: 3879: 3840: 3836: 3821: 3817: 3801: 3791: 3787: 3770: 3766: 3759: 3743: 3739: 3724: 3694: 3690: 3653: 3649: 3634:10.2307/1006040 3616: 3612: 3598:Shockwave Flash 3576: 3572: 3531: 3527: 3484: 3480: 3465: 3461: 3416: 3412: 3398: 3394: 3363: 3359: 3351: 3347: 3339: 3332: 3324: 3315: 3307: 3290: 3281: 3277: 3238: 3234: 3225: 3221: 3176: 3172: 3131: 3127: 3117: 3115: 3110: 3109: 3105: 3098: 3082: 3078: 3055: 3051: 3036: 3032: 3022: 3021: 3017: 3010: 2996: 2989: 2936: 2929: 2915: 2911: 2904: 2893: 2884: 2880: 2870: 2868: 2866: 2832: 2828: 2792: 2785: 2776: 2772: 2761: 2752: 2741: 2734: 2718: 2717: 2709: 2705: 2693: 2689: 2679: 2677: 2667: 2663: 2645: 2640: 2636: 2629: 2604: 2600: 2584: 2576: 2572: 2546: 2527: 2523: 2515: 2506: 2502: 2492: 2490: 2476: 2472: 2460: 2453: 2434: 2428: 2417: 2410: 2394: 2383: 2344: 2340: 2330: 2323: 2321: 2319: 2285: 2281: 2268: 2257: 2253: 2248: 2247: 2241: 2224: 2220: 2214: 2210: 2205: 2201: 2196: 2192: 2187: 2182: 2167:Ptolemy's Canon 2146: 2134: 2033:[Opere] 2009: 1987:Ptolemy Project 1945:4001 Ptolemaeus 1917: 1853:epistemological 1849: 1793: 1778: 1767: 1761: 1752:Harmonice Mundi 1732:just intonation 1631:, known as the 1617: 1599: 1526:Plato of Tivoli 1488: 1482: 1469: 1370: 1368: 1357:map projections 1352: 1348: 1318:Marinus of Tyre 1299: 1296: 1293: 1290: 1258: 1252: 1246: 1234:μετεωροσκοπεῖον 1233: 1229: 1205: 1202: 1199: 1196: 1139: 1112: 1110: 1109: 1102: 1100: 1099: 1092: 1090: 1089: 1069: 1066: 1063: 1060: 1026: 973: 961: 907: 841:, who produced 820: 817: 814: 811: 785:Pages from the 779: 773: 755: 684:also wrote the 668:Ptolemy I Soter 645:or the emperor 601:Ptolemy I Soter 581:Greek mythology 552:Ptolemaic Egypt 532: 523: 479: 441:Catholic Church 419: 416: 413: 410: 308: 304: 247: 243: 197: 193: 189: 185: 181: 177: 173: 169: 136: 130: 127: 116: 113: 101: 94:Justus van Gent 76: 67: 60: 55: 54: 53: 52: 51: 50: 34: 22: 15: 12: 11: 5: 7892: 7882: 7881: 7876: 7871: 7866: 7861: 7856: 7851: 7846: 7841: 7836: 7831: 7826: 7821: 7816: 7811: 7806: 7801: 7796: 7791: 7786: 7781: 7776: 7771: 7766: 7751: 7750: 7738: 7726: 7714: 7702: 7690: 7678: 7666: 7643: 7642: 7615: 7612: 7611: 7608: 7607: 7605: 7604: 7599: 7594: 7589: 7584: 7579: 7574: 7568: 7566: 7565:Other cultures 7562: 7561: 7559: 7558: 7557: 7556: 7546: 7545: 7544: 7534: 7533: 7532: 7522: 7521: 7520: 7510: 7509: 7508: 7498: 7497: 7496: 7486: 7485: 7484: 7474: 7473: 7472: 7462: 7461: 7460: 7446: 7444: 7440: 7439: 7437: 7436: 7431: 7426: 7421: 7416: 7414:Greek numerals 7411: 7409:Attic numerals 7406: 7400: 7394: 7390: 7389: 7387: 7386: 7381: 7376: 7370: 7368: 7364: 7363: 7360: 7359: 7357: 7356: 7351: 7346: 7341: 7336: 7328: 7323: 7318: 7313: 7308: 7303: 7298: 7292: 7290: 7286: 7285: 7283: 7282: 7276: 7274: 7268: 7267: 7265: 7264: 7259: 7254: 7249: 7244: 7239: 7237:Law of cosines 7234: 7229: 7224: 7219: 7214: 7209: 7204: 7199: 7194: 7189: 7184: 7178: 7176: 7164: 7160: 7159: 7157: 7156: 7151: 7146: 7141: 7136: 7131: 7129:Platonic solid 7126: 7121: 7116: 7111: 7109:Greek numerals 7106: 7101: 7096: 7091: 7086: 7081: 7076: 7075: 7074: 7069: 7059: 7054: 7053: 7052: 7042: 7041: 7040: 7035: 7024: 7022: 7016: 7015: 7013: 7012: 7007: 7006: 7005: 7000: 6995: 6984: 6982: 6978: 6977: 6975: 6974: 6967: 6960: 6950: 6940: 6937:Planisphaerium 6933: 6926: 6919: 6912: 6902: 6892: 6882: 6872: 6865: 6858: 6848: 6838: 6831: 6821: 6814: 6809: 6801: 6799: 6795: 6794: 6792: 6791: 6786: 6781: 6776: 6771: 6766: 6761: 6756: 6751: 6746: 6741: 6736: 6731: 6726: 6721: 6716: 6711: 6706: 6701: 6696: 6691: 6686: 6681: 6676: 6671: 6666: 6661: 6656: 6651: 6646: 6641: 6636: 6631: 6626: 6621: 6616: 6611: 6606: 6601: 6596: 6591: 6586: 6581: 6576: 6571: 6566: 6561: 6556: 6551: 6546: 6541: 6536: 6531: 6526: 6521: 6516: 6511: 6506: 6501: 6496: 6491: 6486: 6481: 6476: 6471: 6466: 6461: 6456: 6451: 6446: 6441: 6436: 6431: 6426: 6421: 6415: 6413: 6407:Mathematicians 6403: 6402: 6395: 6394: 6387: 6380: 6372: 6363: 6362: 6360: 6359: 6354: 6349: 6343: 6341: 6337: 6336: 6334: 6333: 6328: 6322: 6320: 6316: 6315: 6313: 6312: 6307: 6302: 6297: 6292: 6287: 6282: 6277: 6272: 6267: 6262: 6257: 6252: 6247: 6242: 6237: 6231: 6229: 6225: 6224: 6222: 6221: 6216: 6211: 6206: 6201: 6196: 6191: 6186: 6180: 6178: 6174: 6173: 6171: 6170: 6164:On the Heavens 6160: 6150: 6140: 6137:(Eratosthenes) 6130: 6119: 6117: 6113: 6112: 6110: 6109: 6104: 6099: 6094: 6089: 6084: 6079: 6074: 6069: 6064: 6059: 6054: 6049: 6044: 6042:Philip of Opus 6039: 6034: 6029: 6024: 6019: 6014: 6009: 6004: 5999: 5994: 5989: 5984: 5979: 5974: 5969: 5964: 5959: 5954: 5949: 5944: 5939: 5934: 5929: 5924: 5919: 5914: 5909: 5903: 5901: 5895: 5894: 5887: 5886: 5879: 5872: 5864: 5857: 5856: 5851: 5834: 5824: 5814: 5808: 5799: 5788: 5782: 5765: 5745: 5724: 5704:Danzer, Gerald 5700: 5690:on 29 May 2005 5679: 5668: 5644: 5635: 5625: 5623: 5622: 5606: 5587: 5578: 5572: 5566: 5557: 5546: 5544: 5543:External links 5541: 5539: 5538: 5532: 5515: 5504: 5483: 5481: 5478: 5476: 5475: 5441:Wade, Nicholas 5437: 5427: 5406: 5381: 5360: 5352:, Greek-German 5336: 5316: 5297: 5291: 5271: 5255: 5248: 5221: 5201: 5192: 5157: 5136: 5129: 5117:Αποτελεσματικα 5101: 5078: 5028: 4998: 4992: 4968: 4948:10.2307/520071 4924: 4922: 4919: 4917: 4916: 4903:(3): 261–276. 4883: 4864: 4857: 4834: 4819: 4790: 4767: 4749: 4714:(3): 221–240. 4696: 4681: 4654:(4): 377–395. 4636: 4622: 4592: 4585: 4565: 4554:(3): 688–705. 4526: 4513:10.1086/657028 4507:(4): 403–420. 4485: 4466:(4): 585–594. 4431: 4424: 4414:. Oxford, UK: 4399: 4358: 4339:(4): 391–403. 4317: 4290:(2): 113–135. 4272: 4265: 4245: 4231: 4211: 4198:10.2307/283969 4174: 4133: 4126: 4105: 4102:. p. 135. 4086: 4074: 4068:978-0670093625 4067: 4045: 4027: 4020: 3987: 3974: 3939: 3904:(6): 483–508. 3877: 3856:(2): 221–240. 3834: 3815: 3785: 3764: 3757: 3737: 3722: 3688: 3669:(4): 416–424. 3647: 3610: 3578:Duke, Dennis. 3570: 3525: 3498:(2): 238–241. 3478: 3459: 3432:(4): 383–393. 3410: 3392: 3357: 3353:Gingerich 1980 3345: 3341:Goldstein 1978 3330: 3313: 3288: 3275: 3232: 3219: 3192:(3): 173–183. 3170: 3125: 3103: 3096: 3076: 3049: 3047:, p. 406–463 . 3030: 3015: 3008: 2987: 2958:10.1086/355836 2952:(3): 440–453. 2927: 2909: 2902: 2878: 2864: 2826: 2813:10.1086/356291 2807:(4): 596–607. 2783: 2770: 2750: 2732: 2703: 2687: 2661: 2634: 2627: 2598: 2570: 2557:Toomer, Gerald 2554: 2553: 2544: 2521: 2500: 2479:Toomer, Gerald 2470: 2451: 2415: 2408: 2381: 2338: 2317: 2279: 2254: 2252: 2249: 2246: 2245: 2238: 2237: 2233: 2232: 2218: 2199: 2189: 2188: 2186: 2183: 2181: 2180: 2175: 2170: 2164: 2159: 2153: 2147: 2145: 2142: 2141: 2140: 2131:Planisphaerium 2122: 2108: 2094: 2080: 2075:Quadripartitum 2066: 2061:Quadripartitum 2052: 2038: 2024: 2019:Quadripartitum 2008: 2005: 2004: 2003: 2000:Ptolemy Slocum 1997: 1984: 1978: 1964: 1953: 1947: 1941: 1931: 1916: 1913: 1848: 1845: 1820:Ibn al-Haytham 1815:Book of Optics 1763:Main article: 1760: 1757: 1681:perfect fourth 1659:harmonic canon 1598: 1595: 1591:Pseudo-Ptolemy 1514:Apotelesmatiká 1510:Quadripartitum 1496:Quadripartitum 1494:A copy of the 1484:Main article: 1481: 1478: 1439:Atlantic Ocean 1398:degrees of arc 1326:Persian Empire 1248:Main article: 1245: 1242: 1230:μετεωροσκόπιον 1181:Planisphaerium 1138: 1135: 1025: 1020: 972: 967: 930:Owen Gingerich 906: 903: 887:Late Antiquity 863:constellations 855:star catalogue 775:Main article: 772: 767: 754: 751: 745:or at least a 696:Upper Egyptian 531: 528: 478: 475: 463:late antiquity 417:On the Effects 404:Αποτελεσματικά 396:Apotelesmatika 329:music theorist 235: 234: 231: 230: 213: 209: 208: 202: 201: 164: 163:Known for 160: 159: 150:Greco-Egyptian 142: 138: 137: 131: 122: 118: 117: 114: 107: 103: 102: 91: 83: 82: 78: 77: 74: 58: 36: 30: 27: 25: 9: 6: 4: 3: 2: 7891: 7880: 7877: 7875: 7872: 7870: 7867: 7865: 7862: 7860: 7857: 7855: 7852: 7850: 7847: 7845: 7842: 7840: 7837: 7835: 7832: 7830: 7827: 7825: 7822: 7820: 7817: 7815: 7812: 7810: 7807: 7805: 7802: 7800: 7797: 7795: 7792: 7790: 7787: 7785: 7782: 7780: 7777: 7775: 7772: 7770: 7767: 7765: 7762: 7761: 7759: 7749: 7744: 7739: 7737: 7727: 7725: 7715: 7713: 7708: 7703: 7701: 7691: 7689: 7679: 7677: 7672: 7667: 7665: 7655: 7654: 7651: 7640: 7639: 7634: 7627: 7626: 7613: 7603: 7600: 7598: 7595: 7593: 7590: 7588: 7585: 7583: 7580: 7578: 7575: 7573: 7570: 7569: 7567: 7563: 7555: 7552: 7551: 7550: 7547: 7543: 7540: 7539: 7538: 7535: 7531: 7528: 7527: 7526: 7523: 7519: 7516: 7515: 7514: 7511: 7507: 7504: 7503: 7502: 7499: 7495: 7492: 7491: 7490: 7487: 7483: 7480: 7479: 7478: 7475: 7471: 7468: 7467: 7466: 7463: 7459: 7455: 7454: 7453: 7452: 7448: 7447: 7445: 7441: 7435: 7432: 7430: 7427: 7425: 7422: 7420: 7417: 7415: 7412: 7410: 7407: 7405: 7402: 7401: 7398: 7395: 7391: 7385: 7382: 7380: 7377: 7375: 7372: 7371: 7369: 7365: 7355: 7352: 7350: 7347: 7345: 7342: 7340: 7337: 7335: 7334: 7329: 7327: 7324: 7322: 7319: 7317: 7314: 7312: 7309: 7307: 7304: 7302: 7299: 7297: 7294: 7293: 7291: 7287: 7281: 7278: 7277: 7275: 7273: 7269: 7263: 7260: 7258: 7255: 7253: 7250: 7248: 7245: 7243: 7242:Pons asinorum 7240: 7238: 7235: 7233: 7230: 7228: 7225: 7223: 7220: 7218: 7215: 7213: 7212:Hinge theorem 7210: 7208: 7205: 7203: 7200: 7198: 7195: 7193: 7190: 7188: 7185: 7183: 7180: 7179: 7177: 7175: 7174: 7168: 7165: 7161: 7155: 7152: 7150: 7147: 7145: 7142: 7140: 7137: 7135: 7132: 7130: 7127: 7125: 7122: 7120: 7117: 7115: 7112: 7110: 7107: 7105: 7102: 7100: 7097: 7095: 7092: 7090: 7087: 7085: 7082: 7080: 7077: 7073: 7070: 7068: 7065: 7064: 7063: 7060: 7058: 7055: 7051: 7048: 7047: 7046: 7043: 7039: 7036: 7034: 7031: 7030: 7029: 7026: 7025: 7023: 7017: 7011: 7008: 7004: 7001: 6999: 6996: 6994: 6991: 6990: 6989: 6986: 6985: 6983: 6979: 6973: 6972: 6968: 6966: 6965: 6961: 6959: 6955: 6951: 6949: 6945: 6941: 6939: 6938: 6934: 6932: 6931: 6927: 6925: 6924: 6920: 6918: 6917: 6913: 6911: 6907: 6903: 6901: 6897: 6893: 6891: 6887: 6883: 6881: 6879:(Aristarchus) 6877: 6873: 6871: 6870: 6866: 6864: 6863: 6859: 6857: 6853: 6849: 6847: 6843: 6839: 6837: 6836: 6832: 6830: 6826: 6822: 6820: 6819: 6815: 6813: 6810: 6808: 6807: 6803: 6802: 6800: 6796: 6790: 6787: 6785: 6784:Zeno of Sidon 6782: 6780: 6777: 6775: 6772: 6770: 6767: 6765: 6762: 6760: 6757: 6755: 6752: 6750: 6747: 6745: 6742: 6740: 6737: 6735: 6732: 6730: 6727: 6725: 6722: 6720: 6717: 6715: 6712: 6710: 6707: 6705: 6702: 6700: 6697: 6695: 6692: 6690: 6687: 6685: 6682: 6680: 6677: 6675: 6672: 6670: 6667: 6665: 6662: 6660: 6657: 6655: 6652: 6650: 6647: 6645: 6642: 6640: 6637: 6635: 6632: 6630: 6627: 6625: 6622: 6620: 6617: 6615: 6612: 6610: 6607: 6605: 6602: 6600: 6597: 6595: 6592: 6590: 6587: 6585: 6582: 6580: 6577: 6575: 6572: 6570: 6567: 6565: 6562: 6560: 6557: 6555: 6552: 6550: 6547: 6545: 6542: 6540: 6537: 6535: 6532: 6530: 6527: 6525: 6522: 6520: 6517: 6515: 6512: 6510: 6507: 6505: 6502: 6500: 6497: 6495: 6492: 6490: 6487: 6485: 6482: 6480: 6477: 6475: 6472: 6470: 6467: 6465: 6462: 6460: 6457: 6455: 6452: 6450: 6447: 6445: 6442: 6440: 6437: 6435: 6432: 6430: 6427: 6425: 6422: 6420: 6417: 6416: 6414: 6412: 6408: 6404: 6400: 6393: 6388: 6386: 6381: 6379: 6374: 6373: 6370: 6358: 6355: 6353: 6350: 6348: 6345: 6344: 6342: 6338: 6332: 6329: 6327: 6324: 6323: 6321: 6317: 6311: 6308: 6306: 6303: 6301: 6298: 6296: 6293: 6291: 6288: 6286: 6285:Metonic cycle 6283: 6281: 6278: 6276: 6273: 6271: 6270:Heliocentrism 6268: 6266: 6263: 6261: 6258: 6256: 6253: 6251: 6250:Counter-Earth 6248: 6246: 6243: 6241: 6238: 6236: 6233: 6232: 6230: 6226: 6220: 6217: 6215: 6212: 6210: 6207: 6205: 6202: 6200: 6197: 6195: 6192: 6190: 6187: 6185: 6182: 6181: 6179: 6175: 6169: 6165: 6161: 6159: 6157:(Aristarchus) 6155: 6151: 6149: 6145: 6141: 6139: 6135: 6131: 6129: 6125: 6121: 6120: 6118: 6114: 6108: 6105: 6103: 6100: 6098: 6095: 6093: 6090: 6088: 6085: 6083: 6080: 6078: 6075: 6073: 6070: 6068: 6065: 6063: 6060: 6058: 6055: 6053: 6050: 6048: 6045: 6043: 6040: 6038: 6035: 6033: 6030: 6028: 6025: 6023: 6020: 6018: 6015: 6013: 6010: 6008: 6005: 6003: 6000: 5998: 5995: 5993: 5990: 5988: 5985: 5983: 5980: 5978: 5975: 5973: 5970: 5968: 5965: 5963: 5960: 5958: 5955: 5953: 5950: 5948: 5945: 5943: 5940: 5938: 5935: 5933: 5930: 5928: 5925: 5923: 5920: 5918: 5915: 5913: 5910: 5908: 5905: 5904: 5902: 5900: 5896: 5892: 5885: 5880: 5878: 5873: 5871: 5866: 5865: 5862: 5855: 5852: 5848: 5844: 5840: 5835: 5832: 5828: 5825: 5822: 5818: 5815: 5812: 5809: 5807: 5803: 5800: 5798: 5794: 5789: 5786: 5783: 5771: 5766: 5755: 5751: 5746: 5734: 5730: 5725: 5713: 5709: 5705: 5701: 5689: 5685: 5680: 5677: 5673: 5669: 5665: 5664: 5658: 5653: 5649: 5645: 5643: 5639: 5636: 5634: 5630: 5627: 5626: 5620: 5616: 5612: 5611: 5607: 5605: 5598:with preface 5594: 5592: 5588: 5585: 5583: 5579: 5576: 5573: 5570: 5567: 5565: 5563: 5558: 5555: 5551: 5548: 5547: 5535: 5533:0-8126-9229-2 5529: 5524: 5523: 5516: 5512: 5511: 5505: 5501: 5497: 5490: 5485: 5484: 5472: 5468: 5464: 5460: 5456: 5452: 5451: 5446: 5442: 5438: 5435: 5431: 5428: 5413: 5409: 5403: 5399: 5398: 5390: 5386: 5382: 5379: 5363: 5357: 5353: 5349: 5345: 5341: 5337: 5334: 5328: 5326:The Geography 5325: 5321: 5317: 5313: 5312: 5307: 5303: 5298: 5294: 5292:90-04-11591-9 5288: 5284: 5280: 5276: 5272: 5270: 5267: 5264: 5260: 5256: 5253: 5249: 5245: 5241: 5237: 5233: 5232: 5227: 5222: 5217: 5214: 5210: 5207: 5202: 5198: 5193: 5189: 5185: 5181: 5177: 5173: 5169: 5168: 5163: 5158: 5153: 5149: 5145: 5141: 5137: 5132: 5126: 5122: 5114: 5110: 5106: 5102: 5098: 5092: 5084: 5079: 5075: 5071: 5067: 5063: 5059: 5055: 5051: 5047: 5046: 5041: 5039: 5033: 5029: 5025: 5021: 5017: 5013: 5012: 5007: 5003: 5002:Gingerich, O. 4999: 4995: 4993:0-691-01042-0 4989: 4985: 4981: 4977: 4973: 4969: 4965: 4961: 4957: 4953: 4949: 4945: 4941: 4937: 4936: 4931: 4926: 4925: 4911: 4906: 4902: 4898: 4894: 4887: 4879: 4875: 4868: 4860: 4854: 4850: 4849: 4841: 4839: 4830: 4823: 4815: 4811: 4807: 4803: 4802: 4794: 4786: 4782: 4778: 4771: 4763: 4759: 4753: 4745: 4741: 4737: 4733: 4729: 4725: 4721: 4717: 4713: 4709: 4708: 4700: 4692: 4685: 4677: 4673: 4669: 4665: 4661: 4657: 4653: 4649: 4648: 4640: 4625: 4623:0-87169-862-5 4619: 4615: 4611: 4610: 4607: 4599: 4597: 4588: 4582: 4578: 4577: 4569: 4561: 4557: 4553: 4549: 4545: 4543: 4539: 4530: 4522: 4518: 4514: 4510: 4506: 4502: 4501: 4496: 4489: 4481: 4477: 4473: 4469: 4465: 4461: 4457: 4455: 4451: 4447: 4438: 4436: 4427: 4425:0-19-814975-1 4421: 4417: 4413: 4409: 4403: 4395: 4391: 4387: 4383: 4379: 4375: 4374: 4369: 4362: 4354: 4350: 4346: 4342: 4338: 4334: 4333: 4328: 4321: 4313: 4309: 4305: 4301: 4297: 4293: 4289: 4285: 4284: 4276: 4268: 4262: 4258: 4257: 4249: 4234: 4232:9788884505811 4228: 4224: 4223: 4215: 4207: 4203: 4199: 4195: 4191: 4187: 4186: 4178: 4170: 4166: 4162: 4158: 4154: 4150: 4149: 4144: 4137: 4129: 4127:0-674-99479-5 4123: 4119: 4112: 4110: 4101: 4097: 4090: 4083: 4078: 4070: 4064: 4056: 4049: 4041: 4040: 4031: 4023: 4017: 4013: 4009: 4005: 4001: 3994: 3992: 3984: 3978: 3971:(4): 254–260. 3970: 3966: 3959: 3957: 3948: 3946: 3944: 3935: 3931: 3927: 3923: 3919: 3915: 3911: 3907: 3903: 3899: 3898: 3893: 3886: 3884: 3882: 3873: 3869: 3864: 3859: 3855: 3851: 3850: 3845: 3838: 3830: 3826: 3819: 3811: 3807: 3800: 3798: 3789: 3781: 3780: 3776: 3768: 3760: 3754: 3750: 3749: 3741: 3733: 3729: 3725: 3719: 3715: 3711: 3707: 3703: 3701: 3692: 3684: 3680: 3676: 3672: 3668: 3664: 3663: 3658: 3651: 3643: 3639: 3635: 3631: 3627: 3623: 3622: 3614: 3607: 3603: 3599: 3593: 3589: 3585: 3581: 3574: 3566: 3562: 3558: 3554: 3550: 3546: 3542: 3538: 3537: 3529: 3521: 3517: 3513: 3509: 3505: 3501: 3497: 3493: 3489: 3482: 3476: 3473: 3469: 3463: 3455: 3451: 3447: 3443: 3439: 3435: 3431: 3427: 3426: 3421: 3414: 3406: 3403: 3396: 3388: 3384: 3380: 3376: 3372: 3368: 3361: 3354: 3349: 3342: 3337: 3335: 3327: 3322: 3320: 3318: 3310: 3305: 3303: 3301: 3299: 3297: 3295: 3293: 3285: 3279: 3271: 3267: 3263: 3259: 3255: 3251: 3247: 3245: 3236: 3229: 3223: 3215: 3211: 3207: 3203: 3199: 3195: 3191: 3187: 3186: 3181: 3174: 3166: 3162: 3158: 3154: 3150: 3146: 3142: 3138: 3137: 3129: 3113: 3107: 3099: 3093: 3089: 3088: 3080: 3074: 3073:0-520-04235-2 3070: 3066: 3062: 3058: 3053: 3046: 3043: 3039: 3038:George Sarton 3034: 3026: 3019: 3011: 3009:0-321-01618-1 3005: 3001: 2994: 2992: 2983: 2979: 2975: 2971: 2967: 2963: 2959: 2955: 2951: 2947: 2946: 2941: 2934: 2932: 2923: 2919: 2913: 2905: 2903:9781949822205 2899: 2891: 2890: 2882: 2867: 2861: 2857: 2853: 2849: 2845: 2841: 2839: 2830: 2822: 2818: 2814: 2810: 2806: 2802: 2801: 2796: 2790: 2788: 2780: 2774: 2766: 2759: 2757: 2755: 2747:. p. 68. 2746: 2745:(Jones, 2010) 2739: 2737: 2728: 2722: 2714: 2707: 2700: 2696: 2691: 2676: 2672: 2665: 2657: 2653: 2649: 2638: 2630: 2628:3-540-63198-4 2624: 2620: 2616: 2612: 2608: 2602: 2594: 2590: 2583: 2582: 2574: 2566: 2562: 2558: 2552: 2551: 2547: 2541: 2537: 2536: 2531: 2525: 2513: 2512: 2504: 2488: 2484: 2480: 2474: 2467: 2463: 2458: 2456: 2447: 2443: 2440: 2433: 2426: 2424: 2422: 2420: 2411: 2405: 2401: 2400: 2392: 2390: 2388: 2386: 2377: 2373: 2369: 2365: 2361: 2357: 2353: 2351: 2342: 2334: 2320: 2314: 2310: 2306: 2302: 2298: 2297: 2291: 2283: 2277: 2276: 2271: 2266: 2264: 2262: 2260: 2255: 2236: 2235: 2231: 2230: 2228: 2222: 2203: 2194: 2190: 2179: 2176: 2174: 2171: 2168: 2165: 2163: 2160: 2157: 2154: 2152: 2149: 2148: 2133: 2132: 2127: 2123: 2119: 2118: 2113: 2109: 2105: 2104: 2099: 2095: 2091: 2090: 2085: 2081: 2077: 2076: 2071: 2067: 2063: 2062: 2057: 2053: 2049: 2048: 2043: 2039: 2035: 2034: 2029: 2025: 2021: 2020: 2015: 2011: 2010: 2001: 1998: 1996: 1993:, real-time, 1992: 1988: 1985: 1982: 1979: 1976: 1972: 1968: 1965: 1962: 1958: 1957:Ptolemy stone 1954: 1951: 1948: 1946: 1943:The asteroid 1942: 1940: 1936: 1932: 1930: 1926: 1922: 1921: 1920: 1912: 1910: 1906: 1902: 1898: 1894: 1888: 1886: 1882: 1878: 1874: 1866: 1862: 1858: 1857:psychological 1854: 1844: 1840: 1837: 1833: 1827: 1825: 1824:Moon illusion 1821: 1817: 1816: 1811: 1807: 1803: 1799: 1788: 1784: 1776: 1772: 1766: 1756: 1754: 1753: 1748: 1744: 1739: 1737: 1733: 1729: 1728:single string 1725: 1721: 1717: 1712: 1710: 1706: 1702: 1698: 1694: 1690: 1686: 1682: 1678: 1674: 1673:perfect fifth 1670: 1666: 1665: 1660: 1655: 1653: 1649: 1644: 1640: 1638: 1634: 1626: 1622: 1616: 1608: 1603: 1594: 1592: 1588: 1584: 1580: 1579: 1574: 1569: 1566: 1561: 1559: 1555: 1551: 1550:numerological 1547: 1543: 1539: 1534: 1529: 1527: 1523: 1519: 1515: 1511: 1507: 1506: 1497: 1492: 1487: 1477: 1475: 1464: 1460: 1454: 1452: 1448: 1444: 1440: 1436: 1432: 1428: 1427: 1422: 1417: 1415: 1411: 1407: 1403: 1399: 1395: 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Retrieved 4221: 4214: 4189: 4183: 4177: 4155:(1): 67–84. 4152: 4146: 4142: 4136: 4117: 4100:Jones (2010) 4099: 4095: 4089: 4077: 4054: 4048: 4038: 4030: 4003: 3999: 3983:sidereal day 3977: 3968: 3965:E-Perimetron 3964: 3955: 3901: 3895: 3891: 3853: 3847: 3837: 3829:Live Science 3828: 3818: 3809: 3805: 3796: 3788: 3778: 3774: 3767: 3747: 3740: 3705: 3699: 3691: 3666: 3660: 3650: 3625: 3619: 3613: 3601: 3592:the original 3583: 3573: 3543:(1): 33–61. 3540: 3534: 3528: 3495: 3491: 3481: 3471: 3468:Handy Tables 3467: 3462: 3429: 3423: 3413: 3405: 3401: 3395: 3370: 3366: 3360: 3348: 3283: 3278: 3253: 3249: 3243: 3235: 3227: 3222: 3189: 3183: 3173: 3140: 3134: 3128: 3116:. Retrieved 3106: 3086: 3079: 3060: 3052: 3044: 3041: 3033: 3024: 3018: 2999: 2949: 2943: 2921: 2912: 2888: 2881: 2869:. Retrieved 2843: 2837: 2829: 2804: 2798: 2778: 2773: 2764: 2744: 2712: 2706: 2695:Toomer (1970 2690: 2678:. Retrieved 2674: 2664: 2651: 2637: 2610: 2601: 2580: 2573: 2564: 2534: 2524: 2510: 2503: 2491:. 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Retrieved 2294: 2282: 2273: 2221: 2202: 2193: 2130: 2125: 2116: 2111: 2102: 2097: 2088: 2083: 2074: 2069: 2060: 2055: 2046: 2041: 2032: 2027: 2018: 2013: 1918: 1905:Aristotelian 1889: 1880: 1876: 1872: 1860: 1850: 1841: 1828: 1813: 1782: 1770: 1768: 1750: 1740: 1723: 1719: 1715: 1713: 1704: 1662: 1658: 1656: 1652:Pythagoreans 1642: 1641: 1637:music theory 1632: 1620: 1618: 1582: 1578:Centiloquium 1576: 1570: 1564: 1562: 1537: 1532: 1530: 1521: 1517: 1513: 1509: 1503: 1501: 1495: 1458: 1455: 1434: 1424: 1420: 1418: 1406:polar circle 1391: 1363: 1361: 1342:Eratosthenes 1303: 1275: 1273: 1265: 1237: 1225:meteoroscope 1223: 1221: 1216: 1210: 1179: 1177: 1164: 1160: 1156: 1154: 1147: 1142: 1140: 1131:heliocentric 1120: 1081: 1074:cosmological 1045: 1043: 1033: 1022: 1015: 1012:Handy Tables 1011: 1009: 1002: 999:Handy Tables 998: 978:Handy Tables 976: 974: 970:Handy Tables 969: 963: 959: 946: 933: 927: 922: 916: 910: 908: 895:heliocentric 882: 874: 872: 867: 850: 848: 836: 824: 796: 794: 786: 769: 762: 758: 756: 732: 719: 685: 679: 675: 671: 651: 638: 630: 624: 619: 617: 585:Homeric form 572: 559: 557: 547: 518: 499: 480: 456: 449:Solar System 438: 433: 423: 395: 389:Aristotelian 374: 368: 354: 348: 239: 238: 205: 148:; ethnicity: 68: 46: 37:This is the 31: 7724:Outer space 7676:Mathematics 7525:mathematics 7333:Arithmetica 6930:Ostomachion 6899:(Autolycus) 6818:Arithmetica 6594:Hippocrates 6524:Dinostratus 6509:Dicaearchus 6439:Aristarchus 6265:Geocentrism 6177:Instruments 6167:(Aristotle) 5972:Cleostratus 5937:Aristarchus 5917:Anaximander 5899:Astronomers 5776:26 November 5759:24 November 5739:24 November 5718:26 November 5694:24 November 5604:archive.org 5562:Tetrabiblos 5228:and more". 5226:Cosmography 5174:: 105–107. 5167:Imago Mundi 5121:Tetrabiblos 4942:: 318–387. 4758:Boyer, C.B. 4450:Hêgemonikon 4192:: 235–256. 4143:Tetrabiblos 4096:Tetrabiblos 4082:Bagrow 1945 3795:"Ptolemy's 3628:(4): 9–12. 3143:(1): 1–12. 3063:, p. 10. 3023:"Ptolemy". 2211: 1360 1933:The crater 1923:The crater 1897:metaphysics 1885:mathematics 1877:hegemonikon 1794: 1154 1775:Koine Greek 1743:Renaissance 1741:During the 1677:tetrachords 1648:Aristoxenus 1583:Tetrabiblos 1565:Tetrabiblos 1533:Tetrabiblos 1522:Tetrabiblos 1505:Tetrabiblos 1486:Tetrabiblos 1431:topographic 1410:stone tower 1376:coordinates 1314:Roman world 1244:Cartography 1137:Other works 1096:Earth radii 763:Tetrabiblos 735:Koine Greek 728:بَطْلُمْيوس 708:geographers 687:Tetrabiblos 599:in 323 BC: 467:Middle Ages 465:and in the 430:Koine Greek 428:, from the 425:Tetrábiblos 141:Citizenship 7774:170 deaths 7769:100 births 7758:Categories 7577:Babylonian 7477:arithmetic 7443:History of 7272:Apollonius 6957:(Menelaus) 6916:On Spirals 6835:Catoptrics 6774:Xenocrates 6769:Thymaridas 6754:Theodosius 6739:Theaetetus 6719:Simplicius 6709:Pythagoras 6694:Posidonius 6679:Philonides 6639:Nicomachus 6634:Metrodorus 6624:Menaechmus 6579:Hipparchus 6569:Heliodorus 6519:Diophantus 6504:Democritus 6484:Chrysippus 6454:Archimedes 6449:Apollonius 6419:Anaxagoras 6411:(timeline) 6340:Influenced 6319:Influences 6290:Octaeteris 6219:Triquetrum 6107:Timocharis 6092:Theodosius 6052:Posidonius 6012:Hipparchus 6002:Heraclides 5942:Aristyllus 5927:Apollonius 5922:Andronicus 5823:Libraries. 5600:(in Latin) 5596:(in Greek) 5584:books 1–13 5208:Geographia 4976:Ptolemy's 4930:Geographia 4647:Perception 3956:Geographia 3326:Lewis 1979 3256:(3): 492. 2795:Bernal, M. 2697:, p. 2646:Πτολεμαῖος 2493:21 January 2464:, p. 2439:Ptolemy's 2299:. Oxford: 2251:References 2178:Zhang Heng 1991:concurrent 1935:Ptolemaeus 1925:Ptolemaeus 1847:Philosophy 1836:refraction 1832:reflection 1802:refraction 1798:reflection 1738:systems. 1693:tetrachord 1621:Harmonikon 1613:See also: 1463:world maps 1351: – c. 1349: 276 1330:Hipparchus 1322:gazetteers 1123:geocentric 949:palimpsest 938:Hipparchus 859:Hipparchus 839:Hipparchus 795:Ptolemy's 749:Egyptian. 747:Hellenized 712:physicists 657:astronomer 589:Macedonian 583:and is of 573:Ptolemaîos 568:Πτολεμαῖος 562:Ptolemaeus 524: 168 510:Roman rule 502:Alexandria 445:geocentric 325:geographer 321:astrologer 317:astronomer 309: 170 307: – c. 305: 100 289:Ptolemaios 282:Πτολεμαῖος 154:Hellenized 133:Alexandria 7700:Astronomy 7688:Geography 7664:Biography 7038:Inscribed 6798:Treatises 6789:Zenodorus 6749:Theodorus 6724:Sosigenes 6669:Philolaus 6654:Oenopides 6649:Nicoteles 6644:Nicomedes 6604:Hypsicles 6499:Ctesibius 6489:Cleomedes 6474:Callippus 6459:Autolycus 6444:Aristotle 6424:Anthemius 6194:Astrolabe 6127:(Ptolemy) 6047:Philolaus 6037:Oenopides 6022:Hypsicles 5967:Cleomedes 5962:Callippus 5952:Autolycus 5907:Aglaonice 5610:Geography 5593:books 1–6 5378:Geography 5348:Ptolemy, 5333:Geography 5279:Harmonics 5231:Quaerendo 5215:Geography 5091:cite book 5074:239876775 4978:Geography 4956:1651-3215 4744:117259123 4728:0003-9519 4560:2159-3159 4538:Harmonics 4521:161714215 4495:Harmonics 4454:Harmonics 4394:170415282 4353:123117827 4327:Harmonics 4304:0031-8868 4283:Phronesis 4238:19 August 4161:0003-049X 4039:Geography 4000:Geography 3934:133641503 3918:0003-9519 3892:Geography 3872:257453722 3775:Ptolemy, 3732:242599669 3565:116006562 3520:125658099 3454:0021-8286 3373:(2): 89. 3367:Centaurus 3309:Wade 1977 3270:1440-2807 3214:116612700 3165:118875902 3118:7 October 3059:(1981). 2966:0021-1753 2918:Aaboe, A. 2821:143901637 2721:cite book 2593:191297168 2335:required) 2290:"Ptolemy" 2156:Messier 7 1950:Messier 7 1724:Geography 1716:Harmonics 1701:monochord 1664:monochord 1643:Harmonics 1633:Harmonics 1629:Ἁρμονικόν 1573:aphorisms 1480:Astrology 1459:Geography 1435:oikoumenē 1426:oikoumenē 1421:Geography 1414:Silk Road 1402:midsummer 1364:Geography 1305:Geography 1167:, a star 1165:parapegma 1086:epicycles 759:Geography 753:Astronomy 720:Baṭlumyus 618:The name 609:Ptolemies 575:), is an 504:, in the 477:Biography 471:epicycles 376:Geography 337:Byzantine 333:treatises 224:Astrology 220:Geography 216:Astronomy 144:possibly 7602:Japanese 7587:Egyptian 7530:timeline 7518:timeline 7506:timeline 7501:geometry 7494:timeline 7489:calculus 7482:timeline 7470:timeline 7173:Elements 7019:Concepts 6981:Problems 6954:Spherics 6944:Spherics 6909:(Euclid) 6855:(Euclid) 6852:Elements 6845:(Euclid) 6806:Almagest 6714:Serenus 6689:Porphyry 6629:Menelaus 6584:Hippasus 6559:Eutocius 6534:Domninus 6429:Archytas 6295:Solstice 6228:Concepts 6124:Almagest 6067:Seleucus 6027:Menelaus 5987:Euctemon 5706:(1988). 5654:(1911). 5591:Almagest 5582:Almagest 5443:(1977). 5421:25 April 5387:(1970). 5066:17757580 5004:(1980). 4760:(1959). 4736:41133649 4676:23948158 4410:(1992). 3926:45211928 3812:: 53–97. 3700:Analemma 3683:57560804 3404:Almagest 3244:Almagest 2982:92988054 2920:(2001). 2838:Almagest 2532:(2004). 2376:68478868 2350:Almagest 2144:See also 2114:(1682). 2100:(1663). 2086:(1663). 2072:(1658). 2058:(1622). 2044:(1559). 2030:(1541). 2016:(1519). 1901:Platonic 1893:theology 1720:Almagest 1695:and the 1538:Almagest 1447:Shetland 1384:Latitude 1238:Analemma 1169:calendar 1149:analemma 1143:Analemma 1082:Almagest 991:eclipses 953:Delambre 934:Almagest 911:Almagest 875:Almagest 868:Almagest 851:Almagest 826:Almagest 788:Almagest 777:Almagest 761:and the 681:Almagest 676:Almagest 672:Almagest 643:Claudius 639:Almagest 620:Claudius 458:Almagest 350:Almagest 199:Quadrant 195:Evection 157:Egyptian 43:reviewed 7859:Claudii 7764:Ptolemy 7748:Science 7650:Portals 7582:Chinese 7537:numbers 7465:algebra 7393:Related 7367:Centers 7163:Results 7033:Central 6704:Ptolemy 6699:Proclus 6664:Perseus 6619:Marinus 6599:Hypatia 6589:Hippias 6564:Geminus 6554:Eudoxus 6544:Eudemus 6514:Diocles 6199:Dioptra 6062:Pytheas 6057:Ptolemy 6007:Hicetas 5997:Geminus 5992:Eudoxus 5947:Attalus 5912:Agrippa 5797:YouTube 5560:Entire 5496:SciAMVS 5459:Bibcode 5450:Science 5188:1150735 5045:Science 5020:Bibcode 5018:: 253. 4921:Sources 4814:i212542 4781:Bibcode 4629:27 June 4542:Timaeus 4468:Bibcode 4452:to the 4373:Apeiron 4312:4182463 4169:3143825 3806:SciAMVS 3779:, Works 3642:1006040 3545:Bibcode 3500:Bibcode 3434:Bibcode 3375:Bibcode 3258:Bibcode 3194:Bibcode 3145:Bibcode 2871:9 March 2680:4 April 2356:Apeiron 2272:at the 2270:Ptolemy 2162:Pei Xiu 2002:, actor 1927:on the 1783:Optics, 1685:octaves 1546:planets 1393:climata 1388:equator 1291: 1267:Ecumene 1213:Canopus 1197: 1173:almanac 1157:Phaseis 1106:radii), 1072:) is a 1061: 1040:(1568). 812: 654:Persian 627:Claudia 597:pharaoh 491:Thebaid 411: 387:to the 341:Islamic 115:Unknown 75:Ptolemy 7597:Indian 7374:Cyrene 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