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:
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
782:
88:
7671:
7633:
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 ...
1261:
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
7743:
1029:
7620:
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.
7731:
7695:
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7707:
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
7683:
7659:
1602:
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
1145:
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
2239:
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
1842:
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
913:
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
955:
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
833:
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
1838:
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.
1366:
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
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.
1456:
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
1890:
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
1535:
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
535:
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.
865:
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
2229:
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
4800:
4184:
6389:
5010:
2197:
Since no contemporary depictions or descriptions of Ptolemy are known to have existed, later artists' impressions are unlikely to have reproduced his appearance accurately.
5310:
3620:
5881:
4147:
1524:
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
5096:
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
7878:
7493:
2726:
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
4219:
Boudet, J.-P. (2014). "Astrology between rational science and divine inspiration: The pseudo-Ptolemy's centiloquium". In Rapisarda, S.; Niblaeus, E. (eds.).
928:
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.
4704:
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".
5662:
5266:. Göteborgs högskolas årsskrift. Vol. 36 (reprint ed.). Göteborg / New York, NY: Elanders boktr. aktiebolag. (1930) / Garland Publishing (1980).
1548:, based upon their combined effects of heating, cooling, moistening, and drying. Ptolemy dismisses other astrological practices, such as considering the
1960:
846:
800 years; however, many astronomers have for centuries suspected that some of his models' parameters were adopted independently of observations.
7571:
5801:
2289:
849:
Ptolemy presented his astronomical models alongside convenient tables, which could be used to compute the future or past position of the planets. The
6874:
6410:
6152:
5839:"The work of Claudius Ptolemy, as the epitome of the Macedonian Legacy in History, and of the Hellenistic and Alexandrian Science and Civilization"
7803:
6382:
6356:
656:
3824:
7838:
7418:
890:
5411:
2698:
7833:
7148:
5874:
5405:
5359:
5128:
4856:
4706:
4584:
4264:
4019:
3896:
3848:
3756:
3721:
3095:
2863:
2543:
2407:
2316:
7788:
7113:
4036:
3535:
3424:
3184:
3135:
5784:
7808:
7481:
7093:
6884:
6346:
6142:
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".
1614:
174:
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
7848:
7828:
7823:
7818:
7548:
6375:
5396:
4613:
4066:
1222:
In 2023, archaeologists were able to read a manuscript which gives instructions for the construction of an astronomical tool called a
1014:
survived separately from the tables themselves (apparently part of a gathering of some of Ptolemy's shorter writings) under the title
281:
5898:
5531:
5290:
4991:
4621:
4423:
4230:
4125:
3072:
3007:
2901:
2626:
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
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.
2847:
7873:
7798:
7783:
5867:
5707:
1367:
provides a catalogue of 8,000 localities he collected from Marinus and others, the biggest such database from antiquity. About
738:
1121:
The work is also notable for having descriptions on how to build instruments to depict the planets and their movements from a
7517:
7450:
7083:
6963:
5135:— The most recent edition of the Greek text of Ptolemy's astrological work, based on earlier editions by F. Boll and E. Boer.
3064:
1990:
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
917:
The overall quality of Claudius Ptolemy's observations has been challenged by several modern scientists, but prominently by
1001:
do not survive as such in Arabic or in Latin, they represent the prototype of most Arabic and Latin astronomical tables or
7863:
7853:
6279:
5568:
3579:
2609:; Dumont, Simone (2001). "From pre-Galilean astronomy to the Hubble Space Telescope and beyond". In Kaufman, Susan (ed.).
952:
7649:
1032:
A depiction of the non-Ptolemaic Universe with no epicycles, possibly from 500 years before Ptolemy, as described in the
7586:
7343:
7231:
6406:
5683:
5281:. Mnemosyne, Bibliotheca Classica Batava, Supplementum. Vol. 203. Translated by Solomon, Jon. Leiden / Boston, MA:
2172:
576:
178:
5115:]. Bibliotheca scriptorum Graecorum et Romanorum Teubneriana (in Latin). Vol. III. De Gruyter. Fascia 1:
38:
7843:
7793:
7778:
7226:
4827:
Ross, H.W.; Plug, C. (1998). "The history of size constancy and size illusions". In Walsh, V.; Kulikowski, J. (eds.).
1934:
1461:
is likely to be of different dates, in addition to containing many scribal errors. However, although the regional and
993:
of the Sun and Moon, making it a useful tool for astronomers and astrologers. The tables themselves are known through
707:
703:
588:
7295:
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
7868:
7813:
6922:
6738:
6713:
5796:
5549:
5224:
Peerlings, R.H.J.; Laurentius, F.; van den Bovenkamp, J. (2017). "The watermarks in the Rome editions of Ptolemy's
4983:
2274:
1490:
781:
344:
7457:
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6788:
6643:
6076:
1924:
711:
641:
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
7591:
6868:
5854:
Database of the Arabic and Latin versions of Ptolemy’s astronomical and astrological texts and related material
3587:
1309:
87:
63:
7325:
659:
5329:. Translated by E.L. Stevenson (Reprint ed.). New York, NY: New York Public Library, 1932 / Dover, 1991.
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7403:
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6942:
6861:
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6633:
6513:
6071:
5890:
4415:
3661:
2300:
1974:
1688:
182:
4367:
2611:
Understanding the Heavens: Thirty centuries of astronomical ideas from ancient thinking to modern cosmology
2347:
1520:), roughly meaning "(books) on the Effects" or "Outcomes", or "Prognostics". As a source of reference, the
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7251:
7201:
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6026:
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significance of names, that he believed to be without sound basis, and leaves out popular topics, such as
1462:
1255:
505:
170:
3842:
Gysembergh, Victor; Jones, Alexander; Zingg, Emanuel; Cotte, Pascal; Apicella, Salvatore (1 March 2023).
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7261:
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6568:
6254:
6183:
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5672:
Studien über Claudius Ptolemaeus. Ein Beitrag zur Geschichte der griechischen Philosophie und Astrologie
3533:
Murschel, A. (1995). "The structure and function of Ptolemy's physical hypotheses of planetary motion".
1409:
898:
482:
198:
7670:
7632:
7320:
2129:
960:
It also confirms that Ptolemy’s Star Catalogue was not based solely on data from Hipparchus’ Catalogue.
5400:. Vol. 11. New York, NY: Scribner & American Council of Learned Societies. pp. 186–206.
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6850:
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6658:
6613:
6593:
6438:
6423:
6325:
6066:
6016:
5936:
5911:
5458:
5031:
5019:
4780:
4646:
4467:
3748:
Geminos's Introduction to the Phenomena: A translation and study of a Hellenistic survey of astronomy
3544:
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3433:
3374:
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3193:
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2579:
1970:
1966:
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830:
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has come to symbolize a very complex theoretical model built in order to explain a false assumption.
388:
384:
186:
5488:
3133:
Goldstein, Bernard R. (1997). "Saving the phenomena: The background to Ptolemy's planetary theory".
7773:
7768:
7735:
7581:
7500:
7488:
7469:
7433:
7353:
7271:
7256:
7246:
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7191:
7133:
7002:
6894:
6823:
6758:
6748:
6648:
6618:
6558:
6533:
6458:
6448:
6433:
6096:
6001:
5951:
5926:
5805:
5671:
5641:
5632:
5574:
4934:
4757:
4499:
4331:
3697:
2445:
2073:
2045:
2017:
1952:, sometimes known as the Ptolemy Cluster, an open cluster of stars in the constellation of Scorpius
1786:
1304:
1249:
1084:
to present a physical realization of the universe as a set of nested spheres, in which he used the
1077:
994:
633:
is a Roman custom, characteristic of Roman citizens. This indicates that Ptolemy would have been a
592:
375:
2115:
2101:
2087:
2059:
2031:
1650:), backed up by empirical observation (in contrast to the excessively theoretical approach of the
1224:
909:
Under the scrutiny of modern scholarship, and the cross-checking of observations contained in the
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7637:
7596:
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7464:
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7123:
7098:
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6608:
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5613:, digitised codex made in Italy between 1460 and 1477, translated to Latin by Jacobus Angelus at
5183:
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5069:
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4671:
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4201:
4164:
3929:
3921:
3867:
3727:
3678:
3637:
3560:
3515:
3365:
Bruin, Franz; Bruin, Margaret (1976). "The equator ring, equinoxes, and atmospheric refraction".
3209:
3160:
2977:
2969:
2816:
2720:
2606:
2588:
2581:
Claudius Ptolemy and self-promotion: A study on Ptolemy's intellectual milieu in Roman Alexandria
2529:
2371:
2295:
1908:
1708:
1668:
1606:
391:
166:
7305:
6904:
5819:
of works by Ptolemy in .jpg and .tiff format. Online Galleries, History of Science Collections,
3890:
Graßhoff, G.; Mittenhuber, F.; Rinner, E. (2017). "Of paths and places: The origin of Ptolemy's
2835:
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
1240:, was identified on the basis of both its content and linguistic analysis as being by Ptolemy.
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7221:
7071:
6997:
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6398:
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5991:
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L'Optique de Claude Ptolémée dans la version latine d'après l'arabe de l'émir Eugène de Sicile
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4723:
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4555:
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4299:
4280:
Barker, A. (1994). "Ptolemy's Pythagoreans, Archytas, and Plato's conception of mathematics".
4260:
4226:
4156:
4121:
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4015:
4004:
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
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1260:
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5621:, it is the oldest manuscript of the codices with maps of Ptolemy with the donis projections.
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Ptolemy's Universe: The natural philosophical and ethical foundations of Ptolemy's astronomy
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2363:
2304:
1764:
1751:
1691:) musical tuning practice of his day, which he then compared to his own subdivisions of the
1541:
1473:
1122:
1037:
918:
245:
97:
5444:
5220:— Until Stückelberger (2006), this was the most recent edition of the complete Greek text.
3286:, New York: Frederick Ungar Publishing, 1967, reprint of the Cambridge, Mass., 1927 edition
1512:. Its original title is unknown, but may have been a term found in some Greek manuscripts,
7153:
7143:
7037:
6763:
6299:
6234:
6203:
6101:
6031:
5651:
3825:"Hidden Ptolemy text, printed beneath a Latin manuscript, deciphered after 200 years"
3597:
2332:
1994:
1986:
1980:
1944:
1904:
1731:
1525:
1430:
1325:
1317:
1175:, based on the appearances and disappearances of stars over the course of the solar year.
878:
870:
was the authoritative text on astronomy across Europe, the Middle East, and North Africa.
842:
742:
723:
667:
600:
580:
440:
340:
93:
1236:). The text, which comes from an eighth-century manuscript which also contains Ptolemy's
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
947:
In 2022 the first Greek fragments of Hipparchus' lost star catalog were discovered in a
7747:
7413:
7408:
7236:
7128:
7108:
6936:
6493:
6463:
6162:
6041:
5976:
5956:
5656:
5001:
3386:
2944:
2799:
2166:
1999:
1864:
1819:
1814:
1680:
1624:
1590:
1438:
1397:
1356:
1333:
1279:
1212:
1185:
1180:
1049:
982:
940:
278 years earlier, rejected the qualification of fraud. Objections were also raised by
929:
886:
854:
800:
561:
462:
399:
358:
328:
293:
275:
149:
5816:
5005:
4493:
Barker, A. (2010). "Mathematical beauty made audible: Musical aesthetics in Ptolemy's
4220:
3618:
Goldstein, Bernard R. (1967). "The Arabic version of Ptolemy's planetary hypotheses".
1834:
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 (
1028:
881:
manuscripts; the modern title is thought to be an Arabic corruption of the Greek name
7757:
7373:
7241:
7211:
7032:
6840:
6783:
6284:
6269:
6249:
5703:
5520:
5440:
5152:
of Claudius Ptolemy in the Latin version based on the Arabic of Emir Eugene of Sicily
5073:
4743:
4520:
4393:
4352:
4182:
Riley, M. (1987). "Theoretical and practical astrology: Ptolemy and his colleagues".
3982:
3933:
3871:
3731:
3564:
3519:
3213:
3164:
3085:
3037:
2820:
2794:
2670:
2592:
2556:
2478:
1956:
1823:
1672:
1586:
1130:
862:
746:
595:
and there were several of this name among Alexander's army, one of whom made himself
584:
543:
513:
497:). This attestation is quite late, however, and there is no evidence to support it.
481:
Ptolemy's date of birth and birthplace are both unknown. The 14th-century astronomer
312:
153:
5711:
4691:
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:
7742:
7711:
7315:
7103:
6778:
6538:
6528:
6132:
5981:
5433:
5057:
4535:
4225:. Micrologus' library. Vol. 65. Sismel edizioni del Galluzzo. pp. 47–73.
2437:. In Juste, D.; van Dalen, B.; Hasse, D.N.; Burnett, C.; Turnhout; Brepols (eds.).
1852:
1651:
1636:
1577:
1405:
1341:
1313:
977:
894:
623:
509:
448:
145:
5559:
4006:. Archimedes. Vol. 23. Dordrecht, NL: Springer Netherlands. pp. 95–119.
3953:
1425:
889:. Because of its reputation, it was widely sought and translated twice into Latin
5508:
5470:
4385:
2887:
2560:
2482:
2397:
2367:
6929:
6817:
6523:
6508:
5971:
5916:
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
5166:
4479:
4444:"Mathematizing the soul: The development of Ptolemy's psychological theory from
4011:
3591:
3241:
2917:
2618:
2444:. Ptolemaeus Arabus et Latinus Studies. Vol. 1. pp. 13–34 – via
1896:
1774:
1742:
1647:
1504:
1485:
1476:), there are some scholars who think that such maps go back to Ptolemy himself.
734:
695:
686:
612:
466:
429:
424:
5787:– at Paul Stoddard's Animated Virtual Planetarium, Northern Illinois University
4295:
3862:
3843:
3713:
3556:
3420:"New evidence for Hipparchus' star catalogue revealed by multispectral imaging"
3205:
3156:
1883:
is also noteworthy for being the only one of Ptolemy's works that is devoid of
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
6915:
6834:
6773:
6768:
6708:
6693:
6638:
6623:
6578:
6518:
6503:
6483:
6453:
6418:
6289:
6106:
6051:
6011:
5941:
5826:
5790:
5243:
5179:
4344:
3909:
3445:
3056:
2855:
2226:
2177:
1856:
1835:
1801:
1692:
1676:
1549:
1375:
1329:
948:
937:
858:
838:
829:, is the only surviving comprehensive ancient treatise on astronomy. Although
501:
444:
324:
320:
316:
132:
5687:
5628:
4955:
4909:
4892:
4727:
4559:
4303:
4160:
3917:
3511:
3453:
3269:
3179:
2965:
2743:
Heilen, Stephan (2010). "Ptolemy's doctrine of the terms and its reception".
607:. Almost all subsequent pharaohs of Egypt, with a few exceptions, were named
379:, which is a thorough discussion on maps and the geographic knowledge of the
6668:
6653:
6603:
6498:
6488:
6473:
6443:
6367:
6193:
6046:
6036:
6021:
5966:
5961:
5906:
5230:
4644:
Ross, H.E.; Ross, G.M. (1976). "Did Ptolemy understand the moon illusion?".
4282:
2155:
1949:
1900:
1727:
1700:
1663:
1540:
was the first, concerned with the influences of the celestial bodies in the
1413:
1408:. One of the places Ptolemy noted specific coordinates for was the now-lost
1401:
1321:
1073:
534:
512:. He had a Latin name, Claudius, which is generally taken to imply he was a
223:
219:
215:
156:
5769:
5637:
5065:
3487:
3402:
On the quality of solar and lunar observations and parameters in Ptolemy's
2939:
1264:
A printed map from the 15th century depicting Ptolemy's description of the
5859:
5749:
2092:(in Latin). Paris: Sebastian Cramoisy (1.) & Sebastian Mabre-Cramoisy.
1796:). In it, Ptolemy writes about properties of sight (not light), including
6805:
6583:
6428:
6294:
6122:
5986:
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:
1892:
1572:
1446:
1383:
1168:
1148:
1085:
990:
825:
787:
776:
680:
653:
642:
550:
showing an early conflation of the mathematician with the royal house of
470:
457:
349:
332:
194:
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,
383:. The third is the astrological treatise in which he attempted to adapt
17:
7378:
6698:
6598:
6588:
6563:
6198:
6061:
6006:
5996:
5614:
5187:
4893:"Meta-mathematical rhetoric: Hero and Ptolemy against the philosophers"
4813:
4719:
4372:
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:
2161:
1545:
1387:
1266:
1172:
670:
were wise "and included Ptolemy the Wise, who composed the book of the
596:
490:
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
6673:
6548:
6309:
6259:
6208:
6081:
5931:
5853:
5827:
Codex Vaticanus graecus 1291 (Vat.gr.1291) in Vatican Digital Library
4606:
Ptolemy's Theory of Visual Perception: An English translation of the
2150:
1805:
1746:
1696:
1684:
1450:
1126:
837:
The earliest person that attempted to merge these two approaches was
715:
691:
539:
287:
227:
190:
5629:
Hieronymi Cardani ... In Cl. Ptolemaei ... IIII De astrorum judiciis
4659:
4042:(Report). Orbis Terrarum. Vol. 9 (2003–2007). pp. 177–180.
3633:
1601:
885:(lit. "The greatest treatise"), as the work was presumably known in
7706:
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:
7049:
7027:
6683:
5608:
3605:
2763:
Robbins, Frank E. (1940). "Introduction". In Robbins, F.E. (ed.).
2139:— medieval Arabic translations and an English translation of those
1600:
1489:
1442:
1404:
day increases from 12h to 24h as one goes from the equator to the
1392:
1259:
1027:
780:
741:. He might have been a Roman citizen, but was ethnically either a
699:
533:
347:
science. The first was his astronomical treatise now known as the
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",
1938:
1928:
1337:
646:
443:
promoted his work, which included the only mathematically sound
6371:
5863:
1859:
discussions across his corpus. He wrote a short essay entitled
1340:
based on scientific principles had been made since the time of
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
1003:
5331:— This is the only complete English translation of Ptolemy's
4798:
Riley, M. (1995). "Ptolemy's use of his predecessors' data".
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
877:
was preserved, like many extant Greek scientific works, in
266:
260:
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:
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
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
2158:– Ptolemy Cluster, star cluster described by Ptolemaeus
461:) never ceased to be copied or commented upon, both in
42:
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
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:
7564:
7442:
7392:
7366:
7288:
7270:
7169:
7162:
7018:
6980:
6797:
6405:
6339:
6318:
6227:
6176:
6115:
5897:
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:
211:
162:
140:
120:
105:
73:
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
3844:"Ptolemy's treatise on the meteoroscope recovered"
3745:Evans, James; Berggren, J. Lennart (5 June 2018).
3621:Transactions of the American Philosophical Society
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.
4148:Proceedings of the American Philosophical Society
3706:Ptolemy's Science of the Stars in the Middle Ages
3228:Astronomies and Cultures in Early Medieval Europe
3114:. The International Journal of Scientific History
432:meaning "Four Books", or by its Latin equivalent
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:
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
5354:] (in German). Basel, CH: Schwabe Verlag.
5218:] (in Latin). Leipzig: Carolus Tauchnitus.
2789:
2787:
2738:
2736:
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
6383:
5875:
5109:Claudius Ptolemaeus, Opera quae exstant omnia
4598:
4596:
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
8:
5676:Neue Jahrbücher für Philologie und Pädagogik
5095:: CS1 maint: multiple names: authors list (
4880:. Oxford University Press. pp. 301–331.
4840:
4838:
4437:
4435:
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
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)
5792:Animation of Ptolemy's two Solar hypotheses
5197:A History of Ancient Mathematical Astronomy
4037:Hipparchus' table of climata and Ptolemy's
3777:Planispherium. Ptolemaeus Arabus et Latinus
3284:Studies in the History of Mediaeval Science
2565:Complete Dictionary of Scientific Biography
2535:A History of Ancient Mathematical Astronomy
2487:Complete Dictionary of Scientific Biography
1287:
1193:
1057:
808:
662:mistakenly presents Ptolemy as a member of
407:
394:of his day. This is sometimes known as the
26:
7396:
7166:
6390:
6376:
6368:
5882:
5868:
5860:
2850:/ Springer Netherlands. pp. 183–225.
2725:: CS1 maint: location missing publisher (
2461:
2103:De iudicandi facultate et animi principatu
2089:De iudicandi facultate et animi principatu
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:
70:
5322:(1991) . Stevenson, Edward Luther (ed.).
5263:Die Harmonielehre des Klaudios Ptolemaios
4908:
4573:Hetherington, Norriss S. (8 April 2014).
4536:"Philosophical presentation in Ptolemy's
4368:"Greek musicologists in the Roman Empire"
4098:in Renaissance and early modern Europe".
3861:
3352:
3340:
3250:Repositorio Institucional CONICET Digital
3087:The Globalization of Knowledge in History
3000:A History of Mathematics: An introduction
2924:. New York, NY: Springer. pp. 62–65.
2215:unsupported." — Toomer & Jones (2018)
1412:which marked the midpoint on the ancient
1332:for having provided the elevation of the
335:, three of which were important to later
3242:"Notes on the transmission of Ptolemy's
1959:used in the mathematics courses at both
1445:, and about 80 degrees of latitude from
32:This is an accepted version of this page
7654:
5785:Java simulation of the Ptolemaic System
5487:Sidoli, Nathan; Berggren, J.L. (2007).
2441:Science of the Stars in the Middle Ages
2309:10.1093/gmo/9781561592630.article.22510
2255:
2190:
1308:, a handbook on how to draw maps using
1215:, around 146–147 AD, known as the
1133:one, presumably for didactic purposes.
28:
7419:Latin translations of the 12th century
5811:Flash animation of Ptolemy's universe.
5710:. The Newberry Library. Archived from
5088:
4081:
4057:. Delhi, IN: Penguin Viking. pp.
2718:
2694:
2050:(in Latin). Basel, CH: Heinrich Petri.
1433:lists, and captions for the maps. His
1010:Additionally, the introduction to the
7879:Epigrammatists of the Greek Anthology
7149:Straightedge and compass construction
5686:. obs.nineplanets.org. Archived from
5550:Ptolemy's Tetrabiblos at LacusCurtius
5302:Ptolemy's Theory of Visual Perception
4762:The Rainbow: From myth to mathematics
4707:Archive for History of Exact Sciences
3897:Archive for History of Exact Sciences
3849:Archive for History of Exact Sciences
3325:
3240:Krisciunas, K.; Bistué, M.B. (2019).
3027:. Encyclopædia Britannica, Inc. 2006.
1593:, remains the subject of conjecture.
7:
7114:Incircle and excircles of a triangle
5156:— Latin text with French translation
3823:Nalewicki, Jennifer (7 April 2023).
3799:and Heliodorus' observation reports"
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
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
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:
5571:(English translation, incomplete)
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.).
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.).
4116:Robbins, Frank E., ed. (1940).
3400:Britton, John Phillips (1967).
3025:Britannica Concise Encyclopedia
3002:. Addison Wesley. p. 184.
2848:Springer Science+Business Media
2781:, p. 177. Wittenberg: Gottlieb.
2671:"Egypt in the Ptolemaic Period"
1718:never had the influence of his
1146:diagram that Ptolemy calls the
997:'s version. Although Ptolemy's
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
1977:, to non-cyclic quadrilaterals
1619:Ptolemy wrote a work entitled
1563:The great popularity that the
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).
2207:
1869:Περὶ Κριτηρίου καὶ Ἡγεμονικοῡ
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
739:Babylonian astronomical data
288:
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
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:
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
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:
7429:Philosophy of mathematics
7399:
7344:Ptolemy's table of chords
6399:Ancient Greek mathematics
6347:Medieval European science
6077:Sosigenes the Peripatetic
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:
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:
204:
179:Ptolemy's table of chords
85:
80:
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).
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
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
16:(Redirected from
7886:
7746:
7745:
7734:
7733:
7732:
7722:
7721:
7720:
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7709:
7698:
7697:
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7685:
7684:
7674:
7673:
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7661:
7660:
7653:
7636:
7635:
7623:
7622:
7621:
7397:
7384:Platonic Academy
7331:Problem II.8 of
7301:Crossbar theorem
7257:Thales's theorem
7197:Euclid's theorem
7167:
7084:Commensurability
7045:Axiomatic system
6993:Angle trisection
6958:
6948:
6910:
6900:
6890:
6880:
6856:
6846:
6829:
6392:
6385:
6378:
6369:
6352:Indian astronomy
6305:Sublunary sphere
6275:Hipparchic cycle
6214:Mural instrument
6189:Armillary sphere
6168:
6158:
6148:
6138:
6128:
5884:
5877:
5870:
5861:
5850:
5793:
5781:
5779:
5777:
5764:
5762:
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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:
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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:
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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:
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4216:
4210:
4209:
4179:
4173:
4172:
4138:
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4131:
4113:
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4091:
4085:
4079:
4073:
4072:
4060:
4050:
4044:
4043:
4032:
4026:
4025:
3995:
3986:
3979:
3973:
3972:
3962:
3949:
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3887:
3876:
3875:
3865:
3839:
3833:
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3814:
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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:
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3391:
3390:
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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:
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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:
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:
5836:
5791:
5775:
5773:
5767:
5758:
5756:
5747:
5738:
5736:
5726:
5717:
5715:
5702:
5693:
5691:
5681:
5657:"Ptolemy"
5646:
5624:
5599:
5595:
5545:
5540:
5534:
5517:
5506:
5491:
5486:
5482:
5480:Further reading
5477:
5439:
5420:
5418:
5414:
5408:
5391:
5383:
5370:
5368:
5367:
5362:
5338:
5318:
5299:
5293:
5273:
5257:
5223:
5203:
5194:
5159:
5138:
5131:
5116:
5103:
5087:
5080:
5030:
5000:
4994:
4970:
4927:
4923:
4918:
4890:
4889:
4885:
4871:
4870:
4866:
4859:
4844:
4843:
4836:
4826:
4825:
4821:
4797:
4796:
4792:
4774:
4773:
4769:
4756:
4755:
4751:
4703:
4702:
4698:
4688:
4687:
4683:
4660:10.1068/p050377
4643:
4642:
4638:
4628:
4626:
4624:
4602:
4601:
4594:
4587:
4572:
4571:
4567:
4533:
4532:
4528:
4492:
4491:
4487:
4441:
4440:
4433:
4426:
4406:
4405:
4401:
4365:
4364:
4360:
4324:
4323:
4319:
4279:
4278:
4274:
4267:
4252:
4251:
4247:
4237:
4235:
4233:
4218:
4217:
4213:
4181:
4180:
4176:
4140:
4139:
4135:
4128:
4115:
4114:
4107:
4093:
4092:
4088:
4080:
4076:
4069:
4058:
4052:
4051:
4047:
4034:
4033:
4029:
4022:
3997:
3996:
3989:
3980:
3976:
3960:
3951:
3950:
3941:
3889:
3888:
3879:
3841:
3840:
3836:
3822:
3821:
3817:
3801:
3792:
3791:
3787:
3771:
3770:
3766:
3759:
3744:
3743:
3739:
3724:
3695:
3694:
3690:
3654:
3653:
3649:
3634:10.2307/1006040
3617:
3616:
3612:
3598:Shockwave Flash
3577:
3576:
3572:
3532:
3531:
3527:
3485:
3484:
3480:
3465:
3461:
3417:
3416:
3412:
3399:
3398:
3394:
3364:
3363:
3359:
3351:
3347:
3339:
3332:
3324:
3315:
3307:
3290:
3281:
3277:
3239:
3238:
3234:
3225:
3221:
3177:
3176:
3172:
3132:
3131:
3127:
3117:
3115:
3110:
3109:
3105:
3098:
3083:
3082:
3078:
3055:
3051:
3036:
3032:
3022:
3021:
3017:
3010:
2997:
2996:
2989:
2937:
2936:
2929:
2916:
2915:
2911:
2904:
2893:
2885:
2884:
2880:
2870:
2868:
2866:
2833:
2832:
2828:
2793:
2792:
2785:
2776:
2772:
2762:
2761:
2752:
2742:
2741:
2734:
2717:
2710:
2709:
2705:
2693:
2689:
2679:
2677:
2668:
2667:
2663:
2645:
2641:
2640:
2636:
2629:
2605:
2604:
2600:
2584:
2577:
2576:
2572:
2555:
2546:
2528:
2527:
2523:
2515:
2507:
2506:
2502:
2492:
2490:
2477:
2476:
2472:
2460:
2453:
2434:
2429:
2428:
2417:
2410:
2395:
2394:
2383:
2345:
2344:
2340:
2330:
2323:
2321:
2319:
2286:
2285:
2281:
2268:
2257:
2253:
2248:
2247:
2241:
2224:
2220:
2214:
2210:
2205:
2201:
2196:
2192:
2187:
2182:
2167:Ptolemy's Canon
2146:
2134:
2124:
2110:
2096:
2082:
2068:
2054:
2040:
2033:[Opere]
2026:
2012:
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:
7890:
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:
7756:
7755:
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:
6397:
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:
5889:
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:
56:
36:
30:
27:
25:
24:
23:
14:
13:
10:
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:
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:
5542:
5535:
5533:0-8126-9229-2
5529:
5524:
5523:
5516:
5512:
5511:
5505:
5501:
5497:
5490:
5485:
5484:
5479:
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:
4920:
4911:
4906:
4902:
4898:
4894:
4887:
4884:
4879:
4875:
4868:
4865:
4860:
4854:
4850:
4849:
4841:
4839:
4835:
4830:
4823:
4820:
4815:
4811:
4807:
4803:
4802:
4794:
4791:
4786:
4782:
4778:
4771:
4768:
4763:
4759:
4753:
4750:
4745:
4741:
4737:
4733:
4729:
4725:
4721:
4717:
4713:
4709:
4708:
4700:
4697:
4692:
4685:
4682:
4677:
4673:
4669:
4665:
4661:
4657:
4653:
4649:
4648:
4640:
4637:
4625:
4623:0-87169-862-5
4619:
4615:
4611:
4610:
4607:
4599:
4597:
4593:
4588:
4582:
4578:
4577:
4569:
4566:
4561:
4557:
4553:
4549:
4545:
4543:
4539:
4530:
4527:
4522:
4518:
4514:
4510:
4506:
4502:
4501:
4496:
4489:
4486:
4481:
4477:
4473:
4469:
4465:
4461:
4457:
4455:
4451:
4447:
4438:
4436:
4432:
4427:
4425:0-19-814975-1
4421:
4417:
4413:
4409:
4403:
4400:
4395:
4391:
4387:
4383:
4379:
4375:
4374:
4369:
4362:
4359:
4354:
4350:
4346:
4342:
4338:
4334:
4333:
4328:
4321:
4318:
4313:
4309:
4305:
4301:
4297:
4293:
4289:
4285:
4284:
4276:
4273:
4268:
4262:
4258:
4257:
4249:
4246:
4234:
4232:9788884505811
4228:
4224:
4223:
4215:
4212:
4207:
4203:
4199:
4195:
4191:
4187:
4186:
4178:
4175:
4170:
4166:
4162:
4158:
4154:
4150:
4149:
4144:
4137:
4134:
4129:
4127:0-674-99479-5
4123:
4119:
4112:
4110:
4106:
4101:
4097:
4090:
4087:
4083:
4078:
4075:
4070:
4064:
4056:
4049:
4046:
4041:
4040:
4031:
4028:
4023:
4017:
4013:
4009:
4005:
4001:
3994:
3992:
3988:
3984:
3978:
3975:
3971:(4): 254–260.
3970:
3966:
3959:
3957:
3948:
3946:
3944:
3940:
3935:
3931:
3927:
3923:
3919:
3915:
3911:
3907:
3903:
3899:
3898:
3893:
3886:
3884:
3882:
3878:
3873:
3869:
3864:
3859:
3855:
3851:
3850:
3845:
3838:
3835:
3830:
3826:
3819:
3816:
3811:
3807:
3800:
3798:
3789:
3786:
3781:
3780:
3776:
3768:
3765:
3760:
3754:
3750:
3749:
3741:
3738:
3733:
3729:
3725:
3719:
3715:
3711:
3707:
3703:
3701:
3692:
3689:
3684:
3680:
3676:
3672:
3668:
3664:
3663:
3658:
3651:
3648:
3643:
3639:
3635:
3631:
3627:
3623:
3622:
3614:
3611:
3607:
3603:
3599:
3593:
3589:
3585:
3581:
3574:
3571:
3566:
3562:
3558:
3554:
3550:
3546:
3542:
3538:
3537:
3529:
3526:
3521:
3517:
3513:
3509:
3505:
3501:
3497:
3493:
3489:
3482:
3479:
3476:
3473:
3469:
3463:
3460:
3455:
3451:
3447:
3443:
3439:
3435:
3431:
3427:
3426:
3421:
3414:
3411:
3406:
3403:
3396:
3393:
3388:
3384:
3380:
3376:
3372:
3368:
3361:
3358:
3354:
3349:
3346:
3342:
3337:
3335:
3331:
3327:
3322:
3320:
3318:
3314:
3310:
3305:
3303:
3301:
3299:
3297:
3295:
3293:
3289:
3285:
3279:
3276:
3271:
3267:
3263:
3259:
3255:
3251:
3247:
3245:
3236:
3233:
3229:
3223:
3220:
3215:
3211:
3207:
3203:
3199:
3195:
3191:
3187:
3186:
3181:
3174:
3171:
3166:
3162:
3158:
3154:
3150:
3146:
3142:
3138:
3137:
3129:
3126:
3113:
3107:
3104:
3099:
3093:
3089:
3088:
3080:
3077:
3074:
3073:0-520-04235-2
3070:
3066:
3062:
3058:
3053:
3050:
3046:
3043:
3039:
3038:George Sarton
3034:
3031:
3026:
3019:
3016:
3011:
3009:0-321-01618-1
3005:
3001:
2994:
2992:
2988:
2983:
2979:
2975:
2971:
2967:
2963:
2959:
2955:
2951:
2947:
2946:
2941:
2934:
2932:
2928:
2923:
2919:
2913:
2910:
2905:
2903:9781949822205
2899:
2891:
2890:
2882:
2879:
2867:
2861:
2857:
2853:
2849:
2845:
2841:
2839:
2830:
2827:
2822:
2818:
2814:
2810:
2806:
2802:
2801:
2796:
2790:
2788:
2784:
2780:
2774:
2771:
2766:
2759:
2757:
2755:
2751:
2747:. p. 68.
2746:
2745:(Jones, 2010)
2739:
2737:
2733:
2728:
2722:
2714:
2707:
2704:
2700:
2696:
2691:
2688:
2676:
2672:
2665:
2662:
2657:
2653:
2649:
2638:
2635:
2630:
2628:3-540-63198-4
2624:
2620:
2616:
2612:
2608:
2602:
2599:
2594:
2590:
2583:
2582:
2574:
2571:
2566:
2562:
2558:
2552:
2551:
2547:
2541:
2537:
2536:
2531:
2525:
2522:
2513:
2512:
2504:
2501:
2488:
2484:
2480:
2474:
2471:
2467:
2463:
2458:
2456:
2452:
2447:
2443:
2440:
2433:
2426:
2424:
2422:
2420:
2416:
2411:
2405:
2401:
2400:
2392:
2390:
2388:
2386:
2382:
2377:
2373:
2369:
2365:
2361:
2357:
2353:
2351:
2342:
2339:
2334:
2320:
2314:
2310:
2306:
2302:
2298:
2297:
2291:
2283:
2280:
2277:
2276:
2271:
2266:
2264:
2262:
2260:
2256:
2250:
2236:
2235:
2231:
2230:
2228:
2222:
2219:
2203:
2200:
2194:
2191:
2184:
2179:
2176:
2174:
2171:
2168:
2165:
2163:
2160:
2157:
2154:
2152:
2149:
2148:
2143:
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:
2006:
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:
1914:
1912:
1910:
1906:
1902:
1898:
1894:
1888:
1886:
1882:
1878:
1874:
1866:
1862:
1858:
1857:psychological
1854:
1846:
1844:
1840:
1837:
1833:
1827:
1825:
1824:Moon illusion
1821:
1817:
1816:
1811:
1807:
1803:
1799:
1788:
1784:
1776:
1772:
1766:
1758:
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:
1596:
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:
1479:
1477:
1475:
1464:
1460:
1454:
1452:
1448:
1444:
1440:
1436:
1432:
1428:
1427:
1422:
1417:
1415:
1411:
1407:
1403:
1399:
1395:
1394:
1389:
1385:
1381:
1377:
1365:
1360:
1358:
1353: 195 BC
1343:
1339:
1335:
1331:
1327:
1323:
1319:
1315:
1311:
1307:
1306:
1281:
1277:
1269:
1268:
1262:
1257:
1251:
1243:
1241:
1239:
1227:
1226:
1220:
1218:
1214:
1209:
1187:
1183:
1182:
1176:
1174:
1170:
1166:
1162:
1158:
1153:
1151:
1150:
1144:
1136:
1134:
1132:
1128:
1124:
1119:
1087:
1083:
1079:
1075:
1051:
1047:
1039:
1035:
1030:
1024:
1021:
1019:
1017:
1013:
1008:
1006:
1005:
1000:
996:
992:
984:
980:
979:
971:
968:
965:
962:
957:
954:
950:
945:
943:
939:
935:
931:
926:
924:
920:
915:
912:
904:
902:
900:
896:
892:
888:
884:
880:
876:
871:
869:
864:
860:
856:
852:
847:
844:
840:
835:
832:
828:
827:
802:
798:
790:
789:
783:
778:
771:
768:
766:
764:
760:
752:
750:
748:
744:
740:
736:
731:
725:
721:
717:
713:
709:
705:
701:
697:
693:
689:
688:
683:
682:
677:
673:
669:
665:
661:
658:
655:
650:
648:
644:
640:
636:
635:Roman citizen
632:
628:
626:
621:
616:
614:
610:
606:
602:
598:
594:
590:
586:
582:
578:
574:
564:
563:
553:
549:
546:(1508), from
545:
544:Gregor Reisch
541:
536:
529:
527:
517:
515:
514:Roman citizen
511:
507:
503:
498:
496:
492:
488:
484:
476:
474:
472:
468:
464:
460:
459:
454:
450:
447:model of the
446:
442:
437:
435:
434:Quadripartite
431:
427:
426:
401:
397:
393:
390:
386:
382:
378:
377:
371:
370:
360:
356:
352:
351:
346:
342:
338:
334:
330:
326:
322:
318:
314:
313:mathematician
299:
295:
290:
283:
277:
271:
241:
232:
229:
225:
221:
217:
214:
210:
207:
203:
200:
196:
192:
188:
184:
180:
176:
172:
168:
165:
161:
158:
155:
151:
147:
143:
139:
134:
123:
119:
108:
104:
99:
95:
89:
84:
79:
72:
69:
65:
48:
44:
40:
33:
19:
7736:Solar System
7629:
7616:
7458:Thomas Heath
7449:
7332:
7316:Law of sines
7172:
7104:Golden ratio
6969:
6962:
6953:
6947:(Theodosius)
6943:
6935:
6928:
6921:
6914:
6905:
6895:
6889:(Hipparchus)
6885:
6875:
6867:
6860:
6851:
6841:
6833:
6828:(Apollonius)
6824:
6816:
6804:
6779:Zeno of Elea
6703:
6539:Eratosthenes
6529:Dionysodorus
6163:
6153:
6147:(Hipparchus)
6143:
6134:Catasterismi
6133:
6123:
6056:
5982:Eratosthenes
5846:
5842:
5831:Handy Tables
5830:
5774:. Retrieved
5757:. Retrieved
5754:Skyscript.co
5753:
5737:. Retrieved
5733:the original
5716:. Retrieved
5712:the original
5692:. Retrieved
5688:the original
5675:
5661:
5618:
5609:
5590:
5581:
5561:
5521:
5509:
5499:
5495:
5454:
5448:
5434:G. J. Toomer
5429:
5419:. Retrieved
5412:the original
5395:
5377:
5351:
5347:
5343:
5339:
5332:
5327:
5323:
5319:
5309:
5305:
5301:
5295:. 0169–8958.
5278:
5274:
5269:
5265:
5262:
5258:
5251:
5235:
5229:
5225:
5216:
5212:
5209:
5205:
5196:
5171:
5165:
5161:
5151:
5147:
5143:
5139:
5120:
5112:
5108:
5104:
5082:
5049:
5043:
5037:
5015:
5009:
4979:
4975:
4971:
4939:
4933:
4929:
4900:
4896:
4886:
4877:
4873:
4867:
4847:
4828:
4822:
4805:
4799:
4793:
4776:
4770:
4761:
4752:
4711:
4705:
4699:
4690:
4684:
4651:
4645:
4639:
4627:. Retrieved
4609:
4605:
4575:
4568:
4551:
4547:
4541:
4537:
4529:
4504:
4498:
4494:
4488:
4463:
4459:
4453:
4449:
4445:
4411:
4402:
4380:(4): 53–74.
4377:
4371:
4361:
4336:
4330:
4326:
4320:
4287:
4281:
4275:
4255:
4248:
4236:. 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:. Retrieved
2486:
2473:
2442:
2438:
2398:
2362:(4): 75–98.
2359:
2355:
2349:
2341:
2324:25 September
2322:. 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
18:Ptolemey
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
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