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CLAUDIUS PTOLEMY (/ˈtɒləmi/ ; Greek : Κλαύδιος Πτολεμαῖος, Klaúdios Ptolemaîos ; Latin : Claudius Ptolemaeus; c. AD 100 – c. 170) was a mathematician , astronomer , geographer , astrologer , and poet of a single epigram in the Greek Anthology . He lived in the city of Alexandria
Alexandria
in the Roman province of Egypt
Egypt
, wrote in Koine Greek
Koine Greek
, and held Roman citizenship
Roman citizenship
. Beyond that, few reliable details of his life are known. His birthplace has been given as Ptolemais Hermiou
Ptolemais Hermiou
in the Thebaid
Thebaid
in an uncorroborated statement by the 14th-century astronomer Theodore Meliteniotes . This is a very late attestation, however, and there is no other reason to suppose that he ever lived elsewhere than Alexandria, where he died around AD 168.

Ptolemy
Ptolemy
wrote several scientific treatises, three of which were of importance to later Byzantine , Islamic and European science. The first is the astronomical treatise now known as the Almagest
Almagest
, although it was originally entitled the Mathematical Treatise (Μαθηματικὴ Σύνταξις, Mathēmatikē Syntaxis) and then known as the Great Treatise (Ἡ Μεγάλη Σύνταξις, Hē Megálē Syntaxis). The second is the Geography
Geography
, which is a thorough discussion of the geographic knowledge of the Greco-Roman world. The third is the astrological treatise in which he attempted to adapt horoscopic astrology to the Aristotelian natural philosophy of his day. This is sometimes known as the Apotelesmatika (Ἀποτελεσματικά) but more commonly known as the Tetrabiblos
Tetrabiblos
from the Greek (Τετράβιβλος) meaning "Four Books" or by the Latin Quadripartitum
Quadripartitum
.

CONTENTS

* 1 Background * 2 Astronomy * 3 The Geography
Geography
* 4 Astrology * 5 Music * 6 Optics * 7 Named after Ptolemy
Ptolemy
* 8 See also * 9 Footnotes

* 10 References

* 10.1 Texts and translations

* 11 External links

* 11.1 Primary sources

* 11.2 Secondary material

* 11.2.1 Animated illustrations * 11.2.2 Galleries

BACKGROUND

Engraving of a crowned Ptolemy
Ptolemy
being guided by the muse Astronomy, from Margarita Philosophica by Gregor Reisch
Gregor Reisch
, 1508. Although Abu Ma\'shar believed Ptolemy
Ptolemy
to be one of the Ptolemies who ruled Egypt
Egypt
after the conquest of Alexander the title ‘King Ptolemy’ is generally viewed as a mark of respect for Ptolemy's elevated standing in science.

The name Claudius
Claudius
is a Roman nomen ; the fact that Ptolemy
Ptolemy
bore it indicates he lived under the Roman rule of Egypt
Egypt
with the privileges and political rights of Roman citizenship
Roman citizenship
. It would have suited custom if the first of Ptolemy's family to become a citizen (whether he or an ancestor) took the nomen from a Roman called Claudius
Claudius
who was responsible for granting citizenship. If, as was common, this was the emperor, citizenship would have been granted between AD 41 and 68 (when Claudius
Claudius
, and then Nero
Nero
, were Roman emperors). The astronomer would also have had a praenomen , which remains unknown.

Ptolemaeus (Πτολεμαῖος – Ptolemaios) is a Greek name. It occurs once in Greek mythology, and is of Homeric form. It was common among the Macedonian upper class at the time of Alexander the Great
Alexander the Great
, and there were several of this name among Alexander's army, one of whom made himself King of Egypt
Egypt
in 323 BC: Ptolemy I Soter . All the kings after him, until Egypt
Egypt
became a Roman province in 30 BC, were also Ptolemies .

Perhaps for no other reason than the association of name, the 9th-century Persian astronomer Abu Ma\'shar assumed Ptolemy
Ptolemy
to be a member of Egypt's royal lineage, stating that the ten kings of Egypt who followed Alexander were wise "and included Ptolemy
Ptolemy
the Wise, who composed the book of the Almagest". Abu Ma\'shar recorded a belief that a different member of this royal line "composed the book on astrology and attributed it to Ptolemy". We can evidence historical confusion on this point 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 Almagest. The correct answer is not known”. There is little evidence on the subject of Ptolemy's ancestry, apart from what can be drawn from the details of his name (see above); however, modern scholars refer to Abu Ma’shar’s account as erroneous, and it is no longer doubted that the astronomer who wrote the Almagest
Almagest
also wrote the Tetrabiblos
Tetrabiblos
as its astrological counterpart.

Ptolemy
Ptolemy
wrote in Greek and can be shown to have utilized Babylonian astronomical data . He was a Roman citizen, but was ethnically either a Greek or a Hellenized Egyptian . He was often known in later Arabic sources as "the Upper Egyptian ", suggesting he may have had origins in southern Egypt
Egypt
. Later Arabic astronomers , geographers and physicists referred to him by his name in Arabic : بَطْلُمْيوس‎‎ Batlamyus.

ASTRONOMY

Further information: Almagest
Almagest
Ptolemy
Ptolemy
with an armillary sphere model, by Joos van Ghent
Joos van Ghent
and Pedro Berruguete
Pedro Berruguete
, 1476, Louvre
Louvre
, Paris

Ptolemy's Almagest
Almagest
is the only surviving comprehensive ancient treatise on astronomy. Babylonian astronomers had developed arithmetical techniques for calculating astronomical phenomena; Greek astronomers such as Hipparchus
Hipparchus
had produced geometric models for calculating celestial motions. Ptolemy, however, claimed to have derived his geometrical models from selected astronomical observations by his predecessors spanning more than 800 years, though astronomers have for centuries suspected that his models' parameters were adopted independently of observations. Ptolemy
Ptolemy
presented his astronomical models in convenient tables, which could be used to compute the future or past position of the planets. The Almagest
Almagest
also contains a star catalogue , which is a version of a catalogue created by Hipparchus. Its list of forty-eight constellations is ancestral to the modern system of constellations, but unlike the modern system they did not cover the whole sky (only the sky Hipparchus
Hipparchus
could see). Across Europe, the Middle East and North Africa
Africa
in the Medieval period, it was the authoritative text on astronomy, with its author becoming an almost mythical figure, called Ptolemy, King of Alexandria. The Almagest
Almagest
was preserved, like most of Classical Greek science, in Arabic manuscripts (hence its familiar name). Because of its reputation, it was widely sought and was translated twice into Latin in the 12th century , once in Sicily and again in Spain. Ptolemy's model, like those of his predecessors, was geocentric and was almost universally accepted until the appearance of simpler heliocentric models during the scientific revolution .

His Planetary Hypotheses went beyond the mathematical model of the Almagest
Almagest
to present a physical realization of the universe as a set of nested spheres, in which he used the epicycles of his planetary model to compute the dimensions of the universe. He estimated the Sun was at an average distance of 1,210 Earth
Earth
radii, while the radius of the sphere of the fixed stars was 20,000 times the radius of the Earth.

Ptolemy
Ptolemy
presented a useful tool for astronomical calculations in his Handy Tables, which tabulated all the data needed to compute the positions of the Sun, Moon
Moon
and planets, the rising and setting of the stars, and eclipses of the Sun and Moon. Ptolemy's Handy Tables provided the model for later astronomical tables or zījes . In the Phaseis (Risings of the Fixed Stars), Ptolemy
Ptolemy
gave a parapegma, a star calendar or almanac , based on the hands and disappearances of stars over the course of the solar year.

THE GEOGRAPHY

Main article: Geography (Ptolemy)
Geography (Ptolemy)
Geography
Geography
by Ptolemy, Latin manuscript of the early 15th century

Ptolemy's other main work is his Geography
Geography
(also called the Geographia), a compilation of geographical coordinates of the part of the world known to the Roman Empire
Roman Empire
during his time. He relied somewhat on the work of an earlier geographer, Marinos of Tyre , and on gazetteers of the Roman and ancient Persian Empire . He also acknowledged ancient astronomer Hipparchus
Hipparchus
for having provided the elevation of the north pole for a few cities.

The first part of the Geography
Geography
is a discussion of the data and of the methods he used. As with the model of the solar system in the Almagest, Ptolemy
Ptolemy
put all this information into a grand scheme. Following Marinos, he assigned coordinates to all the places and geographic features he knew, in a grid that spanned the globe. Latitude
Latitude
was measured from the equator , as it is today, but Ptolemy preferred to express it as climata, the length of the longest day rather than degrees of arc : the length of the midsummer day increases from 12h to 24h as one goes from the equator to the polar circle . In books 2 through 7, he used degrees and put the meridian of 0 longitude at the most western land he knew, the "Blessed Islands ", often identified as the Canary Islands
Canary Islands
, as suggested by the location of the six dots labelled the "FORTUNATA" islands near the left extreme of the blue sea of Ptolemy's map here reproduced. A 15th-century manuscript copy of the Ptolemy world map
Ptolemy world map
, reconstituted from Ptolemy's Geography
Geography
(circa AD 150), indicating the countries of "Serica " and " Sinae
Sinae
" ( China
China
) at the extreme east, beyond the island of "Taprobane" ( Sri Lanka
Sri Lanka
, oversized) and the "Aurea Chersonesus " ( Malay Peninsula
Malay Peninsula
). Prima Europe
Europe
tabula. A 15th century copy of Ptolemy's map of Britain

Ptolemy
Ptolemy
also devised and provided instructions on how to create maps both of the whole inhabited world (oikoumenè ) and of the Roman provinces. In the second part of the Geography, he provided the necessary topographic lists, and captions for the maps. His oikoumenè spanned 180 degrees of longitude from the Blessed Islands in the Atlantic Ocean
Atlantic Ocean
to the middle of China
China
, and about 80 degrees of latitude from Shetland
Shetland
to anti-Meroe (east coast of Africa
Africa
); Ptolemy was well aware that he knew about only a quarter of the globe, and an erroneous extension of China
China
southward suggests his sources did not reach all the way to the Pacific Ocean.

The maps in surviving manuscripts of Ptolemy's Geography, however, only date from about 1300, after the text was rediscovered by Maximus Planudes . It seems likely that the topographical tables in books 2–7 are cumulative texts – texts which were altered and added to as new knowledge became available in the centuries after Ptolemy. This means that information contained in different parts of the Geography
Geography
is likely to be of different dates. A printed map from the 15th century depicting Ptolemy's description of the Ecumene , (1482, Johannes Schnitzer, engraver).

Maps
Maps
based on scientific principles had been made since the time of Eratosthenes
Eratosthenes
, in the 3rd century BC, but Ptolemy
Ptolemy
improved map projections . It is known from a speech by Eumenius that a world map, an orbis pictus, doubtless based on the Geography, was on display in a school in Augustodunum , Gaul
Gaul
in the third century. In the 15th century, Ptolemy's Geography
Geography
began to be printed with engraved maps; the earliest printed edition with engraved maps was produced in Bologna in 1477, followed quickly by a Roman edition in 1478 (Campbell, 1987). An edition printed at Ulm
Ulm
in 1482, including woodcut maps, was the first one printed north of the Alps
Alps
. The maps look distorted when compared to modern maps, because Ptolemy's data were inaccurate. One reason is that Ptolemy
Ptolemy
estimated the size of the Earth as too small: while Eratosthenes
Eratosthenes
found 700 stadia for a great circle degree on the globe, Ptolemy
Ptolemy
uses 500 stadia in the Geography. It is highly probable that these were the same stadion, since Ptolemy switched from the former scale to the latter between the Syntaxis and the Geography, and severely readjusted longitude degrees accordingly. See also Ancient Greek
Ancient Greek
units of measurement and History of geodesy
History of geodesy
.

Because Ptolemy
Ptolemy
derived many of his key latitudes from crude longest day values, his latitudes are erroneous on average by roughly a degree (2 degrees for Byzantium, 4 degrees for Carthage), though capable ancient astronomers knew their latitudes to more like a minute. (Ptolemy's own latitude was in error by 14'.) He agreed (Geography 1.4) that longitude was best determined by simultaneous observation of lunar eclipses, yet he was so out of touch with the scientists of his day that he knew of no such data more recent than 500 years before (Arbela eclipse). When switching from 700 stadia per degree to 500, he (or Marinos) expanded longitude differences between cities accordingly (a point first realized by P.Gosselin in 1790), resulting in serious over-stretching of the Earth's east-west scale in degrees, though not distance. Achieving highly precise longitude remained a problem in geography until the application of Galileo 's Jovian moon method in the 18th century. It must be added that his original topographic list cannot be reconstructed: the long tables with numbers were transmitted to posterity through copies containing many scribal errors, and people have always been adding or improving the topographic data: this is a testimony to the persistent popularity of this influential work in the history of cartography .

ASTROLOGY

Main article: Tetrabiblos
Tetrabiblos
The mathematician Claudius
Claudius
Ptolemy 'the Alexandrian', as depicted by a 16th-century engraving

Ptolemy
Ptolemy
has been referred to as “a pro-astrological authority of the highest magnitude”. His astrological treatise, a work in four parts, is known by the Greek term Tetrabiblos
Tetrabiblos
, or the Latin equivalent Quadripartitum: ‘Four Books’. Ptolemy's own title is unknown, but may have been the term found in some Greek manuscripts: Apotelesmatika, roughly meaning 'Astrological Outcomes,' 'Effects' or ‘Prognostics’.

As a source of reference, the Tetrabiblos
Tetrabiblos
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 Plato of Tivoli
Plato of Tivoli
(Tiburtinus) in 1138, while he was in Spain. The Tetrabiblos
Tetrabiblos
is an extensive and continually reprinted treatise on the ancient principles of horoscopic astrology . That it did not quite attain the unrivaled status of the Almagest
Almagest
was, perhaps, because it did not cover some popular areas of the subject, particularly electional astrology (interpreting astrological charts for a particular moment to determine the outcome of a course of action to be initiated at that time), and medical astrology , which were later adoptions.

The great popularity that the Tetrabiblos
Tetrabiblos
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. Ptolemy
Ptolemy
was concerned to defend astrology by defining its limits, compiling astronomical data that he believed was reliable and dismissing practices (such as considering the numerological significance of names) that he believed to be without sound basis.

Much of the content of the Tetrabiblos
Tetrabiblos
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 Almagest
Almagest
was the first, concerned with the influences of the celestial bodies in the sublunar sphere. Thus explanations of a sort are provided for the astrological effects of the planets , based upon their combined effects of heating, cooling, moistening, and drying.

Ptolemy's astrological outlook was quite practical: he thought that astrology was like medicine , that is conjectural, because of the many variable factors to be taken into account: the race , country , and upbringing of a person affects an individual's personality as much as, if not more than, the positions of the Sun, Moon, and planets at the precise moment of their birth, so Ptolemy
Ptolemy
saw astrology as something to be used in life but in no way relied on entirely.

A collection of one hundred aphorisms about astrology called the Centiloquium , ascribed to Ptolemy, was widely reproduced and commented on by Arabic, Latin and Hebrew scholars, and often bound together in medieval manuscripts after the Tetrabiblos
Tetrabiblos
as a kind of summation. It is now believed to be a much later pseudepigraphical composition. The identity and date of the actual author of the work, referred to now as Pseudo-Ptolemy , remains the subject of conjecture.

MUSIC

Ptolemy
Ptolemy
also wrote an influential work, Harmonics, on music theory and the mathematics of music. After criticizing the approaches of his predecessors, Ptolemy
Ptolemy
argued for basing musical intervals on mathematical ratios (in contrast to the followers of Aristoxenus
Aristoxenus
and in agreement with the followers of Pythagoras
Pythagoras
), backed up by empirical observation (in contrast to the overly theoretical approach of the Pythagoreans ). Ptolemy
Ptolemy
wrote about how musical notes could be translated into mathematical equations and vice versa in Harmonics. This is called Pythagorean tuning because it was first discovered by Pythagoras. However, Pythagoras
Pythagoras
believed that the mathematics of music should be based on the specific ratio of 3:2, whereas Ptolemy
Ptolemy
merely believed that it should just generally involve tetrachords and octaves . He presented his own divisions of the tetrachord and the octave, which he derived with the help of a monochord . His Harmonics never had the influence of his Almagest
Almagest
or Planetary Hypotheses, but a part of it (Book III) did encourage Kepler
Kepler
in his own musings on the harmony of the world (Kepler, Harmonice Mundi, Appendix to Book V). Ptolemy's astronomical interests also appeared in a discussion of the "music of the spheres ". See: Ptolemy\'s intense diatonic scale .

OPTICS

His Optics is a work that survives only in a poor Arabic translation and in about twenty manuscripts of a Latin version of the Arabic, which was translated by Eugene of Palermo (c. 1154). In it Ptolemy writes about properties of light , including reflection , refraction , and colour . The work is a significant part of the early history of optics and influenced the more famous 11th-century Book of Optics
Book of Optics
by Alhazen
Alhazen
(Ibn al-Haytham). It contains the earliest surviving table of refraction from air to water, for which the values (with the exception of the 60° angle of incidence), although historically praised as experimentally derived, appear to have been obtained from an arithmetic progression.

The work is also important for the early history of perception. Ptolemy
Ptolemy
combined the mathematical, philosophical and physiological traditions. He held an extramission-intromission theory of vision: the rays (or flux) from the eye formed a cone, the vertex being within the eye, and the base defining the visual field. The rays were sensitive, and conveyed information back to the observer’s intellect about the distance and orientation of surfaces. Size and shape were determined by the visual angle subtended at the eye combined with perceived distance and orientation. 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. Ptolemy
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 moon illusion (the enlarged apparent size on the horizon) based on the difficulty of looking upwards.

NAMED AFTER PTOLEMY

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

* The crater Ptolemaeus on the Moon
Moon
; * The crater Ptolemaeus on Mars
Mars
; * The asteroid 4001 Ptolemaeus
4001 Ptolemaeus
; * The Ptolemy
Ptolemy
Stone used in the mathematics courses at both St. John\'s College campuses. * Ptolemy\'s theorem on distances in a cyclic quadrilateral , and its generalization, Ptolemy\'s inequality , to non-cyclic quadrilaterals * Ptolemaic graphs , the graphs whose distances obey Ptolemy's inequality

SEE ALSO

* Atlas portal * Astronomy portal * Cosmology portal

* Pei Xiu
Pei Xiu
* Messier 7 Ptolemy
Ptolemy
Cluster, star cluster described by Ptolemaeus * Ptolemy\'s Canon – a dated list of kings used by ancient astronomers. * Ptolemy\'s table of chords * Zhang Heng
Zhang Heng

FOOTNOTES

* ^ A B Since no contemporary depictions or descriptions of Ptolemy are known to have existed, later artist's impressions are unlikely to have reproduced his appearance accurately * ^ A B C D Ptolemy
Ptolemy
at Encyclopædia Britannica
Encyclopædia Britannica
* ^ Select Epigrams from the Greek Anthology
Greek Anthology
By John William Mackail Page 246 ISBN 1406922943 , 2007 * ^ Mortal am I, the creature of a day.. * ^ See 'Background' section on his status as a Roman citizen * ^ A B G. J. Toomer, " Ptolemy
Ptolemy
(or Claudius
Claudius
Ptolemaeus). " Complete Dictionary of Scientific Biography. 2008. Retrieved from Encyclopedia.com. 21 Jan, 2013. * ^ Jean Claude Pecker (2001), Understanding the Heavens: Thirty Centuries of Astronomical Ideas from Ancient Thinking to Modern Cosmology, p. 311, Springer, ISBN 3-540-63198-4 . * ^ Πτολεμαῖος, Georg Autenrieth, A Homeric Dictionary, on Perseus * ^ Abu Ma’shar, De magnis coniunctionibus, ed.-transl. K. Yamamoto, Ch. Burnett, Leiden, 2000, 2 vols. (Arabic 4.1.4. * ^ Jones (2010) ‘Ptolemy’s Doctrine of the Terms and Its Reception’ by Stephan Heilen, p. 68. * ^ Robbins, Ptolemy
Ptolemy
Tetrabiblos
Tetrabiblos
‘Introduction’; p. x. * ^ Asger Aaboe , Episodes from the Early History of Astronomy, New York: Springer, 2001, pp. 62–65. * ^ Alexander Jones, "The Adaptation of Babylonian Methods in Greek Numerical Astronomy," in The Scientific Enterprise in Antiquity and the Middle Ages, p. 99. * ^ A B Victor J. Katz (1998). A History of Mathematics: An Introduction, p. 184. Addison Wesley, ISBN 0-321-01618-1 : "But what we really want to know is to what extent the Alexandrian mathematicians of the period from the first to the fifth centuries C.E. were Greek. Certainly, all of them wrote in Greek and were part of the Greek intellectual community of Alexandria. And most modern studies conclude that the Greek community coexisted So should we assume that Ptolemy
Ptolemy
and Diophantus, Pappus and Hypatia
Hypatia
were ethnically Greek, that their ancestors had come from Greece at some point in the past but had remained effectively isolated from the Egyptians? It is, of course, impossible to answer this question definitively. But research in papyri dating from the early centuries of the common era demonstrates that a significant amount of intermarriage took place between the Greek and Egyptian communities And it is known that Greek marriage contracts increasingly came to resemble Egyptian ones. In addition, even from the founding of Alexandria, small numbers of Egyptians were admitted to the privileged classes in the city to fulfill numerous civic roles. Of course, it was essential in such cases for the Egyptians to become "Hellenized," to adopt Greek habits and the Greek language. Given that the Alexandrian mathematicians mentioned here were active several hundred years after the founding of the city, it would seem at least equally possible that they were ethnically Egyptian as that they remained ethnically Greek. In any case, it is unreasonable to portray them with purely European features when no physical descriptions exist." * ^ "Ptolemy." Britannica Concise Encyclopedia. Encyclopædia Britannica, Inc., 2006. Answers.com 20 Jul. 2008. * ^ George Sarton
George Sarton
(1936). "The Unity and Diversity of the Mediterranean World", Osiris 2, p. 406–463 . * ^ John Horace Parry (1981). The Age of Reconnaissance, p. 10. University of California Press
University of California Press
. ISBN 0-520-04235-2 . * ^ J. F. Weidler (1741). Historia astronomiae, p. 177. Wittenberg: Gottlieb. (cf. Martin Bernal (1992). "Animadversions on the Origins of Western Science", Isis 83 (4), p. 596–607 .) * ^ Martin Bernal (1992). "Animadversions on the Origins of Western Science", Isis 83 (4), p. 596–607 . * ^ Shahid Rahman; Tony Street; Hassan Tahiri, eds. (2008). "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 Almagest". The Unity of Science in the Arabic Tradition. 11. Springer Netherlandsdoi =10.1007/978-1-4020-8405-8. pp. 183–225 . ISBN 978-1-4020-8404-1 . doi :10.1007/978-1-4020-8405-8 . * ^ "Dennis Rawlins". The International Journal of Scientific History. Retrieved 2009-10-07. * ^ Goldstein, Bernard R. (1997). "Saving the Phenomena: The Background to Ptolemy's Planetary Theory". Journal for the History of Astronomy. 28 (1): 1–12. doi :10.1177/002182869702800101 . * ^ S. C. McCluskey, Astronomies and Cultures in Early Medieval Europe, Cambridge: Cambridge Univ. Pr. 1998, pp. 20–21. * ^ Charles Homer
Homer
Haskins, Studies in the History of Mediaeval Science, New York: Frederick Ungar Publishing, 1967, reprint of the Cambridge, Mass., 1927 edition * ^ Dennis Duke, Ptolemy\'s Cosmology * ^ Bernard R. Goldstein, ed., The Arabic Version of Ptolemy's Planetary Hypotheses, Transactions of the American Philosophical Society 57, no. 4 (1967), pp. 9–12. * ^ Shcheglov D.A. (2002–2007): "Hipparchus’ Table of Climata and Ptolemy’s Geography", Orbis Terrarum 9 (2003–2007), 177–180. * ^ Book 8 * ^ Bagrow 1945. * ^ Talbert, Richard J. A. (2012). "Urbs Roma to Orbis Romanus". In Talbert. Ancient Perspectives: Maps
Maps
and Their Places in Mesopotamia, Egypt, Greece and Rome. Chicago. pp. 170–72. ISBN 978-0-226-78940-8 . * ^ Jones (2010) ‘The Use and Abuse of Ptolemy’s Tetrabiblos
Tetrabiblos
in Renaissance and Early Modern Europe’ by H. Darrel Rutkin, p. 135. * ^ Robbins, Ptolemy
Ptolemy
Tetrabiblos
Tetrabiblos
, 'Introduction' p. x. * ^ Jones (2010) p. xii. * ^ Robbins, Ptolemy
Ptolemy
Tetrabiblos
Tetrabiblos
, 'Introduction' p. xii. * ^ FA Robbins, 1940; Thorndike 1923 * ^ Hetherington, Norriss S. Encyclopedia of Cosmology (Routledge Revivals): Historical, Philosophical, and Scientific Foundations of Modern Cosmology Routledge, 8 apr. 2014 ISBN 978-1317677666 p 527 * ^ Smith, A. Mark (1996). Ptolemy\'s Theory of Visual Perception– An English translation of the Optics. The American Philosophical Society. ISBN 0-87169-862-5 . Retrieved 27 June 2009. * ^ Carl Benjamin Boyer
Carl Benjamin Boyer
, The Rainbow: From Myth to Mathematics (1959) * ^ H. W. Ross and C. Plug, "The History of Size Constancy and Size Illusions", in V. Walsh & J. Kulikowski (eds.) Perceptual Constancy: Why Things Look as They Do. Cambridge: Cambridge University Press, 1998, pp. 499–528. * ^ H. E. Ross and G. M. Ross, "Did Ptolemy
Ptolemy
Understand the Moon Illusion?", Perception 5 (1976): 377–395. * ^ A. I. Sabra, "Psychology Versus Mathematics: Ptolemy
Ptolemy
and Alhazen
Alhazen
on the Moon
Moon
Illusion", in E. Grant & J. E. Murdoch (eds.) Mathematics and Its Application to Science and Natural Philosophy in the Middle Ages. Cambridge: Cambridge University Press, 1987, pp. 217–247. * ^ Mars
Mars
Labs. Google Maps.

REFERENCES

TEXTS AND TRANSLATIONS

* Bagrow, L. (January 1, 1945). "The Origin of Ptolemy's Geographia". Geografiska Annaler. Geografiska Annaler, Vol. 27. 27: 318–387. ISSN 1651-3215 . JSTOR
JSTOR
520071 . doi :10.2307/520071 . * Berggren, J. Lennart, and Alexander Jones. 2000. Ptolemy's Geography: An Annotated Translation of the Theoretical Chapters. Princeton and Oxford: Princeton University Press
Princeton University Press
. ISBN 0-691-01042-0 . * Campbell, T. (1987). The Earliest Printed Maps. British Museum Press. * Hübner, Wolfgang, ed. 1998. Claudius
Claudius
Ptolemaeus, Opera quae exstant omnia Vol III/Fasc 1: ΑΠΟΤΕΛΕΣΜΑΤΙΚΑ (= Tetrabiblos). De Gruyter. ISBN 978-3-598-71746-8 (Bibliotheca scriptorum Graecorum et Romanorum Teubneriana). (The most recent edition of the Greek text of Ptolemy's astrological work, based on earlier editions by F. Boll and E. Boer.) * Lejeune, A. (1989) L'Optique de Claude Ptolémée dans la version latine d'après l'arabe de l'émir Eugène de Sicile. . Collection de travaux de l'Académie International d'Histoire des Sciences, No. 31. Leiden: E.J.Brill. * Neugebauer, Otto (1975). A History of Ancient Mathematical Astronomy. I-III. Berlin and New York: Sprnger Verlag. * Nobbe, C. F. A., ed. 1843. Claudii Ptolemaei Geographia. 3 vols. Leipzig: Carolus Tauchnitus. (The most recent edition of the complete Greek text) * Ptolemy. 1930. Die Harmonielehre des Klaudios Ptolemaios, edited by Ingemar Düring. Göteborgs högskolas årsskrift 36, 1930:1. Göteborg: Elanders boktr. aktiebolag. Reprint, New York: Garland Publishing, 1980. * Ptolemy. 2000. Harmonics, translated and commentary by Jon Solomon. Mnemosyne, Bibliotheca Classica Batava, Supplementum, 0169-8958, 203. Leiden and Boston: Brill Publishers
Brill Publishers
. ISBN 90-04-11591-9 * Robbins, Frank E. (ed.) 1940. Ptolemy
Ptolemy
Tetrabiblos. Cambridge, Massachusetts: Harvard University Press (Loeb Classical Library). ISBN 0-674-99479-5 . * Smith, A.M. (1996) Ptolemy's theory of visual perception: An English translation of the Optics with introduction and commentary. Transactions of the American Philosophical Society, Vol. 86, Part 2. Philadelphia: The American Philosophical Society. * Stevenson, Edward Luther (trans. and ed.). 1932. Claudius
Claudius
Ptolemy: The Geography. New York: New York Public Library. Reprint, New York: Dover, 1991. (This is the only complete English translation of Ptolemy's most famous work. Unfortunately, it is marred by numerous mistakes and the placenames are given in Latinised forms, rather than in the original Greek). * Stückelberger, Alfred, and Gerd Graßhoff (eds). 2006. Ptolemaios, Handbuch der Geographie, Griechisch-Deutsch. 2 vols. Basel: Schwabe Verlag. ISBN 978-3-7965-2148-5 . (Massive 1018 pp. scholarly edition by a team of a dozen scholars that takes account of all known manuscripts, with facing Greek and German text, footnotes on manuscript variations, color maps, and a CD with the geographical data) * Taub, Liba Chia (1993). Ptolemy's Universe: The Natural Philosophical and Ethical Foundations of Ptolemy's Astronomy. Chicago: Open Court Press. ISBN 0-8126-9229-2 . * Ptolemy's Almagest, Translated and annotated by G. J. Toomer . Princeton University Press, 1998

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* Ptolemy\'s Tetrabiblos
Tetrabiblos
at LacusCurtius (Transcription of

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