The Avatici ( Gaulish : * Auaticoi ) were a Gallic tribe dwelling near the Étang de Berre , between the mouth of the Rhône river and Massilia (modern Marseille ), during the Roman period .
104-568: They are mentioned as Au̓atilō͂n (Αὐατιλῶν; var. Αὐατικῶν) by Ptolemy (2nd c. AD), and an oppidum Maritima Avaticorum is documented by Pliny (1st c. AD) and Pomponius Mela (mid-1st c. AD). The Avatici dwelled near the Étang de Berre , southwest of the Saluvii , and possibly northwest of the Tricores . Their territory stretched from the eastern part of the mouth of the Rhône river to
208-417: A perfect fourth ) and octaves . Ptolemy reviewed standard (and ancient, disused ) musical tuning practice of his day, which he then compared to his own subdivisions of the tetrachord and the octave , which he derived experimentally using a monochord / harmonic canon. The volume ends with a more speculative exposition of the relationships between harmony, the soul ( psyche ), and the planets ( harmony of
312-612: A Roman citizen, but was ethnically either a Greek or at least a Hellenized Egyptian. 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 Geography and the Tetrabiblos have significant references to astronomy. Ptolemy's Mathēmatikē Syntaxis ( Greek : Μαθηματικὴ Σύνταξις , lit. ' Mathematical Systematic Treatise ' ), better known as
416-638: A certain Syrus, a figure of whom almost nothing is known but who likely shared some of Ptolemy's astronomical interests. Ptolemy died in Alexandria c. 168 . Ptolemy's Greek name , Ptolemaeus ( Πτολεμαῖος , Ptolemaîos ), is an ancient Greek personal 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
520-476: A coherent mathematical description, which persists to the present as just intonation – the standard for comparison of consonance in the many other, less-than exact but more facile compromise tuning systems. During the Renaissance , Ptolemy's ideas inspired Kepler in his own musings on the harmony of the world ( Harmonice Mundi , Appendix to Book V). The Optica ( Koine Greek : Ὀπτικά ), known as
624-517: A dozen scientific treatises , three of which were important to later Byzantine , Islamic , and Western European science. The first was his astronomical treatise now known as the Almagest , originally entitled Mathematical Treatise ( Greek : Μαθηματικὴ Σύνταξις , Mathēmatikḗ Syntaxis ). The second is the Geography , which is a thorough discussion on maps and the geographic knowledge of
728-402: A handful of places. Ptolemy's real innovation, however, occurs in the second part of the book, where he provides a catalogue of 8,000 localities he collected from Marinus and others, the biggest such database from antiquity. About 6 300 of these places and geographic features have assigned coordinates so that they can be placed in a grid that spanned the globe. Latitude was measured from
832-498: A long exposition on the relationship between reason and sense perception in corroborating theoretical assumptions. After criticizing the approaches of his predecessors, Ptolemy argues for basing musical intervals on mathematical ratios (as opposed to the ideas advocated by followers of Aristoxenus ), backed up by empirical observation (in contrast to the excessively theoretical approach of the Pythagoreans ). Ptolemy introduces
936-611: A member of Ptolemaic Egypt's royal lineage , stating that the descendants of the Alexandrine general and Pharaoh Ptolemy I Soter were wise "and included 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". Historical confusion on this point can be inferred from Abu Ma'shar's subsequent remark: "It
1040-601: A method for specifying the location of the Sun in three pairs of locally oriented coordinate arcs as a function of the declination of the Sun, the terrestrial latitude, and the hour. The key to the approach is to represent the solid configuration in a plane diagram that Ptolemy calls the analemma . In another work, the Phaseis ( Risings of the Fixed Stars ), Ptolemy gave a parapegma , a star calendar or almanac , based on
1144-466: 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. Ptolemy wrote a work entitled Harmonikon ( Greek : Ἁρμονικόν ), known as the Harmonics , on music theory and the mathematics behind musical scales in three books. Harmonics begins with a definition of harmonic theory, with
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#17327753855921248-576: A quarter of the globe. Ptolemy's work included a single large and less detailed world map and then separate and more detailed regional maps. The first Greek manuscripts compiled after Maximus Planudes 's rediscovery of the text had as many as 64 regional maps. The standard set in Western Europe came to be 26: 10 European maps, 4 African maps, and 12 Asian maps. As early as the 1420s, these canonical maps were complemented by extra-Ptolemaic regional maps depicting, e.g., Scandinavia . An outline of
1352-688: A scribal error was made and Cattigara was located at eight and a half degrees South of the Equator. On Ptolemaic maps, such as that of Martellus, Catigara was located on the easternmost shore of the Mare Indicum, 180 degrees East of the Cape St Vincent at, due to the scribal error, eight and a half degrees South of the Equator. Catigara is also shown at this location on Martin Waldseemüller's 1507 world map, which avowedly followed
1456-558: A temple at Canopus , around 146–147 AD, known as the Canobic Inscription . Although the inscription has not survived, someone in the sixth century transcribed it, and manuscript copies preserved it through the Middle Ages. It begins: "To the saviour god, Claudius Ptolemy (dedicates) the first principles and models of astronomy", following by a catalogue of numbers that define a system of celestial mechanics governing
1560-482: A thousand years or more". It was first translated from Arabic into Latin by Plato of Tivoli (Tiburtinus) in 1138, while he was in Spain. Much of the content of the 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
1664-562: A view supported by the Stoics. Although mainly known for his contributions to astronomy and other scientific subjects, Ptolemy also engaged in epistemological and psychological discussions across his corpus. He wrote a short essay entitled On the Criterion and Hegemonikon ( Greek : Περὶ Κριτηρίου καὶ Ἡγεμονικοῡ ), which may have been one of his earliest works. Ptolemy deals specifically with how humans obtain scientific knowledge (i.e.,
1768-399: Is a treatise on cartography and chorography , describing the methods used to assemble and arrange Ptolemy's data. From Book II through the beginning of Book VII, a gazetteer provides longitude and latitude values for the world known to the ancient Romans (the " ecumene "). The rest of Book VII provides details on three projections to be used for the construction of a map of
1872-532: 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 Almagest was the authoritative text on astronomy across Europe, the Middle East, and North Africa. The Almagest was preserved, like many extant Greek scientific works, in Arabic manuscripts;
1976-634: Is his Geographike Hyphegesis ( Greek : Γεωγραφικὴ Ὑφήγησις ; lit. ' Guide to Drawing the Earth ' ), known as the Geography , a handbook on how to draw maps using geographical coordinates for parts of the Roman world known at the time. He relied on previous work by an earlier geographer, Marinus of Tyre , as well as on gazetteers of the Roman and ancient Persian Empire . He also acknowledged ancient astronomer Hipparchus for having provided
2080-432: Is quite late, however, and there is no evidence to support it. It is known that Ptolemy lived in or around the city of Alexandria , in the Roman province of Egypt under Roman rule . He had a Latin name, Claudius, which is generally taken to imply he was a Roman citizen . He was familiar with Greek philosophers and used Babylonian observations and Babylonian lunar theory. In half of his extant works, Ptolemy addresses
2184-418: 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." 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
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#17327753855922288-648: Is used now, though Ptolemy used fractions of a degree rather than minutes of arc. His Prime Meridian , of 0 longitude , ran through the Fortunate Isles , the westernmost land recorded, at around the position of El Hierro in the Canary Islands . The maps spanned 180 degrees of longitude from the Fortunate Isles in the Atlantic to China . Ptolemy was aware that Europe knew only about
2392-597: The Geographia and the Cosmographia , is a gazetteer , an atlas , and a treatise on cartography , compiling the geographical knowledge of the 2nd-century Roman Empire . Originally written by Claudius Ptolemy in Greek at Alexandria around 150 AD, the work was a revision of a now-lost atlas by Marinus of Tyre using additional Roman and Persian gazetteers and new principles. Its translation – Kitab Surat al-Ard – into Arabic by Al-Khwarismi in
2496-645: The Almagest also wrote the Tetrabiblos as its astrological counterpart. In later Arabic sources, he was often known as "the Upper Egyptian ", suggesting he may have had origins in southern Egypt . Arabic astronomers , geographers , and physicists referred to his name in Arabic as Baṭlumyus ( Arabic : بَطْلُمْيوس ). Ptolemy wrote in Koine Greek , and can be shown to have used Babylonian astronomical data . He might have been
2600-413: The Almagest , is the only surviving comprehensive ancient treatise on astronomy. Although Babylonian astronomers 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
2704-504: The gens Claudia ; the peculiar multipart form of the whole name Claudius Ptolemaeus is a Roman custom, characteristic of Roman citizens. This indicates that Ptolemy would have been a Roman citizen . Gerald Toomer, the translator of Ptolemy's Almagest into English, suggests that citizenship was probably granted to one of Ptolemy's ancestors by either the emperor Claudius or the emperor Nero . The 9th century Persian astronomer Abu Ma'shar al-Balkhi mistakenly presents Ptolemy as
2808-662: The Almagest was the first, concerned with the influences of the celestial bodies in the sublunary 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 dismisses other astrological practices, such as considering the numerological significance of names, that he believed to be without sound basis, and leaves out popular topics, such as electional astrology (interpreting astrological charts to determine courses of action) and medical astrology , for similar reasons. The great respect in which later astrologers held
2912-488: The Canary Islands . He said that he had sailed 1100 leagues from the Canaries when he found Cuba in 1492. This was approximately where he thought the coast of eastern Asia would be found. On this basis of calculation he identified Hispaniola with Cipangu, which he had expected to find on the outward voyage at a distance of about 700 leagues from the Canaries. His later voyages resulted in further exploration of Cuba and in
3016-649: The Geography in providing the coordinates for 545 cities and regional maps of the Nile , the Island of the Jewel , the Sea of Darkness, and the Sea of Azov . A 1037 copy of these are the earliest extant maps from Islamic lands. The text clearly states that al-Khwārazmī was working from an earlier map, although this could not have been an exact copy of Ptolemy's work: his Prime Meridian
3120-410: The Geography is likely to be of different dates, in addition to containing many scribal errors. However, although the regional and world maps in surviving manuscripts date from c. 1300 AD (after the text was rediscovered by Maximus Planudes ), there are some scholars who think that such maps go back to Ptolemy himself. Ptolemy wrote an astrological treatise, in four parts, known by
3224-779: 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 ( Greek : Αποτελεσματικά , lit. ' On the Effects ' ) but more commonly known as the Tetrábiblos , from the Koine Greek meaning "Four Books", or by its Latin equivalent Quadripartite . The Catholic Church promoted his work, which included
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3328-732: The Magnus Sinus . This known portion of the world was comprised within 180 degrees. In his extreme east Ptolemy placed Serica (the Land of Silk), the Sinarum Situs (the Port of the Sinae ), and the emporium of Cattigara . On the 1489 map of the world by Henricus Martellus, which was based on Ptolemy's work, Asia terminated in its southeastern point in a cape, the Cape of Cattigara. Cattigara
3432-633: The Marvels of the Seven Climes to the End of Habitation . Surviving maps from the medieval period were not done according to mathematical principles. The world map from the 11th-century Book of Curiosities is the earliest surviving map of the Muslim or Christian worlds to include a geographic coordinate system but the copyist seems to have not understood its purpose, starting it from the left using twice
3536-788: The Optics, is a work that survives only in a somewhat poor Latin version, which, in turn, was translated from a lost Arabic version by Eugenius of Palermo ( c. 1154 ). In it, Ptolemy writes about properties of sight (not light), including reflection , refraction , and colour . The work is a significant part of the early history of optics and influenced the more famous and superior 11th-century Book of Optics by Ibn al-Haytham . 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
3640-463: The Tetrabiblos derived from its nature as an exposition of theory, rather than as a manual. 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 as a kind of summation. It is now believed to be
3744-461: 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 . One of the places Ptolemy noted specific coordinates for was the now-lost stone tower which marked the midpoint on the ancient Silk Road , and which scholars have been trying to locate ever since. In
3848-519: The harmonic canon (Greek name) or monochord (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 Pythagorean tuning (and how to demonstrate that their idealized musical scale fails in practice). The Pythagoreans believed that
3952-430: The "criterion" of truth), as well as with the nature and structure of the human psyche or soul, particularly its ruling faculty (i.e., the hegemonikon ). Ptolemy argues that, to arrive at the truth, one should use both reason and sense perception in ways that complement each other. On the Criterion is also noteworthy for being the only one of Ptolemy's works that is devoid of mathematics . Elsewhere, Ptolemy affirms
4056-483: The 12th century AD. However, no copy of that translation has survived. The Greek text of the Geography reached Florence from Constantinople in about 1400 and was translated into Latin by Jacobus Angelus of Scarperia around 1406. The first printed edition with maps, published in 1477 in Bologna , was also the first printed book with engraved illustrations. Many editions followed (more often using woodcut in
4160-403: The 3rd century BC. Ptolemy improved the treatment of map projections . He provided instructions on how to create his maps in the first section of the work. The gazetteer section of Ptolemy's work provided latitude and longitude coordinates for all the places and geographical features in the work. Latitude was expressed in degrees of arc from the equator , the same system that
4264-515: The 9th century was highly influential on the geographical knowledge and cartographic traditions of the Islamic world . Alongside the works of Islamic scholars – and the commentary containing revised and more accurate data by Alfraganus – Ptolemy's work was subsequently highly influential on Medieval and Renaissance Europe. Versions of Ptolemy's work in antiquity were probably proper atlases with attached maps, although some scholars believe that
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4368-527: The Arabs and Byzantines. His work on epicycles has come to symbolize a very complex theoretical model built in order to explain a false assumption. Ptolemy's date of birth and birthplace are both unknown. The 14th-century astronomer Theodore Meliteniotes wrote that Ptolemy's birthplace was Ptolemais Hermiou , a Greek city in the Thebaid region of Egypt (now El Mansha, Sohag Governorate ). This attestation
4472-563: The Elder demonstrated a reluctance to rely on the contemporary accounts of sailors and merchants who plied distant areas of the Indian Ocean , Marinus and Ptolemy betray a much greater receptiveness to incorporating information received from them. For instance, Grant Parker argues that it would be highly implausible for them to have constructed the Bay of Bengal as precisely as they did without
4576-489: The French astronomer Delambre in the early 1800s which were repeated by R.R. Newton. Specifically, it proved Hipparchus was not the sole source of Ptolemy's catalog, as they both had claimed, and proved that Ptolemy did not simply copy Hipparchus' measurements and adjust them to account for precession of the equinoxes, as they had claimed. Scientists analyzing the charts concluded: It also confirms that Ptolemy’s Star Catalogue
4680-582: The Great and there were several of this name among Alexander's army, one of whom made himself pharaoh in 323 BC: Ptolemy I Soter , the first pharaoh of the Ptolemaic Kingdom . Almost all subsequent pharaohs of Egypt, with a few exceptions, were named Ptolemy until Egypt became a Roman province in 30 BC, ending the Macedonian family's rule. The name Claudius is a Roman name, belonging to
4784-477: The Greek term Tetrabiblos (lit. "Four Books") or by its Latin equivalent Quadripartitum . Its original title is unknown, but may have been a term found in some Greek manuscripts, Apotelesmatiká ( biblía ), roughly meaning "(books) on the Effects" or "Outcomes", or "Prognostics". As a source of reference, the Tetrabiblos is said to have "enjoyed almost the authority of a Bible among the astrological writers of
4888-455: The Sun or Moon illusion (the enlarged apparent size on the horizon) based on the difficulty of looking upwards. 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 reflection in plane, convex, concave, and compound mirrors. The last section (Book V) deals with refraction and includes
4992-422: The ability to make any predictions. The earliest person who attempted to merge these two approaches was Hipparchus , who produced geometric models 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
5096-400: The above stemma descends, even if maps existed in antiquity: "The transmission of Ptolemy's text certainly passed through a stage when the manuscripts were too small to contain the maps. Planudes and his assistants therefore probably had no pictorial models, and the success of their enterprise is proof that Ptolemy succeeded in his attempt to encode the map in words and numbers. The copies of
5200-553: The accounts of sailors. When it comes to the account of the Golden Chersonese (i.e. Malay Peninsula ) and the Magnus Sinus (i.e. Gulf of Thailand and South China Sea ), Marinus and Ptolemy relied on the testimony of a Greek sailor named Alexandros, who claimed to have visited a far eastern site called " Cattigara " (most likely Oc Eo , Vietnam , the site of unearthed Antonine -era Roman goods and not far from
5304-476: The appearances and disappearances of stars over the course of the solar year. The Planisphaerium ( Greek : Ἅπλωσις ἐπιφανείας σφαίρας , lit. ' Flattening of the sphere ' ) 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. Ptolemy also erected an inscription in
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#17327753855925408-568: The basis of his (now lost) Chorography of the Ecumene . Later imperial writers and mathematicians, however, seem to have restricted themselves to commenting on Ptolemy's text, rather than improving upon it; surviving records actually show decreasing fidelity to real position. Nevertheless, Byzantine scholars continued these geographical traditions throughout the Medieval period. Whereas previous Greco-Roman geographers such as Strabo and Pliny
5512-503: The coordinates provided by the text, as Planudes was forced to do. Later scribes and publishers could then copy these new maps, as Athanasius did for the emperor Andronicus II Palaeologus . The three earliest surviving texts with maps are those from Constantinople ( Istanbul ) based on Planudes's work. The first Latin translation of these texts was made in 1406 or 1407 by Jacobus Angelus in Florence , Italy , under
5616-510: The data needed to compute the positions of the Sun, Moon and planets, the rising and setting of the stars, and eclipses of the Sun and Moon, making it a useful tool for astronomers and astrologers. The tables themselves are known through Theon of Alexandria 's version. Although Ptolemy's Handy Tables do not survive as such in Arabic or in Latin, they represent the prototype of most Arabic and Latin astronomical tables or zījes . Additionally,
5720-460: The discovery of South and Central America . At first South America, the Mundus Novus ( New World ) was considered to be a great island of continental proportions; but as a result of his fourth voyage , it was apparently considered to be identical with the great Upper India peninsula ( India Superior ) represented by Behaim – the Cape of Cattigara. This seems to be the best interpretation of
5824-569: The district of the Anatilii, and inland those of the Dexivates and Cavares. Returning to the sea we have the districts of the Tricores... Their chief town, located in the province of Gallia Narbonensis , was known as Maritima Avaticorum [ fr ] . The location of the settlement is not precisely indicated by the sources, but most scholars place it in modern Martigues , possibly at
5928-402: 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. Ptolemy's theory of vision consisted of rays (or flux) coming from the eye forming a cone, the vertex being within
6032-520: The early days), some following traditional versions of the maps, and others updating them. An edition printed at Ulm in 1482 was the first one printed north of the Alps . Also in 1482, Francesco Berlinghieri printed the first edition in vernacular Italian . Ptolemy had mapped the whole world from the Fortunatae Insulae ( Cape Verde or Canary Islands ) eastward to the eastern shore of
6136-469: The elevation of the north celestial pole for a few cities. Although maps based on scientific principles had been made since the time of Eratosthenes ( c. 276 – c. 195 BC ), Ptolemy improved on map projections . The first part of the Geography 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
6240-425: 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 single string , hence which were assured to be under equal tension, eliminating one source of error. He analyzed the empirically determined ratios of "pleasant" pairs of pitches, and then synthesised all of them into
6344-474: The encyclopedia follows, with links to the appropriate Misplaced Pages article. The original treatise by Marinus of Tyre that formed the basis of Ptolemy's Geography has been completely lost. A world map based on Ptolemy was displayed in Augustodunum ( Autun , France ) in late Roman times. Pappus , writing at Alexandria in the 4th century, produced a commentary on Ptolemy's Geography and used it as
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#17327753855926448-479: The end of the thirteenth century, which are the earliest extant manuscripts of the Geography; these are U, K & F. Recension, Ξ, is represented by one codex only, X. Mittenhuber agrees with Berggren & Jones, stating that "The so-called Codex X is of particular significance, because it contains many local names and coordinates that differ from the other manuscripts ... which cannot be explained by mere errors in
6552-663: The extensive additions to the Ptolemaic map shown on the 1492 globe of Martin Behaim . The fact that Ptolemy did not represent an eastern coast of Asia made it admissible for Behaim to extend that continent far to the east. Behaim’s globe placed Marco Polo’s Mangi and Cathay east of Ptolemy’s 180th meridian, and the Great Khan’s capital, Cambaluc ( Beijing ), on the 41st parallel of latitude at approximately 233 degrees East. Behaim allowed 60 degrees beyond Ptolemy’s 180 degrees for
6656-419: 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,
6760-435: The highest honour. Despite being a minority position among ancient philosophers, Ptolemy's views were shared by other mathematicians such as Hero of Alexandria . There are several characters and items named after Ptolemy, including: Geography (Ptolemy) The Geography ( Ancient Greek : Γεωγραφικὴ Ὑφήγησις , Geōgraphikḕ Hyphḗgēsis , lit. "Geographical Guidance"), also known by its Latin names as
6864-553: 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". The charges laid by Newton and others have been
6968-409: The intended scale and then (apparently realizing his mistake) giving up halfway through. Its presence does strongly suggest the existence of earlier, now-lost maps which had been mathematically derived in the manner of Ptolemy, al-Khwārazmi, or Suhrāb. There are surviving reports of such maps. Ptolemy's Geography was translated from Arabic into Latin at the court of King Roger II of Sicily in
7072-616: The introduction to the Handy Tables survived separately from the tables themselves (apparently part of a gathering of some of Ptolemy's shorter writings) under the title Arrangement and Calculation of the Handy Tables . The Planetary Hypotheses ( Greek : Ὑποθέσεις τῶν πλανωμένων , lit. ' Hypotheses of the Planets ' ) is a cosmological work, probably one of the last written by Ptolemy, in two books dealing with
7176-467: The length of a degree instead of the longer degree of Ptolemy, and by adopting Marinus of Tyre ’s longitude of 225 degrees for the east coast of the Magnus Sinus . This resulted in a considerable eastward advancement of the longitudes given by Martin Behaim and other contemporaries of Columbus. By some process Columbus reasoned that the longitudes of eastern Asia and Cipangu respectively were about 270 and 300 degrees east, or 90 and 60 degrees west of
7280-549: The mainland of Asia and 30 degrees more to the east coast of Cipangu (Japan). Cipangu and the mainland of Asia were thus placed only 90 and 120 degrees, respectively, west of the Canary Islands. The Codex Seragliensis was used as the base of a new edition of the work in 2006. This new edition was used to "decode" Ptolemy's coordinates of Books 2 and 3 by an interdisciplinary team of TU Berlin , presented in publications in 2010 and 2012. Christopher Columbus modified this geography further by using 53⅔ Italian nautical miles as
7384-413: The maps in later manuscripts and printed editions of the Geography were reproduced from Planudes' reconstructions." Mittenhuber (2010) further divides the stemma into two recensions of the original c.AD 150 lost work: Ξ and Ω (c.3rd/4th cent., lost). Recension Ω contains most of the extant manuscripts and is subdivided into a further two groups: Δ and Π . Group Δ contains parchment manuscripts from
7488-487: The maps were either copied defectively for not at all. "Of the greatest importance for the text of the Geography" they state is manuscript X ( Vat.Gr.191 ); "because it is the only copy that is uninfluenced by the Byzantine revision." e.g. the 13th-14th century corrections of Planudes, possibly associated with recreating the maps. Regarding the maps, they conclude that it was unlikely that extant maps survived from which
7592-500: The mathematics of music should be based on only the one specific ratio of 3:2, the perfect fifth , and believed that tunings mathematically exact to their system would prove to be melodious, if only the extremely large numbers involved could be calculated (by hand). To the contrary, Ptolemy believed that musical scales and tunings should in general involve multiple different ratios arranged to fit together evenly into smaller tetrachords (combinations of four pitch ratios which together make
7696-461: The mid-5th century BC until the end of the 2nd century BC, as the most probable location. Ptolemy This is an accepted version of this page Claudius Ptolemy ( / ˈ t ɒ l ə m i / ; ‹See Tfd› Greek : Πτολεμαῖος , Ptolemaios ; Latin : Claudius Ptolemaeus ; c. 100 – c. 170 AD) was an Alexandrian mathematician , astronomer , astrologer , geographer , and music theorist who wrote about
7800-566: The modern title is thought to be an Arabic corruption of the Greek name Hē Megistē Syntaxis (lit. "The greatest treatise"), as the work was presumably known in Late Antiquity . Because of its reputation, it was widely sought and translated twice into Latin in the 12th century , 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
7904-477: The motions of the Sun, Moon, planets, and stars. In 2023, archaeologists were able to read a manuscript which gives instructions for the construction of an astronomical tool called a meteoroscope ( μετεωροσκόπιον or μετεωροσκοπεῖον ). The text, which comes from an eighth-century manuscript which also contains Ptolemy's Analemma , was identified on the basis of both its content and linguistic analysis as being by Ptolemy. Ptolemy's second most well-known work
8008-488: The name Geographia Claudii Ptolemaei . It is not thought that his edition had maps, although Manuel Chrysoloras had given Palla Strozzi a Greek copy of Planudes's maps in Florence in 1397. Berggren & Jones (2000) place these manuscripts into a stemma whereby U, K, F and N are connected with the activities of Maximos Planudes (c.1255-1305). From a sister manuscript to UKFN descends R, V, W & C, however
8112-461: The observations were taken at 12:30pm. The overall quality of Ptolemy's observations has been challenged by several modern scientists, but prominently by Robert R. Newton in his 1977 book The Crime of Claudius Ptolemy , 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
8216-603: The only mathematically sound geocentric model of the Solar System , and unlike most Greek mathematicians , Ptolemy's writings (foremost the Almagest ) never ceased to be copied or commented upon, both in late antiquity and in the Middle Ages . However, it is likely that only a few truly mastered the mathematics necessary to understand his works, as evidenced particularly by the many abridged and watered-down introductions to Ptolemy's astronomy that were popular among
8320-401: The radius of the sphere of the fixed stars was 20 000 times the radius of the Earth. The work is also notable for having descriptions on how to build instruments to depict the planets and their movements from a geocentric perspective, much as an orrery would have done for a heliocentric one, presumably for didactic purposes. The Analemma is a short treatise where Ptolemy provides
8424-486: The reappearance of heliocentric models during the scientific revolution . Under the scrutiny of modern scholarship, and the cross-checking of observations contained in the Almagest 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
8528-414: The references to maps in the text were later additions. No Greek manuscript of the Geography survives from earlier than the 13th century. A letter written by the Byzantine monk Maximus Planudes records that he searched for one for Chora Monastery in the summer of 1295; one of the earliest surviving texts may have been one of those he then assembled. In Europe, maps were sometimes redrawn using
8632-479: The region of Jiaozhi in northern Vietnam where ancient Chinese sources claim several Roman embassies first landed in the 2nd and 3rd centuries). Muslim cartographers were using copies of Ptolemy's Almagest and Geography by the 9th century. At that time, in the court of the caliph al-Maʾmūm , al-Khwārazmī compiled his Book of the Depiction of the Earth ( Kitab Surat al-Ard ) which mimicked
8736-405: 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. In 2022 the first Greek fragments of Hipparchus' lost star catalog were discovered in a palimpsest and they debunked accusations made by
8840-627: The site of Tholon, on the coast of the Étang de Berre. Ptolemy, and later the Ravenna Cosmography , calls it a Colonia , but this is likely an error since both Mela and Pliny (who used sources from the Augustan period) refer to the settlement as an oppidum in the 1st century AD. The lands situated around the Étang de Berre were probably given to Arelate ( Arles ) by the Romans when their subjugated Massalia in 49 BC. Another oppidum
8944-403: The sketch map made by Alessandro Zorzi on the advice of Bartholomew Columbus (Christopher's brother) around 1506, which bears an inscription saying that according to the ancient geographer Marinus of Tyre and Christopher Columbus the distance from Cape St Vincent on the coast of Portugal to Cattigara on the peninsula of India Superior was 225 degrees, while according to Ptolemy the same distance
9048-474: The spanning of more than 800 years; however, many astronomers have for centuries suspected that some of his models' parameters were adopted independently of observations. Ptolemy presented his astronomical models alongside convenient tables, which could be used to compute the future or past position of the planets. The Almagest also contains a star catalogue , which is a version of a catalogue created by Hipparchus . Its list of forty-eight constellations
9152-451: The spheres ). Although Ptolemy's Harmonics never had the influence of his Almagest or Geography , 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
9256-440: The structure of the universe and the laws that govern celestial motion . Ptolemy goes beyond the mathematical models of the 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 radii (now known to actually be ~23 450 radii), while
9360-517: The subject of wide discussions and received significant push back from other scholars against the findings. Owen Gingerich , while agreeing that the Almagest contains "some remarkably fishy numbers", including in the matter of the 30-hour displaced equinox, which he noted aligned perfectly with predictions made by Hipparchus 278 years earlier, rejected the qualification of fraud. Objections were also raised by Bernard Goldstein , who questioned Newton's findings and suggested that he had misunderstood
9464-501: 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 theology or metaphysics because the latter are conjectural while only the former can secure certain knowledge. This view is contrary to the Platonic and Aristotelian traditions, where theology or metaphysics occupied
9568-446: The surviving manuscript tradition can be seen in the epitomes of Markianos by Stephanus : "Καὶ ἄλλοι οὕτως διὰ του π Πρετανίδες νῆσοι, ὡς Μαρκιανὸς καὶ Πτολεμαῖος ." The tradition preserved within the stemma of surviving (13th-14th century) manuscripts by Stückelberger & Grasshoff only preserves " Β " and not " Π " recentions of " Βρεττανικήσ ". The Geography consists of three sections, divided among 8 books. Book I
9672-587: The third part of the Geography , Ptolemy gives instructions on how to create maps both of the whole inhabited world ( oikoumenē ) and of the Roman provinces, including the necessary topographic lists, and captions for the maps. His oikoumenē spanned 180 degrees of longitude from the Blessed Islands in the Atlantic Ocean to the middle of China , and about 80 degrees of latitude from Shetland to anti-Meroe (east coast of Africa ); Ptolemy
9776-559: The tradition of Ptolemy. Ptolemy's information was thereby misinterpreted so that the coast of China, which should have been represented as part of the coast of eastern Asia, was falsely made to represent an eastern shore of the Indian Ocean. As a result, Ptolemy implied more land east of the 180th meridian and an ocean beyond. Marco Polo ’s account of his travels in eastern Asia described lands and seaports on an eastern ocean apparently unknown to Ptolemy. Marco Polo’s narrative authorized
9880-629: The tradition.". Although no manuscripts survive from earlier than the late 13th century; there are references to the existence of ancient codicies in late antiquity. One such example is in an epistle by Cassiodorus (c.560 A.D.): “Tum, si vos notitiae nobilis cura inflammaverit, habetis Ptolemaei codicem, qui sic omnia loca evidenter expressit, ut eum cunctarum regionum paene incolam fuisse iudicetis. Eoque fit, ut uno loco positi, sicut monachos decet, animo percurratis, quod aliquorum peregrinatio plurimo labore collegit.”( Institutiones 1, 25) . The existence of ancient recensions that differ fundamentally to
9984-848: The west of Massilia , and from the Mediterranean Sea to the Crau in the north. According to historian Guy Barruol , they were part of the Saluvian confederation . Beyond [the mouth of the Rhône] are the canals leading out of the Rhone, famous as the work of Gaius Marius whose distinguished name they bear, Lake Mastromela and the town of Maritima of the Avatici, and above are the Stony Plains, where tradition says that Hercules fought battles,
10088-455: The world, varying in complexity and fidelity. Book VIII constitutes an atlas of regional maps. The maps include a recapitulation of some of the values given earlier in the work, which were intended to be used as captions to clarify the map's contents and maintain their accuracy during copying. Maps based on scientific principles had been made in Europe since the time of Eratosthenes in
10192-535: Was 10° east of Ptolemy's, he adds some places, and his latitudes differ. C.A. Nallino suggests that the work was not based on Ptolemy but on a derivative world map, presumably in Syriac or Arabic . The coloured map of al-Maʾmūm constructed by a team including al-Khwārazmī was described by the Persian encyclopædist al-Masʿūdī around 956 as superior to the maps of Marinus and Ptolemy, probably indicating that it
10296-661: Was 180 degrees. Prior to the 16th century, knowledge of geography in the Ottoman Empire was limited in scope, with almost no access to the works of earlier Islamic scholars that superseded Ptolemy. His Geography would again be translated and updated with commentary into Arabic under Mehmed II , who commissioned works from Byzantine scholar George Amiroutzes in 1465 and the Florentine humanist Francesco Berlinghieri in 1481. There are two related errors: This suggests Ptolemy rescaled his longitude data to fit with
10400-433: Was built along similar mathematical principles. It included 4530 cities and over 200 mountains. Despite beginning to compile numerous gazetteers of places and coordinates indebted to Ptolemy, Muslim scholars made almost no direct use of Ptolemy's principles in the maps which have survived. Instead, they followed al-Khwārazmī's modifications and the orthogonal projection advocated by Suhrāb's early 10th-century treatise on
10504-488: Was located at Mastromela or Mastramélē (Μαστραμέλη). It has been traditionally identified with the Oppidum of Saint-Blaise [ fr ] , although this has been criticized since the settlement is too far from the Étang de Berre (Stagnum Mastromela), after which it is named. Alternatively, archaeologist Jean Chausserie-Laprée [ fr ] has proposed the Île de Martigues [ fr ] , occupied from
10608-464: Was not based solely on data from Hipparchus’ Catalogue. ... These observations are consistent with the view that Ptolemy composed his star catalogue by combining various sources, including Hipparchus’ catalogue, his own observations and, possibly, those of other authors. The Handy Tables ( Greek : Πρόχειροι κανόνες ) are a set of astronomical tables, together with canons for their use. To facilitate astronomical calculations, Ptolemy tabulated all
10712-584: Was understood by Ptolemy to be a port on the Sinus Magnus, or Great Gulf, the actual Gulf of Thailand, at eight and a half degrees north of the Equator, on the coast of Cambodia, which is where he located it in his Canon of Famous Cities . It was the easternmost port reached by shipping trading from the Graeco-Roman world to the lands of the Far East. In Ptolemy's later and better-known Geography ,
10816-506: 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. 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
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