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104-848: The Silingi are first mentioned by Claudius Ptolemaeus in the 2nd century, who wrote that they had lived south of the Suevic Semnone tribe and north of the Carpathian Mountains , around what now is Silesia : Back below the Semnones the Silingae have their seat, [...]; and below the Silingae the Calucones and the Camavi up to Mt. Melibocus , from whom to the east near the Albis river and above them, below Mt. Asciburgius ,

208-542: 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 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

312-417: 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

416-612: 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

520-577: A basis for coinages: anthropology , photography , telephony , isomer , biomechanics , cinematography , etc. Together with Latin words , they form the foundation of international scientific and technical vocabulary ; for example, all words ending in -logy ('discourse'). There are many English words of Greek origin . Greek is an independent branch of the Indo-European language family. The ancient language most closely related to it may be ancient Macedonian , which, by most accounts,

624-476: 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

728-558: A fairly stable set of consonantal contrasts . The main phonological changes occurred during the Hellenistic and Roman period (see Koine Greek phonology for details): In all its stages, the morphology of Greek shows an extensive set of productive derivational affixes , a limited but productive system of compounding and a rich inflectional system. Although its morphological categories have been fairly stable over time, morphological changes are present throughout, particularly in

832-560: A faster, more convenient cursive writing style with the use of ink and quill . The Greek alphabet consists of 24 letters, each with an uppercase ( majuscule ) and lowercase ( minuscule ) form. The letter sigma has an additional lowercase form (ς) used in the final position of a word: In addition to the letters, the Greek alphabet features a number of diacritical signs : three different accent marks ( acute , grave , and circumflex ), originally denoting different shapes of pitch accent on

936-540: A foreign language. It is also often stated that the historical changes have been relatively slight compared with some other languages. According to one estimation, " Homeric Greek is probably closer to Demotic than 12-century Middle English is to modern spoken English ". Greek is spoken today by at least 13 million people, principally in Greece and Cyprus along with a sizable Greek-speaking minority in Albania near

1040-402: 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

1144-498: 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

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1248-601: 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

1352-466: 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

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

1664-472: 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 is quite late, however, and there is no evidence to support it. It

1768-562: 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.,

1872-804: Is also found in Bulgaria near the Greek-Bulgarian border. Greek is also spoken worldwide by the sizable Greek diaspora which has notable communities in the United States , Australia , Canada , South Africa , Chile , Brazil , Argentina , Russia , Ukraine , the United Kingdom , and throughout the European Union , especially in Germany . Historically, significant Greek-speaking communities and regions were found throughout

1976-773: Is an Indo-European language, constituting an independent Hellenic branch within the Indo-European language family. It is native to Greece , Cyprus , Italy (in Calabria and Salento ), southern Albania , and other regions of the Balkans , Caucasus , the Black Sea coast, Asia Minor , and the Eastern Mediterranean . It has the longest documented history of any Indo-European language, spanning at least 3,400 years of written records. Its writing system

2080-479: Is an Indo-European language, but also includes a number of borrowings from the languages of the populations that inhabited Greece before the arrival of Proto-Greeks, some documented in Mycenaean texts ; they include a large number of Greek toponyms . The form and meaning of many words have changed. Loanwords (words of foreign origin) have entered the language, mainly from Latin, Venetian , and Turkish . During

2184-481: 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 a dozen scientific treatises , three of which were important to later Byzantine , Islamic , and Western European science. The first

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2288-587: 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;

2392-689: 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

2496-725: 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 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 ,

2600-462: 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 a certain Syrus, a figure of whom almost nothing

2704-984: 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 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

2808-838: Is often assumed to either derive from the river or the mountain now called the Ślęza River or Mount Ślęża . The hill was a religious center of the Silingi, situated south-south-east of modern-day Wrocław (Breslau), although the religious importance of the location dates back to the sun-worshipping people of the Lusatian culture , as early as 1300 B.C. Corps Silingia Breslau ( de ) is a student organization ( Studentenverbindung ) that has been operating since 1877, currently (2010) in Cologne , Germany, as Corps Silingia Breslau zu Köln (Silingia Corps Wrocław in Cologne). Ptolemy This

2912-519: Is protected and promoted officially as a regional and minority language in Armenia, Hungary , Romania, and Ukraine. It is recognized as a minority language and protected in Turkey by the 1923 Treaty of Lausanne . The phonology , morphology , syntax , and vocabulary of the language show both conservative and innovative tendencies across the entire attestation of the language from the ancient to

3016-683: 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 the only mathematically sound geocentric model of the Solar System , and unlike most Greek mathematicians , Ptolemy's writings (foremost

3120-475: Is spoken by at least 13.5 million people today in Greece, Cyprus, Italy, Albania, Turkey , and the many other countries of the Greek diaspora . Greek roots have been widely used for centuries and continue to be widely used to coin new words in other languages; Greek and Latin are the predominant sources of international scientific vocabulary . Greek has been spoken in the Balkan peninsula since around

3224-763: Is still used internationally for the writing of Ancient Greek . In Greek, the question mark is written as the English semicolon, while the functions of the colon and semicolon are performed by a raised point (•), known as the ano teleia ( άνω τελεία ). In Greek the comma also functions as a silent letter in a handful of Greek words, principally distinguishing ό,τι ( ó,ti , 'whatever') from ότι ( óti , 'that'). Ancient Greek texts often used scriptio continua ('continuous writing'), which means that ancient authors and scribes would write word after word with no spaces or punctuation between words to differentiate or mark boundaries. Boustrophedon , or bi-directional text,

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3328-650: Is the Greek alphabet , which has been used for approximately 2,800 years; previously, Greek was recorded in writing systems such as Linear B and the Cypriot syllabary . The alphabet arose from the Phoenician script and was in turn the basis of the Latin , Cyrillic , Coptic , Gothic , and many other writing systems. The Greek language holds a very important place in the history of the Western world. Beginning with

3432-528: 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 the Arabs and Byzantines. His work on epicycles has come to symbolize

3536-413: 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

3640-662: 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

3744-715: The Corconti and the Lugi Buri up to the head of the Vistula river. The tribe of Nahanarvali is speculated by modern scholars to be the same people as the Silingi. Tacitus Germania, 43 mentions the Naharvali as the keepers of sanctuary of the Lugian federation (the grove to twin gods Alcis ). Tacitus does not mention the Silingi; however, he places the Naharvali in about the same geographical area in which Ptolemaeus placed

3848-495: The Eastern Mediterranean , in what are today Southern Italy , Turkey , Cyprus , Syria , Lebanon , Israel , Palestine , Egypt , and Libya ; in the area of the Black Sea , in what are today Turkey, Bulgaria , Romania , Ukraine , Russia , Georgia , Armenia , and Azerbaijan ; and, to a lesser extent, in the Western Mediterranean in and around colonies such as Massalia , Monoikos , and Mainake . It

3952-410: 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

4056-516: The Indo-Iranian languages (see Graeco-Aryan ), but little definitive evidence has been found. In addition, Albanian has also been considered somewhat related to Greek and Armenian, and it has been proposed that they all form a higher-order subgroup along with other extinct languages of the ancient Balkans; this higher-order subgroup is usually termed Palaeo-Balkan , and Greek has a central position in it. Linear B , attested as early as

4160-788: 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

4264-470: The Prague-Korchak cultures , who are supposed to be new Slavic tribes migrating from the east. According to some historians, the names of Silesia and the Silingi are related. Another hypothesis derives the name of the mountain and river, and hence the region, from the old Polish word "Ślągwa", meaning "humid" or "damp", reflecting the climate of the region. The name of the territory of Silesia

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4368-463: 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

4472-461: 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

4576-519: 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

4680-492: The nominal and verbal systems. The major change in the nominal morphology since the classical stage was the disuse of the dative case (its functions being largely taken over by the genitive ). The verbal system has lost the infinitive , the synthetically -formed future, and perfect tenses and the optative mood . Many have been replaced by periphrastic ( analytical ) forms. Pronouns show distinctions in person (1st, 2nd, and 3rd), number (singular, dual , and plural in

4784-430: 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

4888-470: The 3rd millennium BC, or possibly earlier. The earliest written evidence is a Linear B clay tablet found in Messenia that dates to between 1450 and 1350 BC, making Greek the world's oldest recorded living language . Among the Indo-European languages, its date of earliest written attestation is matched only by the now-extinct Anatolian languages . The Greek language is conventionally divided into

4992-489: 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

5096-486: The Greek alphabet since approximately the 9th century BC. It was created by modifying the Phoenician alphabet , with the innovation of adopting certain letters to represent the vowels. The variant of the alphabet in use today is essentially the late Ionic variant, introduced for writing classical Attic in 403 BC. In classical Greek, as in classical Latin, only upper-case letters existed. The lower-case Greek letters were developed much later by medieval scribes to permit

5200-425: The Greek language are often emphasized. Although Greek has undergone morphological and phonological changes comparable to those seen in other languages, never since classical antiquity has its cultural, literary, and orthographic tradition been interrupted to the extent that one can speak of a new language emerging. Greek speakers today still tend to regard literary works of ancient Greek as part of their own rather than

5304-495: The Greek language was the Cypriot syllabary (also a descendant of Linear A via the intermediate Cypro-Minoan syllabary ), which is closely related to Linear B but uses somewhat different syllabic conventions to represent phoneme sequences. The Cypriot syllabary is attested in Cyprus from the 11th century BC until its gradual abandonment in the late Classical period, in favor of the standard Greek alphabet. Greek has been written in

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5408-425: 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

5512-629: The Greek verb have likewise remained largely the same over the course of the language's history but with significant changes in the number of distinctions within each category and their morphological expression. Greek verbs have synthetic inflectional forms for: Many aspects of the syntax of Greek have remained constant: verbs agree with their subject only, the use of the surviving cases is largely intact (nominative for subjects and predicates, accusative for objects of most verbs and many prepositions, genitive for possessors), articles precede nouns, adpositions are largely prepositional, relative clauses follow

5616-685: The Greek-Albanian border. A significant percentage of Albania's population has knowledge of the Greek language due in part to the Albanian wave of immigration to Greece in the 1980s and '90s and the Greek community in the country. Prior to the Greco-Turkish War and the resulting population exchange in 1923 a very large population of Greek-speakers also existed in Turkey , though very few remain today. A small Greek-speaking community

5720-849: The Silingi. According to some historians, during the reign of the Roman Emperor Marcus Aurelius (A.D. 161–180), the Silingi must have been among the Vandals who were reported to have lived in the "Vandal mountains", possibly the Sudetes , which are now is part of the Czech Republic . Pushed westwards by the Huns around 400, the Vandals crossed the Rhine into Gaul in 406 and the Pyrenees into Iberia in 409. While

5824-455: 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

5928-660: The Vandals relocated to North Africa , where they established a kingdom centered at Carthage . The kingdom collapsed in the Vandalic War of 533–4, in which Justinian I managed to reconquer the Africa province for the Eastern Roman (Byzantine) Empire . After the migratory movement of the 5th century, any Silingi remaining in Silesia were most likely slowly replaced in the sixth century by an influx of people holding

6032-414: 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 is sometimes said that the very learned man who wrote the book of astrology also wrote the book of the Almagest . The correct answer

6136-422: 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

6240-404: The acute during the late 20th century, and it has only been retained in typography . After the writing reform of 1982, most diacritics are no longer used. Since then, Greek has been written mostly in the simplified monotonic orthography (or monotonic system), which employs only the acute accent and the diaeresis. The traditional system, now called the polytonic orthography (or polytonic system),

6344-402: The ancient language; singular and plural alone in later stages), and gender (masculine, feminine, and neuter), and decline for case (from six cases in the earliest forms attested to four in the modern language). Nouns, articles, and adjectives show all the distinctions except for a person. Both attributive and predicative adjectives agree with the noun. The inflectional categories of

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6448-423: 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

6552-458: 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,

6656-402: 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

6760-404: The early 19th century that was used for literary and official purposes in the newly formed Greek state. In 1976, Dimotiki was declared the official language of Greece, after having incorporated features of Katharevousa and thus giving birth to Standard Modern Greek , used today for all official purposes and in education . The historical unity and continuing identity between the various stages of

6864-469: 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

6968-425: 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

7072-448: The epics of Homer , ancient Greek literature includes many works of lasting importance in the European canon . Greek is also the language in which many of the foundational texts in science and philosophy were originally composed. The New Testament of the Christian Bible was also originally written in Greek. Together with the Latin texts and traditions of the Roman world , the Greek texts and Greek societies of antiquity constitute

7176-419: 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,

7280-455: 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 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

7384-452: The following periods: In the modern era, the Greek language entered a state of diglossia : the coexistence of vernacular and archaizing written forms of the language. What came to be known as the Greek language question was a polarization between two competing varieties of Modern Greek: Dimotiki , the vernacular form of Modern Greek proper, and Katharevousa , meaning 'purified', a compromise between Dimotiki and Ancient Greek developed in

7488-432: 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: Greek language Greek ( Modern Greek : Ελληνικά , romanized :  Elliniká , [eliniˈka] ; Ancient Greek : Ἑλληνική , romanized :  Hellēnikḗ )

7592-553: 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

7696-439: The infinitive entirely (employing a raft of new periphrastic constructions instead) and uses participles more restrictively. The loss of the dative led to a rise of prepositional indirect objects (and the use of the genitive to directly mark these as well). Ancient Greek tended to be verb-final, but neutral word order in the modern language is VSO or SVO. Modern Greek inherits most of its vocabulary from Ancient Greek, which in turn

7800-616: 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

7904-467: The late 15th century BC, was the first script used to write Greek. It is basically a syllabary , which was finally deciphered by Michael Ventris and John Chadwick in the 1950s (its precursor, Linear A , has not been deciphered and most likely encodes a non-Greek language). The language of the Linear B texts, Mycenaean Greek , is the earliest known form of Greek. Another similar system used to write

8008-500: 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

8112-640: The membership of Greece and Cyprus in the European Union, Greek is one of the organization's 24 official languages . Greek is recognized as a minority language in Albania, and used co-officially in some of its municipalities, in the districts of Gjirokastër and Sarandë . It is also an official minority language in the regions of Apulia and Calabria in Italy. In the framework of the European Charter for Regional or Minority Languages , Greek

8216-441: The modern period. The division into conventional periods is, as with all such periodizations, relatively arbitrary, especially because, in all periods, Ancient Greek has enjoyed high prestige, and the literate borrowed heavily from it. Across its history, the syllabic structure of Greek has varied little: Greek shows a mixed syllable structure, permitting complex syllabic onsets but very restricted codas. It has only oral vowels and

8320-566: 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

8424-477: 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

8528-399: The noun they modify and relative pronouns are clause-initial. However, the morphological changes also have their counterparts in the syntax, and there are also significant differences between the syntax of the ancient and that of the modern form of the language . Ancient Greek made great use of participial constructions and of constructions involving the infinitive, and the modern variety lacks

8632-536: The objects of study of the discipline of Classics . During antiquity , Greek was by far the most widely spoken lingua franca in the Mediterranean world . It eventually became the official language of the Byzantine Empire and developed into Medieval Greek . In its modern form , Greek is the official language of Greece and Cyprus and one of the 24 official languages of the European Union . It

8736-461: 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

8840-706: The older periods of Greek, loanwords into Greek acquired Greek inflections, thus leaving only a foreign root word. Modern borrowings (from the 20th century on), especially from French and English, are typically not inflected; other modern borrowings are derived from Albanian , South Slavic ( Macedonian / Bulgarian ) and Eastern Romance languages ( Aromanian and Megleno-Romanian ). Greek words have been widely borrowed into other languages, including English. Example words include: mathematics , physics , astronomy , democracy , philosophy , athletics , theatre, rhetoric , baptism , evangelist , etc. Moreover, Greek words and word elements continue to be productive as

8944-770: The other main Vandal group, the Hasdingi , settled in Gallaecia , the Silingi settled in Baetica . In 419, following Roman-sponsored attacks by the Visigoths against the Silingi in 417–18, the remnants of Silingi and the Alans voluntarily subjected to the rule Hasdingian leader Gunderic , who had fled from Gallaecia to Baetica after having been defeated by a Roman- Suebi coalition. After Gunderic's succession by Genseric in 428,

9048-401: 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

9152-486: 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

9256-405: 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

9360-474: 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

9464-451: 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

9568-437: The stressed vowel; the so-called breathing marks ( rough and smooth breathing ), originally used to signal presence or absence of word-initial /h/; and the diaeresis , used to mark the full syllabic value of a vowel that would otherwise be read as part of a diphthong. These marks were introduced during the course of the Hellenistic period. Actual usage of the grave in handwriting saw a rapid decline in favor of uniform usage of

9672-440: 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

9776-517: 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

9880-501: 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

9984-587: 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

10088-574: Was a distinct dialect of Greek itself. Aside from the Macedonian question, current consensus regards Phrygian as the closest relative of Greek, since they share a number of phonological, morphological and lexical isoglosses , with some being exclusive between them. Scholars have proposed a Graeco-Phrygian subgroup out of which Greek and Phrygian originated. Among living languages, some Indo-Europeanists suggest that Greek may be most closely related to Armenian (see Graeco-Armenian ) or

10192-568: Was also used as the official language of government and religion in the Christian Nubian kingdoms , for most of their history. Greek, in its modern form, is the official language of Greece, where it is spoken by almost the entire population. It is also the official language of Cyprus (nominally alongside Turkish ) and the British Overseas Territory of Akrotiri and Dhekelia (alongside English ). Because of

10296-557: Was also used in Ancient Greek. Greek has occasionally been written in the Latin script , especially in areas under Venetian rule or by Greek Catholics . The term Frankolevantinika / Φραγκολεβαντίνικα applies when the Latin script is used to write Greek in the cultural ambit of Catholicism (because Frankos / Φράγκος is an older Greek term for West-European dating to when most of (Roman Catholic Christian) West Europe

10400-568: 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 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

10504-464: 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

10608-580: Was under the control of the Frankish Empire ). Frankochiotika / Φραγκοχιώτικα (meaning 'Catholic Chiot') alludes to the significant presence of Catholic missionaries based on the island of Chios . Additionally, the term Greeklish is often used when the Greek language is written in a Latin script in online communications. The Latin script is nowadays used by the Greek-speaking communities of Southern Italy . The Yevanic dialect

10712-506: 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

10816-621: Was written by Romaniote and Constantinopolitan Karaite Jews using the Hebrew Alphabet . In a tradition, that in modern time, has come to be known as Greek Aljamiado , some Greek Muslims from Crete wrote their Cretan Greek in the Arabic alphabet . The same happened among Epirote Muslims in Ioannina . This also happened among Arabic-speaking Byzantine rite Christians in the Levant ( Lebanon , Palestine, and Syria ). This usage

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