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128-437: 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
256-540: 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
384-415: 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
512-509: A tomb was constructed for them. Shortly after this event, Ptolemy openly joined the coalition against Perdiccas. Perdiccas appears to have suspected Ptolemy of aiming for the throne himself, and may have decided that Ptolemy was his most dangerous rival. Ptolemy executed Cleomenes for spying on behalf of Perdiccas; this removed the chief check on his authority, and allowed Ptolemy to obtain the huge sum that Cleomenes had accumulated. In 321 BC, Perdiccas attempted to invade Egypt, only to fall at
640-777: A 'rebel in Cyprus' who was put to death by his half-brother Ptolemy II –as well as the daughters Ptolemais, who married Demetrius I of Macedon , and Lysandra , first married to Alexander V of Macedon and after to Lysimachus' son Agathocles . Ptolemy married once more to Berenice , Eurydice's cousin, who had come to Egypt as Eurydice's lady-in-waiting with the children from her first marriage to Philip . Their children were Arsinoe II , Philotera , and Ptolemy II. Their eldest child Arsinoe married Lysimachus, then her half-brother Ptolemy Keraunos, and finally her full brother Ptolemy II. In 285, Ptolemy made his son Ptolemy II his co-regent. His eldest legitimate son, Ptolemy Keraunos, fled to
768-605: 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
896-577: 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,
1024-734: A claim to Judea in southern Syria , which was disputed with the Seleucid king Seleucus I . He also took control of Cyprus and Cyrenaica , the latter of which was placed under the control of Ptolemy's stepson Magas . Ptolemy also commanded the construction of the Library of Alexandria and of the Lighthouse of Alexandria , one of the Seven Wonders of the Ancient World . Ptolemy I may have married Thaïs , his mistress during
1152-473: 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
1280-494: A distinctly unheroic role in proceedings to Perdiccas. More recently, J. Roisman has argued that the case for Ptolemy's blackening of Perdiccas and others has been much exaggerated. Ptolemy personally sponsored the great mathematician Euclid . He found Euclid's seminal work, the Elements , too difficult to study, so he asked if there were an easier way to master it. According to Proclus , Euclid famously quipped: "Sire, there
1408-558: 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
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#17327658508991536-560: 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
1664-539: A fleet which detached the coastal towns of Phaselis , Xanthos , Kaunos , Iasos and Myndus in Lycia and Caria from Antigonus, then crossed into Greece, where he took possession of Corinth , Sicyon and Megara (308 BC). In 306, a great fleet under Demetrius attacked Cyprus, and Ptolemy's brother Menelaus was defeated and captured in another decisive Battle of Salamis . Ptolemy's complete loss of Cyprus followed. The satraps Antigonus and Demetrius now each assumed
1792-540: 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
1920-480: A great seat of Greek culture . Ptolemy I was the son of Arsinoe of Macedon by either her husband Lagus or Philip II of Macedon , the father of Alexander. However, the latter is unlikely and may be a myth fabricated to glorify the Ptolemaic Dynasty . Ptolemy was one of Alexander's most trusted companions and military officers. After the death of Alexander in 323 BC, Ptolemy retrieved his body as it
2048-400: 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
2176-496: 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
2304-600: 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
2432-464: 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
2560-558: 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
2688-479: 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
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#17327658508992816-470: 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
2944-560: 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.,
3072-804: 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
3200-773: 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
3328-479: 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
3456-585: 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;
3584-685: 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
3712-721: 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 ,
3840-460: 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
3968-970: 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
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4096-519: 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
4224-916: Is sometimes called aljamiado , as when Romance languages are written in the Arabic alphabet. Article 1 of the Universal Declaration of Human Rights in Greek: Transcription of the example text into Latin alphabet : Article 1 of the Universal Declaration of Human Rights in English: Proto-Greek Mycenaean Ancient Koine Medieval Modern Ptolemy I Soter Ptolemy I Soter ( / ˈ t ɒ l əm i / ; Greek : Πτολεμαῖος Σωτήρ , Ptolemaîos Sōtḗr , "Ptolemy
4352-683: 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
4480-475: 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
4608-763: 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,
4736-650: 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
4864-525: 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
4992-413: 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
5120-658: 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
5248-495: 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
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5376-409: 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
5504-516: 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
5632-787: 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
5760-555: The Seleucid and Ptolemaic dynasties. Henceforth, Ptolemy seems to have involved himself as little as possible in the rivalries between Asia Minor and Greece ; he lost what he held in Greece, but reconquered Cyprus in 295/294. Cyrenaica , after a series of rebellions, was finally subjugated in about 300 and placed under his stepson Magas . While Alexander was alive, Ptolemy had three children with his mistress Thaïs , who may also have been his wife: Lagus; Leontiscus; and Eirene, who
5888-461: 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
6016-459: 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
6144-519: 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
6272-492: 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
6400-428: 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
6528-470: 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
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#17327658508996656-489: 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
6784-486: The Great Library of Alexandria . The Ptolemaic dynasty which he founded ruled Egypt for nearly three hundred years. It was a Hellenistic kingdom known for its capital Alexandria, which became a center of Greek culture . Ptolemaic rule ended with the death of Cleopatra VII in 30 BC. Ptolemy himself wrote an eyewitness history of Alexander's campaigns (now lost). In the second century AD, Ptolemy's history
6912-727: The Great. On his deathbed , Alexander wished to be buried at the Temple of Zeus Ammon in the Siwa Oasis of ancient Libya instead of the royal tombs of Aigai in Macedon. However, his successors including Perdiccas attempted to bury his body in Macedon instead. In late 322 or early 321 BC, Alexander's body was in Syria, on its way to Macedon, when it was captured by Ptolemy I. He brought Alexander's remains back to Egypt, interring them at Memphis , but they were later moved to Alexandria where
7040-486: 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
7168-425: 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
7296-442: 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
7424-422: 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
7552-629: 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
7680-685: 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
7808-571: The Savior "; c. 367 BC – January 282 BC) was a Macedonian Greek general, historian, and successor of Alexander the Great who went on to found the Ptolemaic Kingdom centered on Egypt . Ptolemy was basileus and pharaoh of Ptolemaic Egypt from 305/304 BC to his death in 282 BC, and his descendants continued to rule Egypt until 30 BC. During their rule, Egypt became a thriving bastion of Hellenistic civilization and Alexandria
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#17327658508997936-452: 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
8064-465: 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
8192-420: 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
8320-404: 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),
8448-402: 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
8576-421: 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
8704-540: The author "whom I chiefly follow", and in his Preface writes that Ptolemy seemed to him to be a particularly trustworthy source, "not only because he was present with Alexander on campaign, but also because he was himself a king, and hence lying would be more dishonourable for him than for anyone else". Ptolemy's lost history was long considered an objective work, distinguished by its straightforward honesty and sobriety, but more recent work has called this assessment into question. R. M. Errington argued that Ptolemy's history
8832-464: The campaign against the rebel Bessus whom his own guards captured and handed over to Ptolemy, who then handed him over to Alexander for execution. When Alexander died in 323 BC, Ptolemy is said to have instigated the settlement of the empire made at Babylon . Through the Partition of Babylon , he was appointed satrap of Egypt , under the nominal kings Philip III and the infant Alexander IV ;
8960-483: The court of Lysimachus. Ptolemy I died in January 282 aged 84 or 85. Shrewd and cautious, he had a compact and well-ordered realm to show at the end of forty years of war. His reputation for good nature and liberality attached the floating soldier-class of Macedonians and other Greeks to his service, and was not insignificant; nor did he wholly neglect conciliation of the natives. He was a ready patron of letters, founding
9088-509: 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,
9216-400: 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
9344-404: 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
9472-468: 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
9600-425: 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
9728-567: 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
9856-417: 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,
9984-513: 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
10112-452: 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
10240-527: The former satrap, the Greek Cleomenes , stayed on as his deputy. Ptolemy quickly moved, without authorization, to subjugate Cyrenaica . By custom, kings in Macedonia asserted their right to the throne by burying their predecessor. Probably because he wanted to pre-empt Perdiccas , the imperial regent, from staking his claim in this way, Ptolemy took great pains in acquiring the body of Alexander
10368-463: The fugitive satrap of Babylonia, both invaded Syria, and defeated Demetrius I , the son of Antigonus, in the Battle of Gaza . Again he occupied Syria, and again—after only a few months, when Demetrius had won a battle over his general, and Antigonus entered Syria in force—he evacuated it. In 311, a peace was concluded between the combatants. Soon after this, the surviving 13-year-old king, Alexander IV,
10496-523: The half-brother of Alexander the Great . It is probable that this is a later myth fabricated to glorify the Ptolemaic dynasty. However, through his mother Ptolemy may have been a great-grandson of Amyntas I of Macedon , making him a member of the Argead royal house and a distant relative of Alexander, who was a great-great-grandson of Amyntas. Ptolemy served with Alexander from his first campaigns, and
10624-546: The hands of his own men. Ptolemy's decision to defend the Nile against Perdiccas ended in fiasco for Perdiccas, with the loss of 2,000 men. This failure was a fatal blow to Perdiccas' reputation, and he was murdered in his tent by two of his subordinates. Ptolemy immediately crossed the Nile, to provide supplies to what had the day before been an enemy army. Ptolemy was offered the regency in place of Perdiccas, but he declined. Ptolemy
10752-431: 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 )
10880-549: 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
11008-439: 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
11136-615: 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
11264-467: 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
11392-486: The life of Alexander; he is known to have married the Persian noblewoman Artakama on Alexander's orders. He later married Eurydice , daughter of the Macedonian regent Antipater ; their sons Ptolemy Keraunos and Meleager ruled in turn as kings of Macedon. Ptolemy's final marriage was to Eurydice's cousin and lady-in-waiting, Berenice I . Upon his death, he was succeeded by his son with Berenice, Ptolemy II . Ptolemy
11520-500: 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
11648-640: 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
11776-441: 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
11904-564: 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
12032-474: 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
12160-401: The news came that Antigonus had been defeated and slain by Lysimachus and Seleucus at the Battle of Ipsus in 301, he occupied Syria a fourth time. The other members of the coalition had assigned all Syria to Seleucus, after what they regarded as Ptolemy's desertion, and for the next hundred years, the question of the ownership of southern Syria (i.e., Judea) produced recurring warfare between
12288-399: 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
12416-536: 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
12544-459: 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
12672-706: 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
12800-399: 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
12928-484: 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
13056-402: 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
13184-472: 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
13312-450: 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
13440-437: 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
13568-438: 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
13696-513: 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
13824-501: 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
13952-587: 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
14080-417: The title of king; Ptolemy, as well as Cassander , Lysimachus and Seleucus I Nicator , responded by doing the same. In the winter of 306 BC, Antigonus tried to follow up his victory in Cyprus by invading Egypt; but Ptolemy was strongest there, and successfully held the frontier against him. Ptolemy led no further overseas expeditions against Antigonus. However, he did send great assistance to Rhodes when it
14208-464: Was besieged by Demetrius (305/304) . The Rhodians granted divine honors to Ptolemy as a result of the lifting of the siege. When the coalition against Antigonus was renewed in 302, Ptolemy joined it, and invaded Syria a third time, while Antigonus was engaged with Lysimachus in Asia Minor . On hearing a report that Antigonus had won a decisive victory there, he once again evacuated Syria. But when
14336-515: 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
14464-568: 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
14592-505: 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
14720-545: Was among the seven somatophylakes (bodyguards) of Alexander. He played a principal part in the later campaigns in Afghanistan and India . He participated in the Battle of Issus , commanding troops on the left wing under the authority of Parmenion. Later he accompanied Alexander during his journey to the Oracle in the Siwa Oasis where he was proclaimed a son of Zeus . Ptolemy had his first independent command during
14848-591: Was born in 367 BC in the ancient kingdom of Macedon . His mother was Arsinoe . According to Satyrus the Peripatetic , Arsinoe was a descendant of Alexander I of Macedon and thus a member of the Argead dynasty , claiming ultimate descent from Heracles . Ostensibly, Ptolemy's father was Lagus , a Macedonian nobleman from Eordaea , but many ancient sources claim that he was actually an illegitimate son of Philip II of Macedon . If true, this would have made Ptolemy
14976-555: Was characterised by persistent bias and self-aggrandisement, and by systematic blackening of the reputation of Perdiccas , one of Ptolemy's chief dynastic rivals after Alexander's death. For example, Arrian's account of the fall of Thebes in 335 BC ( Anabasis 1.8.1–1.8.8 , a rare section of narrative explicitly attributed to Ptolemy by Arrian) shows several significant variations from the parallel account preserved in Diodorus Siculus ( 17.11–12 ), most notably in attributing
15104-418: Was consistent in his policy of securing a power base, while never succumbing to the temptation of risking all to succeed Alexander. In the long wars that followed between the different Diadochi , Ptolemy's first goal was to hold Egypt securely, and his second was to secure control in the outlying areas: Cyrenaica and Cyprus , as well as Syria , including the province of Judea . His first occupation of Syria
15232-494: Was en route to be buried in Macedon, placing it in Memphis instead, where it was later moved to Alexandria in a new tomb . Afterwards he joined a coalition against Perdiccas , the royal regent over Philip III of Macedon . The latter invaded Egypt but was assassinated by his own officers in 320 BC, allowing Ptolemy I to consolidate his control over the country. After a series of wars between Alexander's successors , Ptolemy gained
15360-504: Was given in marriage to Eunostos of Soloi in Cyprus. During the Susa weddings , Ptolemy married Persian noblewoman Artakama , as ordered by Alexander the Great. Around 322 BC , he married Eurydice , daughter of Antipater , regent of Macedonia. They had five children before she was repudiated: three sons– Ptolemy Ceraunus , king of Macedon from 281 BC to 279 BC ; his brother and successor Meleager , who ruled for two months in 279 BC; and
15488-568: 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
15616-474: Was in 318, and he established at the same time a protectorate over the petty kings of Cyprus. When Antigonus I , master of Asia in 315, showed expansionist ambitions, Ptolemy joined the coalition against him, and on the outbreak of war, evacuated Syria. In Cyprus, he fought the partisans of Antigonus, and re-conquered the island (313). A revolt in Cyrene was crushed the same year. In 312, Ptolemy and Seleucus ,
15744-471: Was murdered in Macedonia on the orders of Cassander, leaving the satrap of Egypt absolutely his own master. The peace did not last long, early in 310 he was informed that his ally Nicocles of Paphos was planning to defect to Antigonus; he sent some agents, who together with his brother Menelaus , who was still on Cyprus with an army, dealt with the situation, they surrounded Nicocles palace and forced him to commit suicide. In 309 Ptolemy personally commanded
15872-463: 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
16000-580: 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
16128-520: Was used by Arrian of Nicomedia as one of his two main primary sources (alongside the history of Aristobulus of Cassandreia ) for his own extant Anabasis of Alexander, and hence large parts of Ptolemy's history can be assumed to survive in paraphrase or précis in Arrian's work. Arrian cites Ptolemy by name on only a few occasions, but it is likely that large stretches of Arrian's Anabasis reflect Ptolemy's version of events. Arrian once names Ptolemy as
16256-503: 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
16384-621: 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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