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99-600: The district, especially the Campeda, is well suited for grazing and horse and cattle breeding, which is carried on to a considerable extent. Macomer, known to the Greek geographer Ptolemy as "Macopsissa," has been inhabited since antiquity. In 1478 was the scene of the historical battle between the Sardinians and the Aragonese , which ended the independence of Sardinia . In 1767, under

198-417: 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

297-612: A stress accent system , and the monophthongization of several diphthongs: The Koine-period Greek in the table is taken from a reconstruction by Benjamin Kantor of New Testament Judeo-Palestinian Koine Greek. The realizations of most phonemes reflect general changes around the Greek-speaking world, including vowel isochrony and monophthongization, but certain sound values differ from other Koine varieties such as Attic, Egyptian and Anatolian. More general Koine phonological developments include

396-601: 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

495-618: A certain Syrus, a figure of whom almost nothing is known but who likely shared some of Ptolemy's astronomical interests. Ptolemy died in Alexandria c.  168 . Ptolemy's Greek name , Ptolemaeus ( Πτολεμαῖος , Ptolemaîos ), is an ancient Greek personal name . It occurs once in Greek mythology and is of Homeric form . It was common among the Macedonian upper class at the time of Alexander

594-470: 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

693-507: A dozen scientific treatises , three of which were important to later Byzantine , Islamic , and Western European science. The first was his astronomical treatise now known as the Almagest , originally entitled Mathematical Treatise ( Greek : Μαθηματικὴ Σύνταξις , Mathēmatikḗ Syntaxis ). The second is the Geography , which is a thorough discussion on maps and the geographic knowledge of

792-402: 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

891-492: 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

990-596: A member of Ptolemaic Egypt's royal lineage , stating that the descendants of the Alexandrine general and Pharaoh Ptolemy I Soter were wise "and included Ptolemy the Wise, who composed the book of the Almagest ". Abu Ma'shar recorded a belief that a different member of this royal line "composed the book on astrology and attributed it to Ptolemy". Historical confusion on this point can be inferred from Abu Ma'shar's subsequent remark: "It

1089-587: 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

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1188-450: A more open pronunciation than other Koine dialects, distinguished as open-mid /ɛ/ vs. close-mid /e/ , rather than as true-mid /e̞/ vs. close-mid /e̝/ as has been suggested for other varieties such as Egyptian. This is evidenced on the basis of Hebrew transcriptions of ε with pataḥ/qamets /a/ and not tsere/segol /e/ . Additionally, it is posited that α perhaps had a back vowel pronunciation as /ɑ/ , dragged backwards due to

1287-461: 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

1386-506: A simplified form of Ionic . The view accepted by most scholars today was given by the Greek linguist Georgios Hatzidakis , who showed that despite the "composition of the Four", the "stable nucleus" of Koine Greek is Attic. In other words, Koine Greek can be regarded as Attic with the admixture of elements especially from Ionic, but also from other dialects. The degree of importance of the non-Attic linguistic elements on Koine can vary depending on

1485-543: 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

1584-478: 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

1683-460: A very important source of information on the ancient Koine is the modern Greek language with all its dialects and its own Koine form, which have preserved some of the ancient language's oral linguistic details which the written tradition has lost. For example, Pontic and Cappadocian Greek preserved the ancient pronunciation of η as ε ( νύφε, συνέλικος, τίμεσον, πεγάδι for standard Modern Greek νύφη, συνήλικος, τίμησον, πηγάδι etc.), while

1782-553: 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.,

1881-529: A work that is now known as Meditations . Koine Greek continues to be used as the liturgical language of services in the Greek Orthodox Church and in some Greek Catholic churches . The English-language name Koine is derived from the Koine Greek term ἡ κοινὴ διάλεκτος ( hē koinḕ diálektos ), meaning "the common dialect". The Greek word κοινή ( koinḗ ) itself means "common". The word

1980-509: Is a term used for present tense verbs that are used in some narrative sections of the New Testament to describe events that are in the past with respect to the speaker. This is seen more in works attributed to Mark and John than Luke . It is used 151 times in the Gospel of Mark in passages where a reader might expect a past tense verb. Scholars have presented various explanations for this; in

2079-522: 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;

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2178-622: 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

2277-570: Is often mentioned as Common Attic . The first scholars who studied Koine, both in Alexandrian and Early Modern times, were classicists whose prototype had been the literary Attic Greek of the Classical period and frowned upon any other variety of Ancient Greek . Koine Greek was therefore considered a decayed form of Greek which was not worthy of attention. The reconsideration on the historical and linguistic importance of Koine Greek began only in

2376-623: Is pronounced / k ɔɪ ˈ n eɪ / , / ˈ k ɔɪ n eɪ / , or / k iː ˈ n iː / in US English and / ˈ k ɔɪ n iː / in UK English. The pronunciation of the word koine itself gradually changed from [koinéː] (close to the Classical Attic pronunciation [koi̯.nɛ̌ː] ) to [cyˈni] (close to the Modern Greek [ciˈni] ). In Modern Greek,

2475-432: Is quite late, however, and there is no evidence to support it. It is known that Ptolemy lived in or around the city of Alexandria , in the Roman province of Egypt under Roman rule . He had a Latin name, Claudius, which is generally taken to imply he was a Roman citizen . He was familiar with Greek philosophers and used Babylonian observations and Babylonian lunar theory. In half of his extant works, Ptolemy addresses

2574-418: Is sometimes said that the very learned man who wrote the book of astrology also wrote the book of the Almagest . The correct answer is not known." Not much positive evidence is known on the subject of Ptolemy's ancestry, apart from what can be drawn from the details of his name, although modern scholars have concluded that Abu Ma'shar's account is erroneous. It is no longer doubted that the astronomer who wrote

2673-808: Is sometimes used for the Greek written by the Greek Church Fathers , the Early Christian theologians in late antiquity. Christian writers in the earliest time tended to use a simple register of Koiné, relatively close to the spoken language of their time, following the model of the Bible. After the 4th century, when Christianity became the state church of the Roman Empire , more learned registers of Koiné also came to be used. Koine period Greek differs from Classical Greek in many ways: grammar , word formation , vocabulary and phonology (sound system). During

2772-626: 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

2871-413: 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

2970-504: The gens Claudia ; the peculiar multipart form of the whole name Claudius Ptolemaeus is a Roman custom, characteristic of Roman citizens. This indicates that Ptolemy would have been a Roman citizen . Gerald Toomer, the translator of Ptolemy's Almagest into English, suggests that citizenship was probably granted to one of Ptolemy's ancestors by either the emperor Claudius or the emperor Nero . The 9th century Persian astronomer Abu Ma'shar al-Balkhi mistakenly presents Ptolemy as

3069-691: The Alexandrian dialect , Biblical Greek , Septuagint Greek or New Testament Greek , was the common supra-regional form of Greek spoken and written during the Hellenistic period , the Roman Empire and the early Byzantine Empire . It evolved from the spread of Greek following the conquests of Alexander the Great in the fourth century BC, and served as the lingua franca of much of the Mediterranean region and

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3168-662: 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

3267-410: 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

3366-749: The Greco-Roman world . The third is the astrological treatise in which he attempted to adapt horoscopic astrology to the Aristotelian natural philosophy of his day. This is sometimes known as the Apotelesmatika ( Greek : Αποτελεσματικά , lit.   ' On the Effects ' ) but more commonly known as the Tetrábiblos , from the Koine Greek meaning "Four Books", or by its Latin equivalent Quadripartite . The Catholic Church promoted his work, which included

3465-527: The Kingdom of Sardinia , it became the capital of the Marquisate of Marghine . The Marquisate included the nearby villages of Birori , Bolotana , Borore , Bortigali , Dualchi , Lei , Mulargia , Noragugume and Silanus . In 1949, a statue called The Venus of Macomer was discovered in a cave located in "Marras" area, in a gorge of the river S'Adde . The artifact depicts a Goddess Mother dating back to

3564-784: 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

3663-617: The Palaeolithic period. It is about 14 centimetres (5.5 in) high and was built with local basalt . It is currently kept in the National Archaeological Museum of Cagliari . Nowadays, Macomer is a destination for tourists who want to admire the beautiful landscape around the city. The region is richer in the bronze-age towers known as nuraghi than any other part of Sardinia. The old parish church of San Pantaleone has three Roman mile-stones in front of it, belonging to

3762-441: The Roman high-road from Carales to Turris Libisonis . A modern road now follows the ancient one. Recently an ethnographic museum called "Le Arti Antiche" (The ancient Arts) has been opened, where it is possible to see tools traditionally used for agriculture and livestock, folk costumes, and photographs. The Monte di Sant'Antonio (St. Anthony's Mountain) has a great historical and naturalistic importance; on 13 June of every year

3861-625: The Septuagint , the Greek translation of the Hebrew Bible , and the Greek New Testament . The teaching of these texts was aimed at the most common people, and for that reason, they use the most popular language of the era. Other sources can be based on random findings such as inscriptions on vases written by popular painters, mistakes made by Atticists due to their imperfect knowledge of Attic Greek or even some surviving Greco-Latin glossaries of

3960-457: 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

4059-536: The Tsakonian language preserved the long α instead of η ( ἁμέρα, ἀστραπά, λίμνα, χοά etc.) and the other local characteristics of Doric Greek . Dialects from the southern part of the Greek-speaking regions ( Dodecanese , Cyprus , etc.), preserve the pronunciation of the double similar consonants ( ἄλ-λος, Ἑλ-λάδα, θάλασ-σα ), while others pronounce in many words υ as ου or preserve ancient double forms ( κρόμμυον – κρεμ-μυον, ράξ – ρώξ etc.). Linguistic phenomena like

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4158-461: 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

4257-519: 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

4356-430: 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

4455-518: The Arabs and Byzantines. His work on epicycles has come to symbolize a very complex theoretical model built in order to explain a false assumption. Ptolemy's date of birth and birthplace are both unknown. The 14th-century astronomer Theodore Meliteniotes wrote that Ptolemy's birthplace was Ptolemais Hermiou , a Greek city in the Thebaid region of Egypt (now El Mansha, Sohag Governorate ). This attestation

4554-510: The Four). This view was supported in the early twentieth century by Paul Kretschmer in his book Die Entstehung der Koine (1901), while Ulrich von Wilamowitz-Moellendorff and Antoine Meillet , based on the intense Ionic elements of the Koine – σσ instead of ττ and ρσ instead of ρρ ( θάλασσα – θάλαττα , 'sea'; ἀρσενικός – ἀρρενικός , 'potent, virile') – considered Koine to be

4653-485: 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

4752-516: The Great and there were several of this name among Alexander's army, one of whom made himself pharaoh in 323 BC: Ptolemy I Soter , the first pharaoh of the Ptolemaic Kingdom . Almost all subsequent pharaohs of Egypt, with a few exceptions, were named Ptolemy until Egypt became a Roman province in 30 BC, ending the Macedonian family's rule. The name Claudius is a Roman name, belonging to

4851-425: 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

4950-522: The Middle East during the following centuries. It was based mainly on Attic and related Ionic speech forms, with various admixtures brought about through dialect levelling with other varieties. Koine Greek included styles ranging from conservative literary forms to the spoken vernaculars of the time. As the dominant language of the Byzantine Empire, it developed further into Medieval Greek , which then turned into Modern Greek . Literary Koine

5049-491: The New Testament , W.F. Howard argues that the heavy use of the historical present in Herodotus and Thucydides , compared with the relatively infrequent usage by Polybius and Xenophon was evidence that heavy use of this verb tense is a feature of vernacular Koine, but other scholars have argued that the historical present can be a literary form to "denote semantic shifts to more prominent material." The term patristic Greek

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5148-449: The Roman period, e.g.: Καλήμερον, ἦλθες; Bono die, venisti? Good day, you came? Ἐὰν θέλεις, ἐλθὲ μεθ' ἡμῶν. Si vis, veni mecum . If you want, come with us. Ποῦ; Ubi? Where? Πρὸς φίλον ἡμέτερον Λύκιον. Ad amicum nostrum Lucium. To our friend Lucius. Τί γὰρ ἔχει; Quid enim habet? Indeed, what does he have? What is it with him? Ἀρρωστεῖ. Aegrotat. He's sick. Finally,

5247-455: 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

5346-422: 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

5445-556: The above imply that those characteristics survived within Koine, which in turn had countless variations in the Greek-speaking world. Biblical Koine refers to the varieties of Koine Greek used in Bible translations into Greek and related texts. Its main sources are: There has been some debate to what degree Biblical Greek represents the mainstream of contemporary spoken Koine and to what extent it contains specifically Semitic substratum features. These could have been induced either through

5544-472: The anniversary of the Saint of Padua is celebrated there. Ptolemy This is an accepted version of this page Claudius Ptolemy ( / ˈ t ɒ l ə m i / ; Ancient Greek : Πτολεμαῖος , Ptolemaios ; Latin : Claudius Ptolemaeus ; c.  100  – c.  170 AD) was an Alexandrian mathematician , astronomer , astrologer , geographer , and music theorist who wrote about

5643-472: 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

5742-525: The creation and evolution of Koine Greek throughout the entire Hellenistic and Roman eras of history until the start of the Middle Ages. The linguistic roots of the Common Greek dialect had been unclear since ancient times. During the Hellenistic period , most scholars thought of Koine as the result of the mixture of the four main Ancient Greek dialects, " ἡ ἐκ τῶν τεττάρων συνεστῶσα " (the composition of

5841-506: 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,

5940-402: 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

6039-469: The early 19th century, where renowned scholars conducted a series of studies on the evolution of Koine throughout the entire Hellenistic period and Roman Empire . The sources used on the studies of Koine have been numerous and of unequal reliability. The most significant ones are the inscriptions of the post-Classical periods and the papyri , for being two kinds of texts which have authentic content and can be studied directly. Other significant sources are

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6138-525: The early 20th century some scholars argued that the use of the historical present tense in Mark was due to the influence of Aramaic , but this theory fell out of favor in the 1960s. Another group of scholars believed the historical present tense was used to heighten the dramatic effect, and this interpretation was favored in the New American Bible translation. In Volume II of the 1929 edition of A Grammar of

6237-469: 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

6336-425: 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

6435-419: 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,

6534-434: 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: Koine Greek Koine Greek ( ἡ κοινὴ διάλεκτος , hē koinḕ diálektos , lit.   ' the common dialect ' ), also variously known as Hellenistic Greek , common Attic ,

6633-553: 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

6732-453: The initial stage in the fortition of the second element in the αυ/ευ diphthongs) and the loss of vowel-timing distinctions are carried through. On the other hand, Kantor argues for certain vowel qualities differing from the rest of the Koine in the Judean dialect. Although it is impossible to know the exact realizations of vowels, it is tentatively argued that the mid-vowels ε / αι and η had

6831-599: 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

6930-523: The language is referred to as Ελληνιστική Κοινή , "Hellenistic Koiné", in the sense of "Hellenistic supraregional language "). Ancient scholars used the term koine in several different senses. Scholars such as Apollonius Dyscolus (second century AD) and Aelius Herodianus (second century AD) maintained the term koine to refer to the Proto-Greek language , while others used it to refer to any vernacular form of Greek speech which differed somewhat from

7029-403: The literary language. When Koine Greek became a language of literature by the first century BC, some people distinguished two forms: written as the literary post-classical form (which should not be confused with Atticism ), and vernacular as the day-to-day vernacular . Others chose to refer to Koine as "the dialect of Alexandria " or "Alexandrian dialect" ( ἡ Ἀλεξανδρέων διάλεκτος ), or even

7128-725: The main of the Greek language. S. J. Thackeray, in A Grammar of the Old Testament in Greek According to the Septuagint (1909), wrote that only the five books of the Pentateuch , parts of the Book of Joshua and the Book of Isaiah may be considered "good Koine". One issue debated by scholars is whether and how much the translation of the Pentateuch influenced the rest of the Septuagint, including

7227-500: 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

7326-555: 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

7425-477: 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

7524-426: The notion of meeting and gathering of men, without any particular character. Therefore, etymologizing this word could be needless, or even misleading, when it could guide to false meanings, for example that ἐκκλησία is a name used for the people of God, Israel. The authors of the New Testament follow the Septuagint translations for over half their quotations from the Old Testament. The " historical present " tense

7623-461: 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

7722-591: The only mathematically sound geocentric model of the Solar System , and unlike most Greek mathematicians , Ptolemy's writings (foremost the Almagest ) never ceased to be copied or commented upon, both in late antiquity and in the Middle Ages . However, it is likely that only a few truly mastered the mathematics necessary to understand his works, as evidenced particularly by the many abridged and watered-down introductions to Ptolemy's astronomy that were popular among

7821-452: The opening of ε . Influence of the Aramaic substrate could have also caused confusion between α and ο , providing further evidence for the back vowel realization. The following texts show differences from Attic Greek in all aspects – grammar, morphology, vocabulary and can be inferred to show differences in phonology. The following comments illustrate the phonological development within

7920-399: The period generally designated as Koine Greek, a great deal of phonological change occurred. At the start of the period, the pronunciation was virtually identical to Ancient Greek phonology , whereas in the end, it had much more in common with Modern Greek phonology . The three most significant changes were the loss of vowel length distinction, the replacement of the pitch accent system by

8019-523: The period of Koine. The phonetic transcriptions are tentative and are intended to illustrate two different stages in the reconstructed development, an early conservative variety still relatively close to Classical Attic, and a somewhat later, more progressive variety approaching Modern Greek in some respects. The following excerpt, from a decree of the Roman Senate to the town of Thisbae in Boeotia in 170 BC,

8118-438: The post-Classical period of Greek is defined as beginning with the death of Alexander the Great in 323 BC, when cultures under Greek sway in turn began to influence the language. The passage into the next period, known as Medieval Greek , is sometimes dated from the foundation of Constantinople by Constantine the Great in 330 AD, but often only from the end of late antiquity . The post-Classical period of Greek thus refers to

8217-505: The practice of translating closely from Biblical Hebrew or Aramaic originals, or through the influence of the regional non-standard Greek spoken by originally Aramaic-speaking Hellenized Jews . Some of the features discussed in this context are the Septuagint's normative absence of the particles μέν and δέ , and the use of ἐγένετο to denote "it came to pass". Some features of Biblical Greek which are thought to have originally been non-standard elements eventually found their way into

8316-401: 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

8415-486: 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

8514-517: The region of the Hellenistic world. In that respect, the varieties of Koine spoken in the Ionian colonies of Anatolia (e.g. Pontus , cf. Pontic Greek ) would have more intense Ionic characteristics than others and those of Laconia and Cyprus would preserve some Doric and Arcadocypriot characteristics, respectively. The literary Koine of the Hellenistic age resembles Attic in such a degree that it

8613-405: 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

8712-474: 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

8811-451: 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

8910-429: The spirantization of Γ , with palatal allophone before front-vowels and a plosive allophone after nasals, and β . φ, θ and χ still preserve their ancient aspirated plosive values, while the unaspirated stops π, τ, κ have perhaps begun to develop voiced allophones after nasals. Initial aspiration has also likely become an optional sound for many speakers of the popular variety. Monophthongization (including

9009-440: 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

9108-517: 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

9207-496: 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

9306-573: 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

9405-476: The translation of Isaiah. Another point that scholars have debated is the use of ἐκκλησία ekklēsía as a translation for the Hebrew קָהָל qāhāl . Old Testament scholar James Barr has been critical of etymological arguments that ekklēsía refers to "the community called by God to constitute his People". Kyriakoula Papademetriou explains: He maintains that ἐκκλησία is merely used for designating

9504-625: The universal dialect of its time. Modern classicists have often used the former sense. Koine Greek arose as a common dialect within the armies of Alexander the Great . Under the leadership of Macedon , their newly formed common variety was spoken from the Ptolemaic Kingdom of Egypt to the Seleucid Empire of Mesopotamia . It replaced existing ancient Greek dialects with an everyday form that people anywhere could understand. Though elements of Koine Greek took shape in Classical Greece ,

9603-464: 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

9702-658: Was the medium of much post-classical Greek literary and scholarly writing, such as the works of Plutarch and Polybius . Koine is also the language of the Septuagint (the 3rd century BC Greek translation of the Hebrew Bible ), the Christian New Testament , and of most early Christian theological writing by the Church Fathers . In this context, Koine Greek is also known as "Biblical", "New Testament", "ecclesiastical", or "patristic" Greek. The Roman Emperor Marcus Aurelius wrote his private thoughts in Koine Greek in

9801-499: Was well aware that he knew about only a quarter of the globe, and an erroneous extension of China southward suggests his sources did not reach all the way to the Pacific Ocean. It seems likely that the topographical tables in the second part of the work (Books 2–7) are cumulative texts, which were altered as new knowledge became available in the centuries after Ptolemy. This means that information contained in different parts of

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