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95-553: According to Claudius Ptolemy , Diogenes , a merchant in the Indian trade, was blown off course from his usual route from India, and after travelling 25 days south along the coast of Africa arrived at Rhapta, located where the river of the same name enters the Indian Ocean opposite the island of Menouthias . Diogenes further describes this river as having its source near the Mountains of

190-417: 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

285-649: A 70% similarity in lexicon with the Merina dialect. The Eastern dialects are: The Western dialects are: Additionally, the Bushi dialect (41,700 speakers) is spoken on the French overseas territory of Mayotte , which is part of the Comoro island chain situated northwest of Madagascar. The two main dialects of Malagasy are easily distinguished by several phonological features. Sakalava lost final nasal consonants, whereas Merina added

380-601: 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

475-470: 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

570-402: 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

665-508: A likely candidate for Rhapta. However, the first evidence of inhabitation starts solely in the seventh century at a site called Tumbe on the northern end of the island, limpidly contradicting these assertions. Furthermore, John Perkins states this: "Some Roman, Byzantine, and Sasanian coins are reported from the East African coast; however, none of these come from excavations, and the surrounding evidence suggests that they probably did not reach

760-492: 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

855-587: 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

950-461: 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

1045-547: A phonological quality not unlike that of Portuguese . /o/ is marginal in Merina dialect, found in interjections and loan words, though it is also found in place names from other dialectical areas. /ai, au/ are diphthongs [ai̯, au̯] in careful speech, [e, o] or [ɛ, ɔ] in more casual speech. /ai/ , whichever way it is pronounced, affects following /k, ɡ/ as /i/ does. The alveolars /s ts z dz l/ are slightly palatalized . /ts, dz, s, z/ vary between [ts, dz, s, z] and [tʃ, dʒ, ʃ, ʒ] , and are especially likely to be

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1140-543: 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

1235-478: 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

1330-553: 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.,

1425-631: A voiceless [ə̥] : Final *t became -[tse] in the one but -[ʈʂə̥] in the other: Sakalava retains ancestral *li and *ti, whereas in Merina these become [di] (as in huditra 'skin' above) and [tsi] : However, these last changes started in Borneo before the Malagasy arrived in Madagascar. The language has a written literature going back presumably to the 15th century. When the French established Fort-Dauphin in

1520-417: A word, but they are pronounced /p, t/ . @ is used informally as a short form for amin'ny , which is a preposition followed by the definite form, meaning for instance with the . Diacritics are not obligatory in standard Malagasy, except in the case where its absence leads to an ambiguity: tanàna ("city") must have the diacritic to discriminate itself from tanana ("hand"). They may however be used in

1615-536: Is an Austronesian language and dialect continuum spoken in Madagascar . The standard variety, called Official Malagasy, is an official language of Madagascar alongside French . Malagasy is the westernmost Malayo-Polynesian language , brought to Madagascar with the settlement of Austronesian speakers from the Sunda Islands (about 7,300 kilometres or 4,500 miles away) around the 5th century AD or perhaps between

1710-572: 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;

1805-479: Is certain that the people of Rhapta did not speak a Bantu language , since the 1st century AD is too early for Bantu speakers to have reached the East African coast. It is possible that the survivors of the 1st century inhabitants are the Iraqw , Gorowa , Alagwa and Burungi . Roland Anthony Oliver states that there is no evidence where Greco-Roman sources allude to the inhabitants of Rhapta being of Bantu origin. It

1900-499: Is considered the national language of Madagascar. It is one of two official languages alongside French in the 2010 constitution put in place the Fourth Republic. Previously, under the 2007 constitution, Malagasy was one of three official languages alongside French and English. Malagasy is the language of instruction in all public schools through grade five for all subjects, and remains the language of instruction through high school for

1995-668: Is disputed. The Periplus only states that it was a source of ivory and tortoise shell. J. Innes Miller argues that Rhapta formed an important link in the trade route between what is now modern Indonesia and consumers in the Mediterranean region. Miller notes that ancient authorities (e.g. Herodotus 3.111) state that cinnamon and cassia bark were harvested in Africa, yet these species until recently were found only in Southeast Asia , which would hint at some conflation. Miller points to

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2090-456: Is evidence that the predecessors of the Malagasy dialects first arrived in the southern stretch of the east coast of Madagascar. Adelaar (2017) proposes that a distinct Malagasy speech community had already been established in South Borneo before the early Malagasy speakers migrated to East Africa. Malagasy has a tradition of oratory arts and poetic histories and legends. The most well-known

2185-672: 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

2280-646: Is no river at Msasani, and thus concludes Kisuyu or the Rufiji delta are the most likely candidates. However, J. Innes Miller points out that Roman coins have been found on Pemba; that the Ruvu emerges near the Kilimanjaro and Meru mountains—which confirm the account of Diogenes; and that an old inscription in Semitic characters has been found near the Pangani estuary, which make Pemba

2375-740: Is not clear if they are actually trilled, or are simply non- sibilant affricates [ʈɻ̊˔ ᶯʈɻ̊˔ ɖɻ˔ ᶯɖɻ˔] . However, in another Austronesian language with a claimed trilled affricate, Fijian , trilling occurs but is rare, and the primary distinguishing feature is that it is postalveolar. The Malagasy sounds are frequently transcribed [ ʈʂ ᶯʈʂ ɖʐ ᶯɖʐ ], and that is the convention used in this article. In reduplication, compounding, possessive and verbal constructions, as well as after nasals, fricatives and liquids, 'spirants' become stops, as follows: Here, stressed syllables are indicated by grave diacritics ⟨à⟩ , although these diacritics are normally not used. Words are generally accented on

2470-578: 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 , 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

2565-434: Is pronounced [fə̥ˈnurnə̥] . According to Penelope Howe in 2019, Central Malagasy is undergoing tonogenesis , with syllables containing voiced consonants are "fully devoiced" and acquire a low tone ( /ba/ → [b̥à] ), while those containing unvoiced consonants acquire a high tone ( /pa/ → [pá] ). However, this development appears to not occur in posttonic syllables, and she called it " pitch accent " instead. Malagasy has

2660-516: Is spoken by around 25 million people in Madagascar and the Comoros . Most people in Madagascar speak it as a first language, as do some people of Malagasy descent elsewhere. Malagasy is divided across its twelve dialects between two main dialect groups; Eastern and Western. The central plateau of the island, where the capital Antananarivo and the old heartland of the Merina Kingdom is located, speaks

2755-671: Is that the Indonesian Austronesian came directly across the Indian Ocean from Java to Madagascar. It is likely that they went through the Maldives , where evidence of old Indonesian boat design and fishing technology persists until the present. The migrations continued along the first millennium, as confirmed by linguistic researchers who showed the close relationship between the Malagasy language and Old Malay and Old Javanese languages of this period. The Malagasy language originates from

2850-622: 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 is sometimes known as the Apotelesmatika ( Greek : Αποτελεσματικά , lit.   ' On the Effects ' ) but more commonly known as

2945-452: Is the national epic, Ibonia , about a Malagasy folk hero of the same name. Malagasy is the principal language spoken on the island of Madagascar. It is also spoken by Malagasy communities on neighboring Indian Ocean islands such as Réunion , Mayotte and Mauritius . Expatriate Malagasy communities speaking the language also exist in Europe and North America. The Merina dialect of Malagasy

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3040-462: 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

3135-562: 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 the Almagest ) never ceased to be copied or commented upon, both in late antiquity and in

3230-662: 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

3325-410: 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

3420-645: 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 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

3515-784: 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

3610-467: The Periplus focuses on the availability of tortoise shell, and its silence about other goods should not be taken as evidence that other goods were not traded. Claudius 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)

3705-457: 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

3800-461: 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

3895-519: 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

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3990-430: 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

4085-401: The 17th century, they found an Arabico-Malagasy script in use, known as Sorabe ("large writings"). This Arabic-derived Sorabe alphabet was mainly used for astrological and magical texts. The oldest known manuscript in that script is a short Malagasy-Dutch vocabulary from the early 17th century, which was first published in 1908 by Gabriel Ferrand though the script must have been introduced into

4180-617: The 7th and 13th centuries. The Malagasy language is one of the Barito languages and is most closely related to the Ma'anyan language , still spoken on Borneo . Malagasy also includes numerous Malay loanwords, from the time of the early Austronesian settlement and trading between Madagascar and the Sunda Islands. After c.  1000 AD , Malagasy incorporated numerous Bantu and Arabic loanwords brought over by traders and new settlers. Malagasy

4275-697: The Dutch scholar Adriaan Reland in 1708. Among all Austronesian languages, Dahl (1951) demonstrated that Malagasy and Ma'anyan – an East Barito language spoken in Central Kalimantan , Indonesia, on the island of Borneo – were particularly closely related. The language also has apparent influence from early Old Malay . Furthermore, there appears to be a Bantu influence or substratum in Malagasy phonotactics (Dahl 1988). There are some Sanskrit loanwords in Malagasy, which are said to have been borrowed via Malay and Javanese . Adelaar (1995) suggested that

4370-436: 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

4465-473: 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

4560-497: 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 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

4655-509: The Merina dialect. The Merina dialect is the basis of Standard Malagasy, which is used by the government and media in Madagascar. Standard Malagasy is one of two official languages of Madagascar alongside French, in the 2010 constitution of the Fourth Republic of Madagascar. Malagasy is written in the Latin script introduced by Western missionaries in the early 19th century. Previously, the Sorabe script

4750-585: The Moon , near the swamp whence the Nile was said to also have its source. Ptolemy also mentions another Greek captain, called Theophilos, who took twenty days to travel from the Horn of Africa to Rhapta. Rhapta is also mentioned by Stephanus of Byzantium and Cosmas Indicopleustes . Stephanus of Byzantium and Ptolemy write that Rhapta was a metropolis of Barbaria ( Ancient Greek : Βαρβαρίας ). According to Huntingford , it

4845-584: The Protestant London Missionary Society to establish schools and churches. The first book to be printed in Malagasy using Latin characters was the Bible , which was translated into Malagasy in 1835 by British Protestant missionaries working in the highlands area of Madagascar. The current Malagasy alphabet consists of 21 letters: a, b, d, e, f, g, h, i, j, k, l, m, n, o, p, r, s, t, v, y, z. The orthography maps rather straightforwardly to

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4940-496: The Southeast Barito languages , and the Ma'anyan language is its closest relative, with numerous Malay and Javanese loanwords. It is known that Ma'anyan people were brought as labourers and slaves by Malay and Javanese people in their trading fleets, which reached Madagascar by c.  50 –500 AD. Later, c.  1000 , the original Austronesian settlers mixed with Bantus and Arabs , amongst others. There

5035-455: 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

5130-560: The Swahili Coast in antiquity. Evidence for contacts and trade between this part of Africa and the Roman and Persian worlds is mainly recorded in the limited written records." In recent years, professor Felix Chami has found archaeological evidence for extensive Roman trade on Mafia Island and, not far away, on the mainland, near the mouth of the Rufiji River, which he dated to the first few centuries CE. Which goods were traded at Rhapta

5225-422: 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

5320-472: 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

5415-403: 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 is not known." Not much positive evidence is known on the subject of Ptolemy's ancestry, apart from what can be drawn from

5510-506: 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,

5605-734: 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

5700-402: 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

5795-469: 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

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5890-543: 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 the Wise, who composed the book of the Almagest ". Abu Ma'shar recorded a belief that a different member of this royal line "composed

5985-425: 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

6080-419: 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,

6175-539: The following ways: After a stressed syllable, as at the end of most words and in the final two syllables of some, /a, u, i/ are reduced to [ə, ʷ, ʲ] . ( /i/ is spelled ⟨y⟩ in such cases, though in monosyllabic words like ny and vy , ⟨y⟩ is pronounced as a full [i] .) Final /a/ , and sometimes final syllables, are devoiced at the end of an utterance . /e/ and /o/ are never reduced or devoiced. The large number of reduced vowels, and their effect on neighbouring consonants, give Malagasy

6270-418: 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: Malagasy language Malagasy ( / ˌ m æ l ə ˈ ɡ æ s i / MAL -ə- GASS -ee ; Malagasy pronunciation: [malaˈɡasʲ] ; Sorabe : مَلَغَسِ )

6365-553: 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

6460-599: 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

6555-412: The latter when followed by unstressed /i/ : Thus French malgache [malɡaʃ] 'Malagasy'. The velars /k ɡ ᵑk ᵑɡ h/ are palatalized after /i/ (e.g. alika /alikʲa/ 'dog'). /h/ is frequently elided in casual speech. The reported postalveolar trilled affricates /ʈʳ ᶯʈʳ ɖʳ ᶯɖʳ/ are sometimes simple stops, [ʈ ᶯʈ ɖ ᶯɖ] , but they often have a rhotic release, [ʈɽ̊˔ ᶯʈɽ̊˔ ɖɽ˔ ᶯɖɽ˔] . It

6650-500: 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

6745-555: 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

6840-477: 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

6935-461: 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

7030-528: The penultimate syllable, unless the word ends in ka , tra and often na , in which case they are stressed on the antepenultimate syllable. Secondary stresses exist in even-numbered syllables from the last stressed syllable, when the word has more than four syllables ( fàmantàranàndro [ˌfamˌtarˈnandʐʷ] "watch, clock"). Neither prefixation nor suffixation affect the placement of stress. In many dialects, unstressed vowels (except /e/ ) are devoiced, and in some cases almost completely elided ; thus fanòrona

7125-480: The phonemic inventory. The letters i and y both represent the /i/ sound ( y is used word-finally, and i elsewhere), while o is pronounced /u/ . The affricates /ʈʂ/ and /ɖʐ/ are written tr and dr , respectively, while /ts/ and /dz/ are written ts and j . The letter h is often silent. All other letters have essentially their IPA values. The letters c, q, u, w and x are all not used in native Malagasy words. Mp and occasionally nt may begin

7220-401: 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

7315-486: 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

7410-405: 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

7505-512: The southeast area of Madagascar in the 15th century. The first bilingual renderings of religious texts are those by Étienne de Flacourt , who also published the first dictionary of the language. Radama I , the first literate representative of the Merina monarchy , though extensively versed in the Arabico-Malagasy tradition, opted in 1823 for a Latin system derived by David Jones and invited

7600-474: 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

7695-451: 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

7790-440: 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

7885-517: 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

7980-415: The subjects of history and Malagasy language. There are two principal dialects of Malagasy: Eastern (including Merina ) and Western (including Sakalava ), with the isogloss running down the spine of the island, the south being western, and the central plateau and much of the north (apart from the very tip) being eastern. Ethnologue encodes 12 variants of Malagasy as distinct languages. They have about

8075-496: 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

8170-573: 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

8265-472: The vocabulary of Malagasy also contains many words that are of South Sulawesi origin. Further evidence for this suggestion was presented by Blench (2018). Malagasy is the demonym of Madagascar , from which it is taken to refer to the people of Madagascar in addition to their language. Madagascar was first settled by Austronesian peoples from Maritime Southeast Asia from the Sunda Islands ( Malay archipelago ). As for their route, one possibility

8360-505: The well-documented cultural links between Indonesia and East Africa (e.g., the Malagasy language is related to Malay , both people use double outrigger canoes ). He then posits that the use of monsoons began far earlier than previously thought, allowing traders to bring their spices westward perhaps as early as the 2nd millennium BC . It is possible that both the account of the Periplus and at least part of Miller's theory are correct, for

8455-461: 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 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

8550-431: 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 was his astronomical treatise now known as the Almagest , originally entitled Mathematical Treatise ( Greek : Μαθηματικὴ Σύνταξις , Mathēmatikḗ Syntaxis ). The second

8645-614: 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 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

8740-451: Was named Rhapta (meaning sewn in Greek), due to the sewed boats (ῥαπτῶν πλοιαρίων) which were used there. G.W.B. Huntingford lists five proposed locations for Rhapta: Huntingford dismisses the first two as being too close to Zanzibar and Pemba islands (which he identifies with Menouthis, and follows the author of the Periplus in locating Menouthis north of Rhapta). He observes that there

8835-464: 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

8930-623: Was used, a local development of the Arabic script . The Malagasy language is the westernmost member of the Malayo-Polynesian branch of the Austronesian language family , a grouping that includes languages from Indonesia , Malaysia , the Philippines and the Pacific Islands . In fact, Malagasy's relation with other Austronesian languages had already been noted by early scholars, such as

9025-499: 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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