139-448: Hipparchus ( / h ɪ ˈ p ɑːr k ə s / ; Greek : Ἵππαρχος , Hípparkhos ; c. 190 – c. 120 BC) was a Greek astronomer , geographer , and mathematician . He is considered the founder of trigonometry , but is most famous for his incidental discovery of the precession of the equinoxes . Hipparchus was born in Nicaea , Bithynia , and probably died on
278-499: A cyclic quadrilateral , today called Ptolemy's theorem because its earliest extant source is a proof in the Almagest (I.10). The stereographic projection was ambiguously attributed to Hipparchus by Synesius (c. 400 AD), and on that basis Hipparchus is often credited with inventing it or at least knowing of it. However, some scholars believe this conclusion to be unjustified by available evidence. The oldest extant description of
417-543: A pitch accent . In Modern Greek, all vowels and consonants are short. Many vowels and diphthongs once pronounced distinctly are pronounced as /i/ ( iotacism ). Some of the stops and glides in diphthongs have become fricatives , and the pitch accent has changed to a stress accent . Many of the changes took place in the Koine Greek period. The writing system of Modern Greek, however, does not reflect all pronunciation changes. The examples below represent Attic Greek in
556-577: 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,
695-671: A corruption of another value attributed to a Babylonian source: 365 + 1 / 4 + 1 / 144 days (= 365.25694... days = 365 days 6 hours 10 min). It is not clear whether Hipparchus got the value from Babylonian astronomers or calculated by himself. Before Hipparchus, astronomers knew that the lengths of the seasons are not equal. Hipparchus made observations of equinox and solstice, and according to Ptolemy ( Almagest III.4) determined that spring (from spring equinox to summer solstice) lasted 94 1 ⁄ 2 days, and summer (from summer solstice to autumn equinox) 92 + 1 ⁄ 2 days. This
834-460: A difference of approximately one day in approximately 300 years. So he set the length of the tropical year to 365 + 1 ⁄ 4 − 1 ⁄ 300 days (= 365.24666... days = 365 days 5 hours 55 min, which differs from the modern estimate of the value (including earth spin acceleration), in his time of approximately 365.2425 days, an error of approximately 6 min per year, an hour per decade, and ten hours per century. Between
973-558: 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
1112-560: 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
1251-525: A fifth major dialect group, or it is Mycenaean Greek overlaid by Doric, with a non-Greek native influence. Regarding the speech of the ancient Macedonians diverse theories have been put forward, but the epigraphic activity and the archaeological discoveries in the Greek region of Macedonia during the last decades has brought to light documents, among which the first texts written in Macedonian , such as
1390-540: 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
1529-510: A more detailed discussion. Pliny ( Naturalis Historia II.X) tells us that Hipparchus demonstrated that lunar eclipses can occur five months apart, and solar eclipses seven months (instead of the usual six months); and the Sun can be hidden twice in thirty days, but as seen by different nations. Ptolemy discussed this a century later at length in Almagest VI.6. The geometry, and the limits of
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#17327733562781668-436: A popular poem by Aratus based on the work by Eudoxus . Hipparchus also made a list of his major works that apparently mentioned about fourteen books, but which is only known from references by later authors. His famous star catalog was incorporated into the one by Ptolemy and may be almost perfectly reconstructed by subtraction of two and two-thirds degrees from the longitudes of Ptolemy's stars . The first trigonometric table
1807-498: A prefix /e-/, called the augment . This was probably originally a separate word, meaning something like "then", added because tenses in PIE had primarily aspectual meaning. The augment is added to the indicative of the aorist, imperfect, and pluperfect, but not to any of the other forms of the aorist (no other forms of the imperfect and pluperfect exist). The two kinds of augment in Greek are syllabic and quantitative. The syllabic augment
1946-504: A simpler sexagesimal system dividing a circle into 60 parts. Hipparchus also adopted the Babylonian astronomical cubit unit ( Akkadian ammatu , Greek πῆχυς pēchys ) that was equivalent to 2° or 2.5° ('large cubit'). Hipparchus probably compiled a list of Babylonian astronomical observations; Gerald J. Toomer , a historian of astronomy, has suggested that Ptolemy's knowledge of eclipse records and other Babylonian observations in
2085-542: A strong Northwest Greek influence, and can in some respects be considered a transitional dialect, as exemplified in the poems of the Boeotian poet Pindar who wrote in Doric with a small Aeolic admixture. Thessalian likewise had come under Northwest Greek influence, though to a lesser degree. Pamphylian Greek , spoken in a small area on the southwestern coast of Anatolia and little preserved in inscriptions, may be either
2224-540: A table giving the daily motion of the Moon according to the date within a long period. However, the Greeks preferred to think in geometrical models of the sky. At the end of the third century BC, Apollonius of Perga had proposed two models for lunar and planetary motion: Apollonius demonstrated that these two models were in fact mathematically equivalent. However, all this was theory and had not been put to practice. Hipparchus
2363-523: A tight range of only approximately ± 1 ⁄ 2 hour, guaranteeing (after division by 4,267) an estimate of the synodic month correct to one part in order of magnitude 10 million. Hipparchus could confirm his computations by comparing eclipses from his own time (presumably 27 January 141 BC and 26 November 139 BC according to Toomer) with eclipses from Babylonian records 345 years earlier ( Almagest IV.2). Later al-Biruni ( Qanun VII.2.II) and Copernicus ( de revolutionibus IV.4) noted that
2502-453: A triangle formed by the two places and the Moon, and from simple geometry was able to establish a distance of the Moon, expressed in Earth radii. Because the eclipse occurred in the morning, the Moon was not in the meridian , and it has been proposed that as a consequence the distance found by Hipparchus was a lower limit. In any case, according to Pappus, Hipparchus found that the least distance
2641-510: A vowel or /n s r/ ; final stops were lost, as in γάλα "milk", compared with γάλακτος "of milk" (genitive). Ancient Greek of the classical period also differed in both the inventory and distribution of original PIE phonemes due to numerous sound changes, notably the following: The pronunciation of Ancient Greek was very different from that of Modern Greek . Ancient Greek had long and short vowels ; many diphthongs ; double and single consonants; voiced, voiceless, and aspirated stops ; and
2780-485: Is 71 (from this eclipse), and the greatest 83 Earth radii. In the second book, Hipparchus starts from the opposite extreme assumption: he assigns a (minimum) distance to the Sun of 490 Earth radii. This would correspond to a parallax of 7′, which is apparently the greatest parallax that Hipparchus thought would not be noticed (for comparison: the typical resolution of the human eye is about 2′; Tycho Brahe made naked eye observation with an accuracy down to 1′). In this case,
2919-418: Is added to stems beginning with consonants, and simply prefixes e (stems beginning with r , however, add er ). The quantitative augment is added to stems beginning with vowels, and involves lengthening the vowel: Some verbs augment irregularly; the most common variation is e → ei . The irregularity can be explained diachronically by the loss of s between vowels, or that of the letter w , which affected
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#17327733562783058-399: Is also close to an integer number of years (4,267 moons : 4,573 anomalistic periods : 4,630.53 nodal periods : 4,611.98 lunar orbits : 344.996 years : 344.982 solar orbits : 126,007.003 days : 126,351.985 rotations). What was so exceptional and useful about the cycle was that all 345-year-interval eclipse pairs occur slightly more than 126,007 days apart within
3197-804: 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
3336-773: 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
3475-479: 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
3614-448: Is considered by some linguists to have been closely related to Greek . Among Indo-European branches with living descendants, Greek is often argued to have the closest genetic ties with Armenian (see also Graeco-Armenian ) and Indo-Iranian languages (see Graeco-Aryan ). Ancient Greek differs from Proto-Indo-European (PIE) and other Indo-European languages in certain ways. In phonotactics , ancient Greek words could end only in
3753-424: Is consistent with 94 + 1 ⁄ 4 and 92 + 1 ⁄ 2 days, an improvement on the results ( 94 + 1 ⁄ 2 and 92 + 1 ⁄ 2 days) attributed to Hipparchus by Ptolemy. Ptolemy made no change three centuries later, and expressed lengths for the autumn and winter seasons which were already implicit (as shown, e.g., by A. Aaboe ). Hipparchus also undertook to find the distances and sizes of
3892-512: Is inconsistent with a premise of the Sun moving around the Earth in a circle at uniform speed. Hipparchus's solution was to place the Earth not at the center of the Sun's motion, but at some distance from the center. This model described the apparent motion of the Sun fairly well. It is known today that the planets , including the Earth, move in approximate ellipses around the Sun, but this was not discovered until Johannes Kepler published his first two laws of planetary motion in 1609. The value for
4031-411: Is post-Hipparchus so the direction of transmission is not settled by the tablets. Hipparchus was recognized as the first mathematician known to have possessed a trigonometric table , which he needed when computing the eccentricity of the orbits of the Moon and Sun. He tabulated values for the chord function, which for a central angle in a circle gives the length of the straight line segment between
4170-519: 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
4309-475: 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
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4448-763: 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,
4587-650: 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
4726-532: Is the first astronomer known to attempt to determine the relative proportions and actual sizes of these orbits. Hipparchus devised a geometrical method to find the parameters from three positions of the Moon at particular phases of its anomaly. In fact, he did this separately for the eccentric and the epicycle model. Ptolemy describes the details in the Almagest IV.11. Hipparchus used two sets of three lunar eclipse observations that he carefully selected to satisfy
4865-484: Is visible simultaneously on half of the Earth, and the difference in longitude between places can be computed from the difference in local time when the eclipse is observed. His approach would give accurate results if it were correctly carried out but the limitations of timekeeping accuracy in his era made this method impractical. Late in his career (possibly about 135 BC) Hipparchus compiled his star catalog. Scholars have been searching for it for centuries. In 2022, it
5004-473: The Almagest came from a list made by Hipparchus. Hipparchus's use of Babylonian sources has always been known in a general way, because of Ptolemy's statements, but the only text by Hipparchus that survives does not provide sufficient information to decide whether Hipparchus's knowledge (such as his usage of the units cubit and finger, degrees and minutes, or the concept of hour stars) was based on Babylonian practice. However, Franz Xaver Kugler demonstrated that
5143-543: The Almagest . Some claim the table of Hipparchus may have survived in astronomical treatises in India, such as the Surya Siddhanta . Trigonometry was a significant innovation, because it allowed Greek astronomers to solve any triangle, and made it possible to make quantitative astronomical models and predictions using their preferred geometric techniques. Hipparchus must have used a better approximation for π than
5282-679: The Archaic or Epic period ( c. 800–500 BC ), and the Classical period ( c. 500–300 BC ). Ancient Greek was the language of Homer and of fifth-century Athenian historians, playwrights, and philosophers . It has contributed many words to English vocabulary and has been a standard subject of study in educational institutions of the Western world since the Renaissance . This article primarily contains information about
5421-495: 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
5560-606: The Epic and Classical periods of the language, which are the best-attested periods and considered most typical of Ancient Greek. From the Hellenistic period ( c. 300 BC ), Ancient Greek was followed by Koine Greek , which is regarded as a separate historical stage, though its earliest form closely resembles Attic Greek , and its latest form approaches Medieval Greek . There were several regional dialects of Ancient Greek; Attic Greek developed into Koine. Ancient Greek
5699-516: 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
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5838-501: The Pella curse tablet , as Hatzopoulos and other scholars note. Based on the conclusions drawn by several studies and findings such as Pella curse tablet , Emilio Crespo and other scholars suggest that ancient Macedonian was a Northwest Doric dialect , which shares isoglosses with its neighboring Thessalian dialects spoken in northeastern Thessaly . Some have also suggested an Aeolic Greek classification. The Lesbian dialect
5977-570: The eccentricity attributed to Hipparchus by Ptolemy is that the offset is 1 ⁄ 24 of the radius of the orbit (which is a little too large), and the direction of the apogee would be at longitude 65.5° from the vernal equinox . Hipparchus may also have used other sets of observations, which would lead to different values. One of his two eclipse trios' solar longitudes are consistent with his having initially adopted inaccurate lengths for spring and summer of 95 + 3 ⁄ 4 and 91 + 1 ⁄ 4 days. His other triplet of solar positions
6116-603: The epic poems , the Iliad and the Odyssey , and in later poems by other authors. Homeric Greek had significant differences in grammar and pronunciation from Classical Attic and other Classical-era dialects. The origins, early form and development of the Hellenic language family are not well understood because of a lack of contemporaneous evidence. Several theories exist about what Hellenic dialect groups may have existed between
6255-492: 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
6394-501: The present , future , and imperfect are imperfective in aspect; the aorist , present perfect , pluperfect and future perfect are perfective in aspect. Most tenses display all four moods and three voices, although there is no future subjunctive or imperative. Also, there is no imperfect subjunctive, optative or imperative. The infinitives and participles correspond to the finite combinations of tense, aspect, and voice. The indicative of past tenses adds (conceptually, at least)
6533-643: The "father of astronomy", a title conferred on him by Jean Baptiste Joseph Delambre in 1817. Hipparchus was born in Nicaea ( ‹See Tfd› Greek : Νίκαια ), in Bithynia . The exact dates of his life are not known, but Ptolemy attributes astronomical observations to him in the period from 147 to 127 BC, and some of these are stated as made in Rhodes ; earlier observations since 162 BC might also have been made by him. His birth date ( c. 190 BC)
6672-470: 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
6811-482: The 4th century BC and Timocharis and Aristillus in the 3rd century BC already divided the ecliptic in 360 parts (our degrees , Greek: moira) of 60 arcminutes and Hipparchus continued this tradition. It was only in Hipparchus's time (2nd century BC) when this division was introduced (probably by Hipparchus's contemporary Hypsikles) for all circles in mathematics. Eratosthenes (3rd century BC), in contrast, used
6950-1031: The 5th century BC. Ancient pronunciation cannot be reconstructed with certainty, but Greek from the period is well documented, and there is little disagreement among linguists as to the general nature of the sounds that the letters represent. /oː/ raised to [uː] , probably by the 4th century BC. Greek, like all of the older Indo-European languages , is highly inflected. It is highly archaic in its preservation of Proto-Indo-European forms. In ancient Greek, nouns (including proper nouns) have five cases ( nominative , genitive , dative , accusative , and vocative ), three genders ( masculine , feminine , and neuter ), and three numbers (singular, dual , and plural ). Verbs have four moods ( indicative , imperative , subjunctive , and optative ) and three voices (active, middle, and passive ), as well as three persons (first, second, and third) and various other forms. Verbs are conjugated through seven combinations of tenses and aspect (generally simply called "tenses"):
7089-495: The Archaic period of ancient Greek (see Homeric Greek for more details): Μῆνιν ἄειδε, θεά, Πηληϊάδεω Ἀχιλῆος οὐλομένην, ἣ μυρί' Ἀχαιοῖς ἄλγε' ἔθηκε, πολλὰς δ' ἰφθίμους ψυχὰς Ἄϊδι προΐαψεν ἡρώων, αὐτοὺς δὲ ἑλώρια τεῦχε κύνεσσιν οἰωνοῖσί τε πᾶσι· Διὸς δ' ἐτελείετο βουλή· ἐξ οὗ δὴ τὰ πρῶτα διαστήτην ἐρίσαντε Ἀτρεΐδης τε ἄναξ ἀνδρῶν καὶ δῖος Ἀχιλλεύς. The beginning of Apology by Plato exemplifies Attic Greek from
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#17327733562787228-661: The Classical period of ancient Greek. (The second line is the IPA , the third is transliterated into the Latin alphabet using a modern version of the Erasmian scheme .) Ὅτι [hóti Hóti μὲν men mèn ὑμεῖς, hyːmêːs hūmeîs, Greek language Greek ( Modern Greek : Ελληνικά , romanized : Elliniká , [eliniˈka] ; Ancient Greek : Ἑλληνική , romanized : Hellēnikḗ )
7367-545: The Dorians. The Greeks of this period believed there were three major divisions of all Greek people – Dorians, Aeolians, and Ionians (including Athenians), each with their own defining and distinctive dialects. Allowing for their oversight of Arcadian, an obscure mountain dialect, and Cypriot, far from the center of Greek scholarship, this division of people and language is quite similar to the results of modern archaeological-linguistic investigation. One standard formulation for
7506-399: The Earth, but the observer is at the surface—the Moon, Earth and observer form a triangle with a sharp angle that changes all the time. From the size of this parallax, the distance of the Moon as measured in Earth radii can be determined. For the Sun however, there was no observable parallax (we now know that it is about 8.8", several times smaller than the resolution of the unaided eye). In
7645-533: The Geography of Eratosthenes"). It is known to us from Strabo of Amaseia, who in his turn criticised Hipparchus in his own Geographia . Hipparchus apparently made many detailed corrections to the locations and distances mentioned by Eratosthenes. It seems he did not introduce many improvements in methods, but he did propose a means to determine the geographical longitudes of different cities at lunar eclipses (Strabo Geographia 1 January 2012). A lunar eclipse
7784-486: 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
7923-425: 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
8062-495: The Greek language was the Cypriot syllabary (also a descendant of Linear A via the intermediate Cypro-Minoan syllabary ), which is closely related to Linear B but uses somewhat different syllabic conventions to represent phoneme sequences. The Cypriot syllabary is attested in Cyprus from the 11th century BC until its gradual abandonment in the late Classical period, in favor of the standard Greek alphabet. Greek has been written in
8201-629: 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
8340-685: 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
8479-549: The Greek. Prediction of a solar eclipse, i.e., exactly when and where it will be visible, requires a solid lunar theory and proper treatment of the lunar parallax. Hipparchus must have been the first to be able to do this. A rigorous treatment requires spherical trigonometry , thus those who remain certain that Hipparchus lacked it must speculate that he may have made do with planar approximations. He may have discussed these things in Perí tēs katá plátos mēniaías tēs selēnēs kinēseōs ("On
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#17327733562788618-584: The Hellespont and are thought by many to be more likely possibilities for the eclipse Hipparchus used for his computations.) Ptolemy later measured the lunar parallax directly ( Almagest V.13), and used the second method of Hipparchus with lunar eclipses to compute the distance of the Sun ( Almagest V.15). He criticizes Hipparchus for making contradictory assumptions, and obtaining conflicting results ( Almagest V.11): but apparently he failed to understand Hipparchus's strategy to establish limits consistent with
8757-409: The Moon eclipsed while apparently it was not in exact opposition to the Sun. Parallax lowers the altitude of the luminaries; refraction raises them, and from a high point of view the horizon is lowered. Hipparchus and his predecessors used various instruments for astronomical calculations and observations, such as the gnomon , the astrolabe , and the armillary sphere . Hipparchus is credited with
8896-458: The Moon's equation of the center in the Hipparchan model.) Before Hipparchus, Meton , Euctemon , and their pupils at Athens had made a solstice observation (i.e., timed the moment of the summer solstice ) on 27 June 432 BC ( proleptic Julian calendar ). Aristarchus of Samos is said to have done so in 280 BC, and Hipparchus also had an observation by Archimedes . He observed
9035-399: The Sun and Moon with his diopter . Like others before and after him, he found that the Moon's size varies as it moves on its (eccentric) orbit, but he found no perceptible variation in the apparent diameter of the Sun. He found that at the mean distance of the Moon, the Sun and Moon had the same apparent diameter; at that distance, the Moon's diameter fits 650 times into the circle, i.e.,
9174-475: The Sun and the Moon, in the now-lost work On Sizes and Distances ( ‹See Tfd› Greek : Περὶ μεγεθῶν καὶ ἀποστημάτων Peri megethon kai apostematon ). His work is mentioned in Ptolemy's Almagest V.11, and in a commentary thereon by Pappus ; Theon of Smyrna (2nd century) also mentions the work, under the title On Sizes and Distances of the Sun and Moon . Hipparchus measured the apparent diameters of
9313-576: The Sun is on the equator (i.e., in one of the equinoctial points on the ecliptic ), but the shadow falls above or below the opposite side of the ring when the Sun is south or north of the equator. Ptolemy quotes (in Almagest III.1 (H195)) a description by Hipparchus of an equatorial ring in Alexandria; a little further he describes two such instruments present in Alexandria in his own time. Hipparchus applied his knowledge of spherical angles to
9452-404: 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),
9591-402: 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
9730-550: The aorist. Following Homer 's practice, the augment is sometimes not made in poetry , especially epic poetry. The augment sometimes substitutes for reduplication; see below. Almost all forms of the perfect, pluperfect, and future perfect reduplicate the initial syllable of the verb stem. (A few irregular forms of perfect do not reduplicate, whereas a handful of irregular aorists reduplicate.) The three types of reduplication are: Irregular duplication can be understood diachronically. For example, lambanō (root lab ) has
9869-448: The apparent diameter of the Sun and Moon. Pappus of Alexandria described it (in his commentary on the Almagest of that chapter), as did Proclus ( Hypotyposis IV). It was a four-foot rod with a scale, a sighting hole at one end, and a wedge that could be moved along the rod to exactly obscure the disk of Sun or Moon. Hipparchus also observed solar equinoxes , which may be done with an equatorial ring : its shadow falls on itself when
10008-419: The augment when it was word-initial. In verbs with a preposition as a prefix, the augment is placed not at the start of the word, but between the preposition and the original verb. For example, προσ(-)βάλλω (I attack) goes to προσ έ βαλoν in the aorist. However compound verbs consisting of a prefix that is not a preposition retain the augment at the start of the word: αὐτο(-)μολῶ goes to ηὐ τομόλησα in
10147-466: The change in the length of the day (see ΔT ) we estimate that the error in the assumed length of the synodic month was less than 0.2 second in the fourth century BC and less than 0.1 second in Hipparchus's time. It had been known for a long time that the motion of the Moon is not uniform: its speed varies. This is called its anomaly and it repeats with its own period; the anomalistic month . The Chaldeans took account of this arithmetically, and used
10286-466: The chords for angles with increments of 7.5°. In modern terms, the chord subtended by a central angle in a circle of given radius R equals R times twice the sine of half of the angle, i.e.: The now-lost work in which Hipparchus is said to have developed his chord table, is called Tōn en kuklōi eutheiōn ( Of Lines Inside a Circle ) in Theon of Alexandria 's fourth-century commentary on section I.10 of
10425-455: The constellations, and these are likely to have been based on his own measurements. Ancient Greek Ancient Greek ( Ἑλληνῐκή , Hellēnikḗ ; [hellɛːnikɛ́ː] ) includes the forms of the Greek language used in ancient Greece and the ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: Mycenaean Greek ( c. 1400–1200 BC ), Dark Ages ( c. 1200–800 BC ),
10564-615: The dialect of Sparta ), and Northern Peloponnesus Doric (including Corinthian ). All the groups were represented by colonies beyond Greece proper as well, and these colonies generally developed local characteristics, often under the influence of settlers or neighbors speaking different Greek dialects. After the conquests of Alexander the Great in the late 4th century BC, a new international dialect known as Koine or Common Greek developed, largely based on Attic Greek , but with influence from other dialects. This dialect slowly replaced most of
10703-530: The dialects is: West vs. non-West Greek is the strongest-marked and earliest division, with non-West in subsets of Ionic-Attic (or Attic-Ionic) and Aeolic vs. Arcadocypriot, or Aeolic and Arcado-Cypriot vs. Ionic-Attic. Often non-West is called 'East Greek'. Arcadocypriot apparently descended more closely from the Mycenaean Greek of the Bronze Age. Boeotian Greek had come under
10842-510: The divergence of early Greek-like speech from the common Proto-Indo-European language and the Classical period. They have the same general outline but differ in some of the detail. The only attested dialect from this period is Mycenaean Greek , but its relationship to the historical dialects and the historical circumstances of the times imply that the overall groups already existed in some form. Scholars assume that major Ancient Greek period dialect groups developed not later than 1120 BC, at
10981-404: 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
11120-618: 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
11259-572: The first book, Hipparchus assumes that the parallax of the Sun is 0, as if it is at infinite distance. He then analyzed a solar eclipse, which Toomer presumes to be the eclipse of 14 March 190 BC. It was total in the region of the Hellespont (and in his birthplace, Nicaea); at the time Toomer proposes the Romans were preparing for war with Antiochus III in the area, and the eclipse is mentioned by Livy in his Ab Urbe Condita Libri VIII.2. It
11398-479: The first century; Ptolemy's second-century Almagest ; and additional references to him in the fourth century by Pappus and Theon of Alexandria in their commentaries on the Almagest . Hipparchus's only preserved work is Commentary on the Phaenomena of Eudoxus and Aratus ( ‹See Tfd› Greek : Τῶν Ἀράτου καὶ Εὐδόξου φαινομένων ἐξήγησις ). This is a highly critical commentary in the form of two books on
11537-419: The first method is very sensitive to the accuracy of the observations and parameters. (In fact, modern calculations show that the size of the 189 BC solar eclipse at Alexandria must have been closer to 9 ⁄ 10 ths and not the reported 4 ⁄ 5 ths, a fraction more closely matched by the degree of totality at Alexandria of eclipses occurring in 310 and 129 BC which were also nearly total in
11676-429: The first surviving text discussing it is by Menelaus of Alexandria in the first century, who now, on that basis, commonly is credited with its discovery. (Previous to the finding of the proofs of Menelaus a century ago, Ptolemy was credited with the invention of spherical trigonometry.) Ptolemy later used spherical trigonometry to compute things such as the rising and setting points of the ecliptic , or to take account of
11815-418: The first to develop a reliable method to predict solar eclipses . His other reputed achievements include the discovery and measurement of Earth's precession, the compilation of the first known comprehensive star catalog from the western world, and possibly the invention of the astrolabe , as well as of the armillary sphere that he may have used in creating the star catalogue. Hipparchus is sometimes called
11954-452: 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
12093-440: The geometry of book 2 it follows that the Sun is at 2,550 Earth radii, and the mean distance of the Moon is 60 + 1 ⁄ 2 radii. Similarly, Cleomedes quotes Hipparchus for the sizes of the Sun and Earth as 1050:1; this leads to a mean lunar distance of 61 radii. Apparently Hipparchus later refined his computations, and derived accurate single values that he could use for predictions of solar eclipses. See Toomer (1974) for
12232-439: 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
12371-447: The invention or improvement of several astronomical instruments, which were used for a long time for naked-eye observations. According to Synesius of Ptolemais (4th century) he made the first astrolabion : this may have been an armillary sphere (which Ptolemy however says he constructed, in Almagest V.1); or the predecessor of the planar instrument called astrolabe (also mentioned by Theon of Alexandria ). With an astrolabe Hipparchus
12510-453: The island of Rhodes , Greece. He is known to have been a working astronomer between 162 and 127 BC. Hipparchus is considered the greatest ancient astronomical observer and, by some, the greatest overall astronomer of antiquity . He was the first whose quantitative and accurate models for the motion of the Sun and Moon survive. For this he certainly made use of the observations and perhaps
12649-448: The large total lunar eclipse of 26 November 139 BC, when over a clean sea horizon as seen from Rhodes, the Moon was eclipsed in the northwest just after the Sun rose in the southeast. This would be the second eclipse of the 345-year interval that Hipparchus used to verify the traditional Babylonian periods: this puts a late date to the development of Hipparchus's lunar theory. We do not know what "exact reason" Hipparchus found for seeing
12788-467: 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
12927-642: The lunar parallax . If he did not use spherical trigonometry, Hipparchus may have used a globe for these tasks, reading values off coordinate grids drawn on it, or he may have made approximations from planar geometry, or perhaps used arithmetical approximations developed by the Chaldeans. Hipparchus also studied the motion of the Moon and confirmed the accurate values for two periods of its motion that Chaldean astronomers are widely presumed to have possessed before him. The traditional value (from Babylonian System B) for
13066-468: The mathematical techniques accumulated over centuries by the Babylonians and by Meton of Athens (fifth century BC), Timocharis , Aristyllus , Aristarchus of Samos , and Eratosthenes , among others. He developed trigonometry and constructed trigonometric tables , and he solved several problems of spherical trigonometry . With his solar and lunar theories and his trigonometry, he may have been
13205-479: The mean synodic month is 29 days; 31,50,8,20 (sexagesimal) = 29.5305941... days. Expressed as 29 days + 12 hours + 793 / 1080 hours this value has been used later in the Hebrew calendar . The Chaldeans also knew that 251 synodic months ≈ 269 anomalistic months . Hipparchus used the multiple of this period by a factor of 17, because that interval is also an eclipse period, and
13344-399: The mean apparent diameters are 360 ⁄ 650 = 0°33′14″. Like others before and after him, he also noticed that the Moon has a noticeable parallax , i.e., that it appears displaced from its calculated position (compared to the Sun or stars ), and the difference is greater when closer to the horizon. He knew that this is because in the then-current models the Moon circles the center of
13483-640: 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
13622-441: 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
13761-515: The monthly motion of the Moon in latitude"), a work mentioned in the Suda . Pliny also remarks that "he also discovered for what exact reason, although the shadow causing the eclipse must from sunrise onward be below the earth, it happened once in the past that the Moon was eclipsed in the west while both luminaries were visible above the earth" (translation H. Rackham (1938), Loeb Classical Library 330 p. 207). Toomer argued that this must refer to
13900-399: 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
14039-536: 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
14178-539: The observation made on Alexandria 's large public equatorial ring that same day (at 1 hour before noon). Ptolemy claims his solar observations were on a transit instrument set in the meridian. At the end of his career, Hipparchus wrote a book entitled Peri eniausíou megéthous ("On the Length of the Year") regarding his results. The established value for the tropical year , introduced by Callippus in or before 330 BC
14317-419: The observations, rather than a single value for the distance. His results were the best so far: the actual mean distance of the Moon is 60.3 Earth radii, within his limits from Hipparchus's second book. Theon of Smyrna wrote that according to Hipparchus, the Sun is 1,880 times the size of the Earth, and the Earth twenty-seven times the size of the Moon; apparently this refers to volumes , not diameters . From
14456-508: The older dialects, although the Doric dialect has survived in the Tsakonian language , which is spoken in the region of modern Sparta. Doric has also passed down its aorist terminations into most verbs of Demotic Greek . By about the 6th century AD, the Koine had slowly metamorphosed into Medieval Greek . Phrygian is an extinct Indo-European language of West and Central Anatolia , which
14595-706: 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
14734-488: The one given by Archimedes of between 3 + 10 ⁄ 71 (≈ 3.1408) and 3 + 1 ⁄ 7 (≈ 3.1429). Perhaps he had the approximation later used by Ptolemy, sexagesimal 3;08,30 (≈ 3.1417) ( Almagest VI.7). Hipparchus could have constructed his chord table using the Pythagorean theorem and a theorem known to Archimedes. He also might have used the relationship between sides and diagonals of
14873-510: The other way around is debatable. Hipparchus also gave the value for the sidereal year to be 365 + 1 / 4 + 1 / 144 days (= 365.25694... days = 365 days 6 hours 10 min). Another value for the sidereal year that is attributed to Hipparchus (by the physician Galen in the second century AD) is 365 + 1 / 4 + 1 / 288 days (= 365.25347... days = 365 days 6 hours 5 min), but this may be
15012-411: The parallax of the Sun decreases (i.e., its distance increases), the minimum limit for the mean distance is 59 Earth radii—exactly the mean distance that Ptolemy later derived. Hipparchus thus had the problematic result that his minimum distance (from book 1) was greater than his maximum mean distance (from book 2). He was intellectually honest about this discrepancy, and probably realized that especially
15151-487: The perfect stem eilēpha (not * lelēpha ) because it was originally slambanō , with perfect seslēpha , becoming eilēpha through compensatory lengthening. Reduplication is also visible in the present tense stems of certain verbs. These stems add a syllable consisting of the root's initial consonant followed by i . A nasal stop appears after the reduplication in some verbs. The earliest extant examples of ancient Greek writing ( c. 1450 BC ) are in
15290-560: The period of 4,267 moons is approximately five minutes longer than the value for the eclipse period that Ptolemy attributes to Hipparchus. However, the timing methods of the Babylonians had an error of no fewer than eight minutes. Modern scholars agree that Hipparchus rounded the eclipse period to the nearest hour, and used it to confirm the validity of the traditional values, rather than to try to derive an improved value from his own observations. From modern ephemerides and taking account of
15429-438: The points where the angle intersects the circle. He may have computed this for a circle with a circumference of 21,600 units and a radius (rounded) of 3,438 units; this circle has a unit length for each arcminute along its perimeter. (This was “proven” by Toomer, but he later “cast doubt“ upon his earlier affirmation. Other authors have argued that a circle of radius 3,600 units may instead have been used by Hipparchus.) He tabulated
15568-403: The positions of Sun and Moon when a solar or lunar eclipse is possible, are explained in Almagest VI.5. Hipparchus apparently made similar calculations. The result that two solar eclipses can occur one month apart is important, because this can not be based on observations: one is visible on the northern and the other on the southern hemisphere—as Pliny indicates—and the latter was inaccessible to
15707-438: The problem of denoting locations on the Earth's surface. Before him a grid system had been used by Dicaearchus of Messana , but Hipparchus was the first to apply mathematical rigor to the determination of the latitude and longitude of places on the Earth. Hipparchus wrote a critique in three books on the work of the geographer Eratosthenes of Cyrene (3rd century BC), called Pròs tèn Eratosthénous geographían ("Against
15846-405: The ratio of the epicycle model ( 3122 + 1 ⁄ 2 : 247 + 1 ⁄ 2 ), which is too small (60 : 4;45 sexagesimal). Ptolemy established a ratio of 60 : 5 + 1 ⁄ 4 . (The maximum angular deviation producible by this geometry is the arcsin of 5 + 1 ⁄ 4 divided by 60, or approximately 5° 1', a figure that is sometimes therefore quoted as the equivalent of
15985-550: The representative figure for astronomy. It is not certain that the figure is meant to represent him. Previously, Eudoxus of Cnidus in the fourth century BC had described the stars and constellations in two books called Phaenomena and Entropon . Aratus wrote a poem called Phaenomena or Arateia based on Eudoxus's work. Hipparchus wrote a commentary on the Arateia —his only preserved work—which contains many stellar positions and times for rising, culmination, and setting of
16124-686: The requirements. The eccentric model he fitted to these eclipses from his Babylonian eclipse list: 22/23 December 383 BC, 18/19 June 382 BC, and 12/13 December 382 BC. The epicycle model he fitted to lunar eclipse observations made in Alexandria at 22 September 201 BC, 19 March 200 BC, and 11 September 200 BC. These figures are due to the cumbersome unit he used in his chord table and may partly be due to some sloppy rounding and calculation errors by Hipparchus, for which Ptolemy criticised him while also making rounding errors. A simpler alternate reconstruction agrees with all four numbers. Hipparchus found inconsistent results; he later used
16263-508: The second and third centuries, coins were made in his honour in Bithynia that bear his name and show him with a globe . Relatively little of Hipparchus's direct work survives into modern times. Although he wrote at least fourteen books, only his commentary on the popular astronomical poem by Aratus was preserved by later copyists. Most of what is known about Hipparchus comes from Strabo 's Geography and Pliny 's Natural History in
16402-417: The shadow of the Earth is a cone rather than a cylinder as under the first assumption. Hipparchus observed (at lunar eclipses) that at the mean distance of the Moon, the diameter of the shadow cone is 2 + 1 ⁄ 2 lunar diameters. That apparent diameter is, as he had observed, 360 ⁄ 650 degrees. With these values and simple geometry, Hipparchus could determine the mean distance; because it
16541-507: The solstice observation of Meton and his own, there were 297 years spanning 108,478 days; this implies a tropical year of 365.24579... days = 365 days;14,44,51 (sexagesimal; = 365 days + 14 / 60 + 44 / 60 + 51 / 60 ), a year length found on one of the few Babylonian clay tablets which explicitly specifies the System B month. Whether Babylonians knew of Hipparchus's work or
16680-512: The stereographic projection is found in Ptolemy 's Planisphere (2nd century AD). Besides geometry, Hipparchus also used arithmetic techniques developed by the Chaldeans . He was one of the first Greek mathematicians to do this and, in this way, expanded the techniques available to astronomers and geographers. There are several indications that Hipparchus knew spherical trigonometry, but
16819-437: 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
16958-473: The summer solstices in 146 and 135 BC both accurately to a few hours, but observations of the moment of equinox were simpler, and he made twenty during his lifetime. Ptolemy gives an extensive discussion of Hipparchus's work on the length of the year in the Almagest III.1, and quotes many observations that Hipparchus made or used, spanning 162–128 BC, including an equinox timing by Hipparchus (at 24 March 146 BC at dawn) that differs by 5 hours from
17097-517: The syllabic script Linear B . Beginning in the 8th century BC, however, the Greek alphabet became standard, albeit with some variation among dialects. Early texts are written in boustrophedon style, but left-to-right became standard during the classic period. Modern editions of ancient Greek texts are usually written with accents and breathing marks , interword spacing , modern punctuation , and sometimes mixed case , but these were all introduced later. The beginning of Homer 's Iliad exemplifies
17236-465: The synodic and anomalistic periods that Ptolemy attributes to Hipparchus had already been used in Babylonian ephemerides , specifically the collection of texts nowadays called "System B" (sometimes attributed to Kidinnu ). Hipparchus's long draconitic lunar period (5,458 months = 5,923 lunar nodal periods) also appears a few times in Babylonian records . But the only such tablet explicitly dated,
17375-467: The time of the Dorian invasions —and that their first appearances as precise alphabetic writing began in the 8th century BC. The invasion would not be "Dorian" unless the invaders had some cultural relationship to the historical Dorians . The invasion is known to have displaced population to the later Attic-Ionic regions, who regarded themselves as descendants of the population displaced by or contending with
17514-555: Was 365 + 1 ⁄ 4 days. Speculating a Babylonian origin for the Callippic year is difficult to defend, since Babylon did not observe solstices thus the only extant System B year length was based on Greek solstices (see below). Hipparchus's equinox observations gave varying results, but he points out (quoted in Almagest III.1(H195)) that the observation errors by him and his predecessors may have been as large as 1 ⁄ 4 day. He used old solstice observations and determined
17653-480: Was Aeolic. For example, fragments of the works of the poet Sappho from the island of Lesbos are in Aeolian. Most of the dialect sub-groups listed above had further subdivisions, generally equivalent to a city-state and its surrounding territory, or to an island. Doric notably had several intermediate divisions as well, into Island Doric (including Cretan Doric ), Southern Peloponnesus Doric (including Laconian ,
17792-452: Was a pluricentric language , divided into many dialects. The main dialect groups are Attic and Ionic , Aeolic , Arcadocypriot , and Doric , many of them with several subdivisions. Some dialects are found in standardized literary forms in literature , while others are attested only in inscriptions. There are also several historical forms. Homeric Greek is a literary form of Archaic Greek (derived primarily from Ionic and Aeolic) used in
17931-574: Was a distinct dialect of Greek itself. Aside from the Macedonian question, current consensus regards Phrygian as the closest relative of Greek, since they share a number of phonological, morphological and lexical isoglosses , with some being exclusive between them. Scholars have proposed a Graeco-Phrygian subgroup out of which Greek and Phrygian originated. Among living languages, some Indo-Europeanists suggest that Greek may be most closely related to Armenian (see Graeco-Armenian ) or
18070-572: Was also observed in Alexandria, where the Sun was reported to be obscured 4/5ths by the Moon. Alexandria and Nicaea are on the same meridian. Alexandria is at about 31° North, and the region of the Hellespont about 40° North. (It has been contended that authors like Strabo and Ptolemy had fairly decent values for these geographical positions, so Hipparchus must have known them too. However, Strabo's Hipparchus dependent latitudes for this region are at least 1° too high, and Ptolemy appears to copy them, placing Byzantium 2° high in latitude.) Hipparchus could draw
18209-568: 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
18348-505: 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
18487-829: Was announced that a part of it was discovered in a medieval parchment manuscript, Codex Climaci Rescriptus , from Saint Catherine's Monastery in the Sinai Peninsula , Egypt as hidden text ( palimpsest ). Hipparchus also constructed a celestial globe depicting the constellations, based on his observations. His interest in the fixed stars may have been inspired by the observation of a supernova (according to Pliny), or by his discovery of precession, according to Ptolemy, who says that Hipparchus could not reconcile his data with earlier observations made by Timocharis and Aristillus . For more information see Discovery of precession . In Raphael 's painting The School of Athens , Hipparchus may be depicted holding his celestial globe, as
18626-541: Was apparently compiled by Hipparchus, who is consequently now known as "the father of trigonometry". Earlier Greek astronomers and mathematicians were influenced by Babylonian astronomy to some extent, for instance the period relations of the Metonic cycle and Saros cycle may have come from Babylonian sources (see " Babylonian astronomical diaries "). Hipparchus seems to have been the first to exploit Babylonian astronomical knowledge and techniques systematically. Eudoxus in
18765-417: Was calculated by Delambre based on clues in his work. Hipparchus must have lived some time after 127 BC because he analyzed and published his observations from that year. Hipparchus obtained information from Alexandria as well as Babylon , but it is not known when or if he visited these places. He is believed to have died on the island of Rhodes, where he seems to have spent most of his later life. In
18904-404: Was computed for a minimum distance of the Sun, it is the maximum mean distance possible for the Moon. With his value for the eccentricity of the orbit, he could compute the least and greatest distances of the Moon too. According to Pappus, he found a least distance of 62, a mean of 67 + 1 ⁄ 3 , and consequently a greatest distance of 72 + 2 ⁄ 3 Earth radii. With this method, as
19043-405: Was the first to be able to measure the geographical latitude and time by observing fixed stars. Previously this was done at daytime by measuring the shadow cast by a gnomon, by recording the length of the longest day of the year or with the portable instrument known as a scaphe . Ptolemy mentions ( Almagest V.14) that he used a similar instrument as Hipparchus, called dioptra , to measure
19182-580: 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
19321-673: 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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