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157-444: 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
314-494: 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
471-537: 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
628-603: A synonym (a metonym ) for poetry. Poetry has a long and varied history , evolving differentially across the globe. It dates back at least to prehistoric times with hunting poetry in Africa and to panegyric and elegiac court poetry of the empires of the Nile , Niger , and Volta River valleys. Some of the earliest written poetry in Africa occurs among the Pyramid Texts written during
785-400: A characteristic metrical foot and the number of feet per line. The number of metrical feet in a line are described using Greek terminology: tetrameter for four feet and hexameter for six feet, for example. Thus, " iambic pentameter " is a meter comprising five feet per line, in which the predominant kind of foot is the " iamb ". This metric system originated in ancient Greek poetry , and
942-435: A common meter alone. Other poems may be organized into verse paragraphs , in which regular rhymes with established rhythms are not used, but the poetic tone is instead established by a collection of rhythms, alliterations, and rhymes established in paragraph form. Many medieval poems were written in verse paragraphs, even where regular rhymes and rhythms were used. In many forms of poetry, stanzas are interlocking, so that
1099-671: 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
1256-545: A critique of poetic tradition, testing the principle of euphony itself or altogether forgoing rhyme or set rhythm. Poets – as, from the Greek , "makers" of language – have contributed to the evolution of the linguistic, expressive, and utilitarian qualities of their languages. In an increasingly globalized world, poets often adapt forms, styles, and techniques from diverse cultures and languages. A Western cultural tradition (extending at least from Homer to Rilke ) associates
1413-572: A definition that could encompass formal differences as great as those between Chaucer's Canterbury Tales and Matsuo Bashō 's Oku no Hosomichi , as well as differences in content spanning Tanakh religious poetry , love poetry, and rap . Until recently, the earliest examples of stressed poetry had been thought to be works composed by Romanos the Melodist ( fl. 6th century CE). However, Tim Whitmarsh writes that an inscribed Greek poem predated Romanos' stressed poetry. Classical thinkers in
1570-460: 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
1727-722: A given foot or line and to avoid boring repetition. For example, the stress in a foot may be inverted, a caesura (or pause) may be added (sometimes in place of a foot or stress), or the final foot in a line may be given a feminine ending to soften it or be replaced by a spondee to emphasize it and create a hard stop. Some patterns (such as iambic pentameter) tend to be fairly regular, while other patterns, such as dactylic hexameter, tend to be highly irregular. Regularity can vary between language. In addition, different patterns often develop distinctively in different languages, so that, for example, iambic tetrameter in Russian will generally reflect
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#17328456943551884-401: A key part of their structure, so that the metrical pattern determines when the listener expects instances of alliteration to occur. This can be compared to an ornamental use of alliteration in most Modern European poetry, where alliterative patterns are not formal or carried through full stanzas. Alliteration is particularly useful in languages with less rich rhyming structures. Assonance, where
2041-472: A lack of contemporaneous evidence. Several theories exist about what Hellenic dialect groups may have existed between 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
2198-419: A lesser degree. Pamphylian Greek , spoken in a small area on the southwestern coast of Anatolia and little preserved in inscriptions, may be either 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
2355-416: A meaning separate from the repetitive sound patterns created. For example, Chaucer used heavy alliteration to mock Old English verse and to paint a character as archaic. Rhyme consists of identical ("hard-rhyme") or similar ("soft-rhyme") sounds placed at the ends of lines or at locations within lines (" internal rhyme "). Languages vary in the richness of their rhyming structures; Italian, for example, has
2512-501: 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
2669-669: A number of poets, including William Shakespeare and Henry Wadsworth Longfellow , respectively. The most common metrical feet in English are: There are a wide range of names for other types of feet, right up to a choriamb , a four syllable metric foot with a stressed syllable followed by two unstressed syllables and closing with a stressed syllable. The choriamb is derived from some ancient Greek and Latin poetry . Languages which use vowel length or intonation rather than or in addition to syllabic accents in determining meter, such as Ottoman Turkish or Vedic , often have concepts similar to
2826-436: 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
2983-543: 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
3140-420: A process known as lineation . These lines may be based on the number of metrical feet or may emphasize a rhyming pattern at the ends of lines. Lines may serve other functions, particularly where the poem is not written in a formal metrical pattern. Lines can separate, compare or contrast thoughts expressed in different units, or can highlight a change in tone. See the article on line breaks for information about
3297-473: A regularity in the use of accents to reinforce the meter, which does not occur, or occurs to a much lesser extent, in English. Some common metrical patterns, with notable examples of poets and poems who use them, include: Rhyme, alliteration, assonance and consonance are ways of creating repetitive patterns of sound. They may be used as an independent structural element in a poem, to reinforce rhythmic patterns, or as an ornamental element. They can also carry
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#17328456943553454-693: A resonance between otherwise disparate images—a layering of meanings, forming connections previously not perceived. Kindred forms of resonance may exist, between individual verses , in their patterns of rhyme or rhythm. Some poetry types are unique to particular cultures and genres and respond to characteristics of the language in which the poet writes. Readers accustomed to identifying poetry with Dante , Goethe , Mickiewicz , or Rumi may think of it as written in lines based on rhyme and regular meter . There are, however, traditions, such as Biblical poetry and alliterative verse , that use other means to create rhythm and euphony . Much modern poetry reflects
3611-430: A rich rhyming structure permitting maintenance of a limited set of rhymes throughout a lengthy poem. The richness results from word endings that follow regular forms. English, with its irregular word endings adopted from other languages, is less rich in rhyme. The degree of richness of a language's rhyming structures plays a substantial role in determining what poetic forms are commonly used in that language. Alliteration
3768-414: A sentence without putting the sound only at the front of a word. Consonance provokes a more subtle effect than alliteration and so is less useful as a structural element. In many languages, including Arabic and modern European languages, poets use rhyme in set patterns as a structural element for specific poetic forms, such as ballads , sonnets and rhyming couplets . However, the use of structural rhyme
3925-468: A series of more subtle, more flexible prosodic elements. Thus poetry remains, in all its styles, distinguished from prose by form; some regard for basic formal structures of poetry will be found in all varieties of free verse, however much such structures may appear to have been ignored. Similarly, in the best poetry written in classic styles there will be departures from strict form for emphasis or effect. Among major structural elements used in poetry are
4082-498: 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
4239-532: 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
4396-523: 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
4553-449: 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
4710-510: 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
4867-487: A wider sense. There were several regional dialects of Ancient Greek; Attic Greek developed into Koine. Ancient Greek 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
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5024-485: 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,
5181-556: Is a literary form of Archaic Greek (derived primarily from Ionic and Aeolic) used in 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
5338-418: 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
5495-399: 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
5652-404: Is an attempt to render the beautiful or sublime without the burden of engaging the logical or narrative thought-process. English Romantic poet John Keats termed this escape from logic " negative capability ". This "romantic" approach views form as a key element of successful poetry because form is abstract and distinct from the underlying notional logic. This approach remained influential into
5809-644: Is called 'East Greek'. Arcadocypriot apparently descended more closely from the Mycenaean Greek of the Bronze Age. Boeotian Greek had come under 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
5966-457: Is called a poem and is written by a poet . Poets use a variety of techniques called poetic devices, such as assonance , alliteration , euphony and cacophony , onomatopoeia , rhythm (via metre ), and sound symbolism , to produce musical or other artistic effects. Most written poems are formatted in verse : a series or stack of lines on a page, which follow a rhythmic or other deliberate structure. For this reason, verse has also become
6123-448: 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
6280-588: Is considered to be one of the official Confucian classics . His remarks on the subject have become an invaluable source in ancient music theory . The efforts of ancient thinkers to determine what makes poetry distinctive as a form, and what distinguishes good poetry from bad, resulted in " poetics "—the study of the aesthetics of poetry. Some ancient societies, such as China's through the Shijing , developed canons of poetic works that had ritual as well as aesthetic importance. More recently, thinkers have struggled to find
6437-424: 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
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6594-512: 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
6751-451: Is most often founded on the pattern of stressed and unstressed syllables (alone or elided ). In the classical languages , on the other hand, while the metrical units are similar, vowel length rather than stresses define the meter. Old English poetry used a metrical pattern involving varied numbers of syllables but a fixed number of strong stresses in each line. The chief device of ancient Hebrew Biblical poetry , including many of
6908-622: Is not universal even within the European tradition. Much modern poetry avoids traditional rhyme schemes . Classical Greek and Latin poetry did not use rhyme. Rhyme entered European poetry in the High Middle Ages , due to the influence of the Arabic language in Al Andalus . Arabic language poets used rhyme extensively not only with the development of literary Arabic in the sixth century , but also with
7065-522: Is perceived. Languages can rely on either pitch or tone. Some languages with a pitch accent are Vedic Sanskrit or Ancient Greek. Tonal languages include Chinese, Vietnamese and most Subsaharan languages . Metrical rhythm generally involves precise arrangements of stresses or syllables into repeated patterns called feet within a line. In Modern English verse the pattern of stresses primarily differentiate feet, so rhythm based on meter in Modern English
7222-411: 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
7379-526: 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
7536-409: Is the repetition of letters or letter-sounds at the beginning of two or more words immediately succeeding each other, or at short intervals; or the recurrence of the same letter in accented parts of words. Alliteration and assonance played a key role in structuring early Germanic, Norse and Old English forms of poetry. The alliterative patterns of early Germanic poetry interweave meter and alliteration as
7693-407: Is the speaker, not the poet, who is the killer (unless this "confession" is a form of metaphor which needs to be considered in closer context – via close reading ). Some scholars believe that the art of poetry may predate literacy , and developed from folk epics and other oral genres. Others, however, suggest that poetry did not necessarily predate writing. The oldest surviving epic poem,
7850-484: 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
8007-573: The Epic of Gilgamesh , dates from the 3rd millennium BCE in Sumer (in Mesopotamia , present-day Iraq ), and was written in cuneiform script on clay tablets and, later, on papyrus . The Istanbul tablet#2461 , dating to c. 2000 BCE, describes an annual rite in which the king symbolically married and mated with the goddess Inanna to ensure fertility and prosperity; some have labelled it
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#17328456943558164-473: 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
8321-532: 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
8478-658: 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
8635-537: 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 , and Koine may be classified as Ancient Greek in
8792-698: The Greek region of Macedonia during the last decades has brought to light documents, among which the first texts written in Macedonian , such as 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
8949-699: The Tamil language , had rigid grammars (to the point that they could be expressed as a context-free grammar ) which ensured a rhythm. Classical Chinese poetics , based on the tone system of Middle Chinese , recognized two kinds of tones: the level (平 píng ) tone and the oblique (仄 zè ) tones, a category consisting of the rising (上 sháng ) tone, the departing (去 qù ) tone and the entering (入 rù ) tone. Certain forms of poetry placed constraints on which syllables were required to be level and which oblique. The formal patterns of meter used in Modern English verse to create rhythm no longer dominate contemporary English poetry. In
9106-587: The West employed classification as a way to define and assess the quality of poetry. Notably, the existing fragments of Aristotle 's Poetics describe three genres of poetry—the epic, the comic, and the tragic—and develop rules to distinguish the highest-quality poetry in each genre, based on the perceived underlying purposes of the genre. Later aestheticians identified three major genres: epic poetry, lyric poetry , and dramatic poetry , treating comedy and tragedy as subgenres of dramatic poetry. Aristotle's work
9263-570: 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
9420-501: 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)
9577-519: The psalms , was parallelism , a rhetorical structure in which successive lines reflected each other in grammatical structure, sound structure, notional content, or all three. Parallelism lent itself to antiphonal or call-and-response performance, which could also be reinforced by intonation . Thus, Biblical poetry relies much less on metrical feet to create rhythm, but instead creates rhythm based on much larger sound units of lines, phrases and sentences. Some classical poetry forms, such as Venpa of
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#17328456943559734-608: The scanning of poetic lines to show meter. The methods for creating poetic rhythm vary across languages and between poetic traditions. Languages are often described as having timing set primarily by accents , syllables , or moras , depending on how rhythm is established, although a language can be influenced by multiple approaches. Japanese is a mora -timed language. Latin , Catalan , French , Leonese , Galician and Spanish are called syllable-timed languages. Stress-timed languages include English , Russian and, generally, German . Varying intonation also affects how rhythm
9891-437: The "a-bc" convention, such as the ottava rima and terza rima . The types and use of differing rhyming schemes are discussed further in the main article . Poetic form is more flexible in modernist and post-modernist poetry and continues to be less structured than in previous literary eras. Many modern poets eschew recognizable structures or forms and write in free verse . Free verse is, however, not "formless" but composed of
10048-623: The "father of astronomy", a title conferred on him by Jean Baptiste Joseph Delambre in 1817. Hipparchus was born in Nicaea ( Ancient 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)
10205-514: The 20th century. During the 18th and 19th centuries, there was also substantially more interaction among the various poetic traditions, in part due to the spread of European colonialism and the attendant rise in global trade. In addition to a boom in translation , during the Romantic period numerous ancient works were rediscovered. Some 20th-century literary theorists rely less on the ostensible opposition of prose and poetry, instead focusing on
10362-805: The 25th century BCE. The earliest surviving Western Asian epic poem , the Epic of Gilgamesh , was written in the Sumerian language . Early poems in the Eurasian continent evolved from folk songs such as the Chinese Shijing as well as from religious hymns (the Sanskrit Rigveda , the Zoroastrian Gathas , the Hurrian songs , and the Hebrew Psalms ); or from a need to retell oral epics, as with
10519-476: 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
10676-1031: 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"):
10833-490: 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
10990-696: 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, Poem Poetry (from the Greek word poiesis , "making") is a form of literary art that uses aesthetic and often rhythmic qualities of language to evoke meanings in addition to, or in place of, literal or surface-level meanings. Any particular instance of poetry
11147-399: 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
11304-523: The Egyptian Story of Sinuhe , Indian epic poetry , and the Homeric epics, the Iliad and the Odyssey . Ancient Greek attempts to define poetry, such as Aristotle 's Poetics , focused on the uses of speech in rhetoric , drama , song , and comedy . Later attempts concentrated on features such as repetition , verse form , and rhyme , and emphasized aesthetics which distinguish poetry from
11461-528: 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
11618-546: 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
11775-578: 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
11932-578: The Indian Sanskrit -language Rigveda , the Avestan Gathas , the Hurrian songs , and the Hebrew Psalms , possibly developed directly from folk songs . The earliest entries in the oldest extant collection of Chinese poetry , the Classic of Poetry ( Shijing ), were initially lyrics . The Shijing, with its collection of poems and folk songs, was heavily valued by the philosopher Confucius and
12089-409: 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
12246-452: 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
12403-399: 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.,
12560-462: The Sun and the Moon, in the now-lost work On Sizes and Distances ( Ancient 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
12717-564: 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
12874-550: 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
13031-448: 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
13188-419: 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
13345-499: The case of free verse , rhythm is often organized based on looser units of cadence rather than a regular meter. Robinson Jeffers , Marianne Moore , and William Carlos Williams are three notable poets who reject the idea that regular accentual meter is critical to English poetry. Jeffers experimented with sprung rhythm as an alternative to accentual rhythm. In the Western poetic tradition, meters are customarily grouped according to
13502-438: 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 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
13659-466: 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
13816-462: 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
13973-554: The complex cultural web within which a poem is read. Today, throughout the world, poetry often incorporates poetic form and diction from other cultures and from the past, further confounding attempts at definition and classification that once made sense within a tradition such as the Western canon . The early 21st-century poetic tradition appears to continue to strongly orient itself to earlier precursor poetic traditions such as those initiated by Whitman , Emerson , and Wordsworth . The literary critic Geoffrey Hartman (1929–2016) used
14130-455: 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 ),
14287-611: 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
14444-444: The division between lines. Lines of poems are often organized into stanzas , which are denominated by the number of lines included. Thus a collection of two lines is a couplet (or distich ), three lines a triplet (or tercet ), four lines a quatrain , and so on. These lines may or may not relate to each other by rhyme or rhythm. For example, a couplet may be two lines with identical meters which rhyme or two lines held together by
14601-562: 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
14758-465: 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 ( Ancient Greek : Τῶν Ἀράτου καὶ Εὐδόξου φαινομένων ἐξήγησις ). This is a highly critical commentary in the form of two books on
14915-506: The first half of the 20th century coincided with a questioning of the purpose and meaning of traditional definitions of poetry and of distinctions between poetry and prose, particularly given examples of poetic prose and prosaic poetry. Numerous modernist poets have written in non-traditional forms or in what traditionally would have been considered prose, although their writing was generally infused with poetic diction and often with rhythm and tone established by non-metrical means. While there
15072-419: 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
15229-429: 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
15386-418: 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
15543-495: The first, second and fourth lines of a quatrain rhyme with each other and the third line do not rhyme, the quatrain is said to have an AA BA rhyme scheme . This rhyme scheme is the one used, for example, in the rubaiyat form. Similarly, an A BB A quatrain (what is known as " enclosed rhyme ") is used in such forms as the Petrarchan sonnet . Some types of more complicated rhyming schemes have developed names of their own, separate from
15700-457: The format of more objectively-informative, academic, or typical writing, which is known as prose . Poetry uses forms and conventions to suggest differential interpretations of words, or to evoke emotive responses. The use of ambiguity , symbolism , irony , and other stylistic elements of poetic diction often leaves a poem open to multiple interpretations. Similarly, figures of speech such as metaphor , simile , and metonymy establish
15857-440: 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
16014-556: 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 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
16171-472: 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 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
16328-414: The iamb and dactyl to describe common combinations of long and short sounds. Each of these types of feet has a certain "feel," whether alone or in combination with other feet. The iamb, for example, is the most natural form of rhythm in the English language, and generally produces a subtle but stable verse. Scanning meter can often show the basic or fundamental pattern underlying a verse, but does not show
16485-447: 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
16642-450: 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
16799-418: The language. Actual rhythm is significantly more complex than the basic scanned meter described above, and many scholars have sought to develop systems that would scan such complexity. Vladimir Nabokov noted that overlaid on top of the regular pattern of stressed and unstressed syllables in a line of verse was a separate pattern of accents resulting from the natural pitch of the spoken words, and suggested that
16956-448: 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
17113-403: The line, the stanza or verse paragraph , and larger combinations of stanzas or lines such as cantos . Also sometimes used are broader visual presentations of words and calligraphy . These basic units of poetic form are often combined into larger structures, called poetic forms or poetic modes (see the following section), as in the sonnet . Poetry is often separated into lines on a page, in
17270-633: 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
17427-523: The major American verse of the twenty-first century, may yet be seen as what Stevens called 'a great shadow's last embellishment,' the shadow being Emerson's." In the 2020s, advances in artificial intelligence (AI), particularly large language models , enabled the generation of poetry in specific styles and formats. A 2024 study found that AI-generated poems were rated by non-expert readers as more rhythmic, beautiful, and human-like than those written by well-known human authors. This preference may stem from
17584-462: 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
17741-475: 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
17898-399: 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
18055-511: 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
18212-507: The much older oral poetry, as in their long, rhyming qasidas . Some rhyming schemes have become associated with a specific language, culture or period, while other rhyming schemes have achieved use across languages, cultures or time periods. Some forms of poetry carry a consistent and well-defined rhyming scheme, such as the chant royal or the rubaiyat , while other poetic forms have variable rhyme schemes. Most rhyme schemes are described using letters that correspond to sets of rhymes, so if
18369-531: 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
18526-419: 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
18683-499: 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
18840-482: 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
18997-510: 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
19154-411: 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
19311-487: 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
19468-554: 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
19625-564: The phrase "the anxiety of demand" to describe the contemporary response to older poetic traditions as "being fearful that the fact no longer has a form", building on a trope introduced by Emerson. Emerson had maintained that in the debate concerning poetic structure where either "form" or "fact" could predominate, that one need simply "Ask the fact for the form." This has been challenged at various levels by other literary scholars such as Harold Bloom (1930–2019), who has stated: "The generation of poets who stand together now, mature and ready to write
19782-443: The poet as simply one who creates using language, and poetry as what the poet creates. The underlying concept of the poet as creator is not uncommon, and some modernist poets essentially do not distinguish between the creation of a poem with words, and creative acts in other media. Other modernists challenge the very attempt to define poetry as misguided. The rejection of traditional forms and structures for poetry that began in
19939-438: 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
20096-403: 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
20253-438: 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
20410-457: The production of poetry with inspiration – often by a Muse (either classical or contemporary), or through other (often canonised) poets' work which sets some kind of example or challenge. In first-person poems, the lyrics are spoken by an "I", a character who may be termed the speaker , distinct from the poet (the author ). Thus if, for example, a poem asserts, "I killed my enemy in Reno", it
20567-405: 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
20724-463: The relative simplicity and accessibility of AI-generated poetry, which some participants found easier to understand. Prosody is the study of the meter, rhythm , and intonation of a poem. Rhythm and meter are different, although closely related. Meter is the definitive pattern established for a verse (such as iambic pentameter ), while rhythm is the actual sound that results from a line of poetry. Prosody also may be used more specifically to refer to
20881-545: 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
21038-686: 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
21195-420: The rhyming scheme or other structural elements of one stanza determine those of succeeding stanzas. Examples of such interlocking stanzas include, for example, the ghazal and the villanelle , where a refrain (or, in the case of the villanelle, refrains) is established in the first stanza which then repeats in subsequent stanzas. Related to the use of interlocking stanzas is their use to separate thematic parts of
21352-503: 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
21509-417: 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
21666-503: 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
21823-502: 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
21980-473: 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
22137-517: 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
22294-459: 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,
22451-522: The term "scud" be used to distinguish an unaccented stress from an accented stress. Different traditions and genres of poetry tend to use different meters, ranging from the Shakespearean iambic pentameter and the Homeric dactylic hexameter to the anapestic tetrameter used in many nursery rhymes. However, a number of variations to the established meter are common, both to provide emphasis or attention to
22608-421: The use of similar vowel sounds within a word rather than similar sounds at the beginning or end of a word, was widely used in skaldic poetry but goes back to the Homeric epic. Because verbs carry much of the pitch in the English language, assonance can loosely evoke the tonal elements of Chinese poetry and so is useful in translating Chinese poetry. Consonance occurs where a consonant sound is repeated throughout
22765-437: The varying degrees of stress , as well as the differing pitches and lengths of syllables. There is debate over how useful a multiplicity of different "feet" is in describing meter. For example, Robert Pinsky has argued that while dactyls are important in classical verse, English dactylic verse uses dactyls very irregularly and can be better described based on patterns of iambs and anapests, feet which he considers natural to
22922-943: The world's oldest love poem. An example of Egyptian epic poetry is The Story of Sinuhe (c. 1800 BCE). Other ancient epics includes the Greek Iliad and the Odyssey ; the Persian Avestan books (the Yasna ); the Roman national epic , Virgil 's Aeneid (written between 29 and 19 BCE); and the Indian epics , the Ramayana and the Mahabharata . Epic poetry appears to have been composed in poetic form as an aid to memorization and oral transmission in ancient societies. Other forms of poetry, including such ancient collections of religious hymns as
23079-550: 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
23236-475: 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 ,
23393-402: Was a substantial formalist reaction within the modernist schools to the breakdown of structure, this reaction focused as much on the development of new formal structures and syntheses as on the revival of older forms and structures. Postmodernism goes beyond modernism's emphasis on the creative role of the poet, to emphasize the role of the reader of a text ( hermeneutics ), and to highlight
23550-572: 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
23707-822: 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
23864-536: 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
24021-417: 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
24178-404: 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
24335-600: Was influential throughout the Middle East during the Islamic Golden Age , as well as in Europe during the Renaissance . Later poets and aestheticians often distinguished poetry from, and defined it in opposition to prose , which they generally understood as writing with a proclivity to logical explication and a linear narrative structure. This does not imply that poetry is illogical or lacks narration, but rather that poetry
24492-405: 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
24649-416: Was used by poets such as Pindar and Sappho , and by the great tragedians of Athens . Similarly, " dactylic hexameter ", comprises six feet per line, of which the dominant kind of foot is the " dactyl ". Dactylic hexameter was the traditional meter of Greek epic poetry , the earliest extant examples of which are the works of Homer and Hesiod . Iambic pentameter and dactylic hexameter were later used by
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