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91-849: The Pivka is a karst lost river in Slovenia . The river is 27 kilometres (17 mi) in length. The Pivka ends in Planina Cave , where it merges with the Rak River and then the Unica River. The confluence of the Pivka and the Rak is one of the largest subterranean confluences in Europe. The Pivka created Postojna Cave , the longest cave system in Slovenia as well as one of its top tourism sites . This article related to
182-417: A perfect fourth ) and octaves . Ptolemy reviewed standard (and ancient, disused ) musical tuning practice of his day, which he then compared to his own subdivisions of the tetrachord and the octave , which he derived experimentally using a monochord / harmonic canon. The volume ends with a more speculative exposition of the relationships between harmony, the soul ( psyche ), and the planets ( harmony of
273-601: A Roman citizen, but was ethnically either a Greek or at least a Hellenized Egyptian. Astronomy was the subject to which Ptolemy devoted the most time and effort; about half of all the works that survived deal with astronomical matters, and even others such as the Geography and the Tetrabiblos have significant references to astronomy. Ptolemy's Mathēmatikē Syntaxis ( Greek : Μαθηματικὴ Σύνταξις , lit. ' Mathematical Systematic Treatise ' ), better known as
364-470: A coherent mathematical description, which persists to the present as just intonation – the standard for comparison of consonance in the many other, less-than exact but more facile compromise tuning systems. During the Renaissance , Ptolemy's ideas inspired Kepler in his own musings on the harmony of the world ( Harmonice Mundi , Appendix to Book V). The Optica ( Koine Greek : Ὀπτικά ), known as
455-402: A handful of places. Ptolemy's real innovation, however, occurs in the second part of the book, where he provides a catalogue of 8,000 localities he collected from Marinus and others, the biggest such database from antiquity. About 6 300 of these places and geographic features have assigned coordinates so that they can be placed in a grid that spanned the globe. Latitude was measured from
546-492: A long exposition on the relationship between reason and sense perception in corroborating theoretical assumptions. After criticizing the approaches of his predecessors, Ptolemy argues for basing musical intervals on mathematical ratios (as opposed to the ideas advocated by followers of Aristoxenus ), backed up by empirical observation (in contrast to the excessively theoretical approach of the Pythagoreans ). Ptolemy introduces
637-587: A method for specifying the location of the Sun in three pairs of locally oriented coordinate arcs as a function of the declination of the Sun, the terrestrial latitude, and the hour. The key to the approach is to represent the solid configuration in a plane diagram that Ptolemy calls the analemma . In another work, the Phaseis ( Risings of the Fixed Stars ), Ptolemy gave a parapegma , a star calendar or almanac , based on
728-461: A much later pseudepigraphical composition. The identity and date of the actual author of the work, referred to now as Pseudo-Ptolemy , remains the subject of conjecture. Ptolemy wrote a work entitled Harmonikon ( Greek : Ἁρμονικόν ), known as the Harmonics , on music theory and the mathematics behind musical scales in three books. Harmonics begins with a definition of harmonic theory, with
819-457: A pioneer of the study of karst in Slovenia and a fellow of the Royal Society , London, introduced the word karst to European scholars in 1689 to describe the phenomenon of underground flows of rivers in his account of Lake Cerknica . Jovan Cvijić greatly advanced the knowledge of karst regions to the point where he became known as the "father of karst geomorphology". Primarily discussing
910-562: A proper noun, the Slovene form Grast was first attested in 1177. Ultimately, the word is of Mediterranean origin. It has also been suggested that the word may derive from the Proto-Indo-European root karra- 'rock'. The name may also be connected to the oronym Kar(u)sádios oros cited by Ptolemy , and perhaps also to Latin Carusardius . Johann Weikhard von Valvasor ,
1001-459: A river in Slovenia is a stub . You can help Misplaced Pages by expanding it . Karst Karst ( / k ɑːr s t / ) is a topography formed from the dissolution of soluble carbonate rocks such as limestone and dolomite . It is characterized by features like poljes above and drainage systems with sinkholes and caves underground. There is some evidence that karst may occur in more weathering -resistant rocks such as quartzite given
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#17328631610901092-401: A sport than a science and so the underground karst caves and their associated watercourses were, from a scientific perspective, understudied. Karst is most strongly developed in dense carbonate rock , such as limestone, that is thinly bedded and highly fractured . Karst is not typically well developed in chalk , because chalk is highly porous rather than dense, so the flow of groundwater
1183-543: A temple at Canopus , around 146–147 AD, known as the Canobic Inscription . Although the inscription has not survived, someone in the sixth century transcribed it, and manuscript copies preserved it through the Middle Ages. It begins: "To the saviour god, Claudius Ptolemy (dedicates) the first principles and models of astronomy", following by a catalogue of numbers that define a system of celestial mechanics governing
1274-478: A thousand years or more". It was first translated from Arabic into Latin by Plato of Tivoli (Tiburtinus) in 1138, while he was in Spain. Much of the content of the Tetrabiblos was collected from earlier sources; Ptolemy's achievement was to order his material in a systematic way, showing how the subject could, in his view, be rationalized. It is, indeed, presented as the second part of the study of astronomy of which
1365-471: A variety of spatial and temporal scales in karst regions, with the purpose of understanding karst aquifers and ecosystems, and the development of the surface and underground structure, so that the environment can be protected and human activities planned effectively. Ptolemy Claudius Ptolemy ( / ˈ t ɒ l ə m i / ; Ancient Greek : Πτολεμαῖος , Ptolemaios ; Latin : Claudius Ptolemaeus ; c. 100 – c. 170 AD)
1456-553: A view supported by the Stoics. Although mainly known for his contributions to astronomy and other scientific subjects, Ptolemy also engaged in epistemological and psychological discussions across his corpus. He wrote a short essay entitled On the Criterion and Hegemonikon ( Greek : Περὶ Κριτηρίου καὶ Ἡγεμονικοῡ ), which may have been one of his earliest works. Ptolemy deals specifically with how humans obtain scientific knowledge (i.e.,
1547-519: A well in a fracture trace or intersection of fracture traces increases the likelihood to encounter good water production. Voids in karst aquifers can be large enough to cause destructive collapse or subsidence of the ground surface that can initiate a catastrophic release of contaminants. Groundwater flow rate in karst aquifers is much more rapid than in porous aquifers. For example, in the Barton Springs Edwards aquifer, dye traces measured
1638-493: Is a UNESCO World Heritage Site. Many karst-related terms derive from South Slavic languages , entering scientific vocabulary through early research in the Western Balkan Dinaric Alpine karst. The study of the various aspects of karst regions is called karstology. This includes biological, chemical, ecological, geomorphological, hydrogeological, hydrological, political, socio-economical, and other processes over
1729-542: Is a development of karst observed in geological history and preserved within the rock sequence, effectively a fossil karst. There are for example palaeokarst surfaces exposed within the Clydach Valley Subgroup of the Carboniferous Limestone sequence of South Wales which developed as sub-aerial weathering of recently formed limestones took place during periods of non-deposition within the early part of
1820-525: Is a karst landscape which is developed beneath a cover of insoluble rocks. Typically this will involve a cover of sandstone overlying limestone strata undergoing solution. In the United Kingdom for example extensive doline fields have developed at Cefn yr Ystrad , Mynydd Llangatwg and Mynydd Llangynidr in South Wales across a cover of Twrch Sandstone which overlies concealed Carboniferous Limestone ,
1911-572: Is ancestral to the modern system of constellations but, unlike the modern system, they did not cover the whole sky (only what could be seen with the naked eye in the northern hemisphere). For over a thousand years, the Almagest was the authoritative text on astronomy across Europe, the Middle East, and North Africa. The Almagest was preserved, like many extant Greek scientific works, in Arabic manuscripts;
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#17328631610902002-468: Is developed in areas where salt is undergoing solution underground. It can lead to surface depressions and collapses which present a geo-hazard. Karst areas tend to have unique types of forests. The karst terrain is difficult for humans to traverse, so that their ecosystems are often relatively undisturbed. The soil tends to have a high pH, which encourages growth of unusual species of orchids, palms, mangroves, and other plants. Paleokarst or palaeokarst
2093-612: Is frequently unseen until the roof of a cavern suddenly collapses. Such events have swallowed homes, cattle, cars, and farm machinery. In the United States, sudden collapse of such a cavern-sinkhole swallowed part of the collection of the National Corvette Museum in Bowling Green, Kentucky in 2014. The world's largest limestone karst is Australia's Nullarbor Plain . Slovenia has the world's highest risk of sinkholes, while
2184-672: Is his Geographike Hyphegesis ( Greek : Γεωγραφικὴ Ὑφήγησις ; lit. ' Guide to Drawing the Earth ' ), known as the Geography , a handbook on how to draw maps using geographical coordinates for parts of the Roman world known at the time. He relied on previous work by an earlier geographer, Marinus of Tyre , as well as on gazetteers of the Roman and ancient Persian Empire . He also acknowledged ancient astronomer Hipparchus for having provided
2275-407: Is important in petroleum geology because as much as 50% of the world's hydrocarbon reserves are hosted in carbonate rock , and much of this is found in porous karst systems. The English word karst was borrowed from German Karst in the late 19th century, which entered German usage much earlier, to describe a number of geological, geomorphological, and hydrological features found within
2366-399: Is not concentrated along fractures. Karst is also most strongly developed where the water table is relatively low, such as in uplands with entrenched valleys , and where rainfall is moderate to heavy. This contributes to rapid downward movement of groundwater, which promotes dissolution of the bedrock, whereas standing groundwater becomes saturated with carbonate minerals and ceases to dissolve
2457-578: Is of Homeric form . It was common among the Macedonian upper class at the time of Alexander the Great and there were several of this name among Alexander's army, one of whom made himself pharaoh in 323 BC: Ptolemy I Soter , the first pharaoh of the Ptolemaic Kingdom . Almost all subsequent pharaohs of Egypt, with a few exceptions, were named Ptolemy until Egypt became a Roman province in 30 BC, ending
2548-622: Is the Geography , which is a thorough discussion on maps and the geographic knowledge of the Greco-Roman world . The third is the astrological treatise in which he attempted to adapt horoscopic astrology to the Aristotelian natural philosophy of his day. This is sometimes known as the Apotelesmatika ( Greek : Αποτελεσματικά , lit. ' On the Effects ' ) but more commonly known as
2639-611: Is the following: In very rare conditions, oxidation can play a role. Oxidation played a major role in the formation of ancient Lechuguilla Cave in the US state of New Mexico and is presently active in the Frasassi Caves of Italy. The oxidation of sulfides leading to the formation of sulfuric acid can also be one of the corrosion factors in karst formation. As oxygen (O 2 )-rich surface waters seep into deep anoxic karst systems, they bring oxygen, which reacts with sulfide present in
2730-462: The Almagest , is the only surviving comprehensive ancient treatise on astronomy. Although Babylonian astronomers had developed arithmetical techniques for calculating and predicting astronomical phenomena, these were not based on any underlying model of the heavens; early Greek astronomers, on the other hand, provided qualitative geometrical models to "save the appearances" of celestial phenomena without
2821-562: The Tetrábiblos , from the Koine Greek meaning "Four Books", or by its Latin equivalent Quadripartite . The Catholic Church promoted his work, which included the only mathematically sound geocentric model of the Solar System , and unlike most Greek mathematicians , Ptolemy's writings (foremost the Almagest ) never ceased to be copied or commented upon, both in late antiquity and in
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2912-662: The Almagest was the first, concerned with the influences of the celestial bodies in the sublunary sphere . Thus explanations of a sort are provided for the astrological effects of the planets , based upon their combined effects of heating, cooling, moistening, and drying. Ptolemy dismisses other astrological practices, such as considering the numerological significance of names, that he believed to be without sound basis, and leaves out popular topics, such as electional astrology (interpreting astrological charts to determine courses of action) and medical astrology , for similar reasons. The great respect in which later astrologers held
3003-410: The Geography is likely to be of different dates, in addition to containing many scribal errors. However, although the regional and world maps in surviving manuscripts date from c. 1300 AD (after the text was rediscovered by Maximus Planudes ), there are some scholars who think that such maps go back to Ptolemy himself. Ptolemy wrote an astrological treatise, in four parts, known by
3094-645: The Middle Ages . However, it is likely that only a few truly mastered the mathematics necessary to understand his works, as evidenced particularly by the many abridged and watered-down introductions to Ptolemy's astronomy that were popular among the Arabs and Byzantines. His work on epicycles has come to symbolize a very complex theoretical model built in order to explain a false assumption. Ptolemy's date of birth and birthplace are both unknown. The 14th-century astronomer Theodore Meliteniotes wrote that Ptolemy's birthplace
3185-784: The Optics, is a work that survives only in a somewhat poor Latin version, which, in turn, was translated from a lost Arabic version by Eugenius of Palermo ( c. 1154 ). In it, Ptolemy writes about properties of sight (not light), including reflection , refraction , and colour . The work is a significant part of the early history of optics and influenced the more famous and superior 11th-century Book of Optics by Ibn al-Haytham . Ptolemy offered explanations for many phenomena concerning illumination and colour, size, shape, movement, and binocular vision. He also divided illusions into those caused by physical or optical factors and those caused by judgmental factors. He offered an obscure explanation of
3276-457: The Tetrabiblos derived from its nature as an exposition of theory, rather than as a manual. A collection of one hundred aphorisms about astrology called the Centiloquium , ascribed to Ptolemy, was widely reproduced and commented on by Arabic, Latin, and Hebrew scholars, and often bound together in medieval manuscripts after the Tetrabiblos as a kind of summation. It is now believed to be
3367-461: The equator , as it is today, but Ptolemy preferred to express it as climata , the length of the longest day rather than degrees of arc : The length of the midsummer day increases from 12h to 24h as one goes from the equator to the polar circle . One of the places Ptolemy noted specific coordinates for was the now-lost stone tower which marked the midpoint on the ancient Silk Road , and which scholars have been trying to locate ever since. In
3458-519: The harmonic canon (Greek name) or monochord (Latin name), which is an experimental musical apparatus that he used to measure relative pitches, and used to describe to his readers how to demonstrate the relations discussed in the following chapters for themselves. After the early exposition on to build and use monochord to test proposed tuning systems, Ptolemy proceeds to discuss Pythagorean tuning (and how to demonstrate that their idealized musical scale fails in practice). The Pythagoreans believed that
3549-626: The range of the Dinaric Alps , stretching from the northeastern corner of Italy above the city of Trieste , across the Balkan peninsula along the coast of the eastern Adriatic to Kosovo and North Macedonia , where the massif of the Šar Mountains begins. The karst zone is at the northwesternmost section, described in early topographical research as a plateau between Italy and Slovenia . Languages preserving this form include Italian : Carso , German : Karst , and Albanian : karsti . In
3640-430: The "criterion" of truth), as well as with the nature and structure of the human psyche or soul, particularly its ruling faculty (i.e., the hegemonikon ). Ptolemy argues that, to arrive at the truth, one should use both reason and sense perception in ways that complement each other. On the Criterion is also noteworthy for being the only one of Ptolemy's works that is devoid of mathematics . Elsewhere, Ptolemy affirms
3731-485: The French astronomer Delambre in the early 1800s which were repeated by R.R. Newton. Specifically, it proved Hipparchus was not the sole source of Ptolemy's catalog, as they both had claimed, and proved that Ptolemy did not simply copy Hipparchus' measurements and adjust them to account for precession of the equinoxes, as they had claimed. Scientists analyzing the charts concluded: It also confirms that Ptolemy’s Star Catalogue
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3822-473: The Greek term Tetrabiblos (lit. "Four Books") or by its Latin equivalent Quadripartitum . Its original title is unknown, but may have been a term found in some Greek manuscripts, Apotelesmatiká ( biblía ), roughly meaning "(books) on the Effects" or "Outcomes", or "Prognostics". As a source of reference, the Tetrabiblos is said to have "enjoyed almost the authority of a Bible among the astrological writers of
3913-497: The Macedonian family's rule. The name Claudius is a Roman name, belonging to the gens Claudia ; the peculiar multipart form of the whole name Claudius Ptolemaeus is a Roman custom, characteristic of Roman citizens. This indicates that Ptolemy would have been a Roman citizen . Gerald Toomer, the translator of Ptolemy's Almagest into English, suggests that citizenship was probably granted to one of Ptolemy's ancestors by either
4004-455: The Sun or Moon illusion (the enlarged apparent size on the horizon) based on the difficulty of looking upwards. The work is divided into three major sections. The first section (Book II) deals with direct vision from first principles and ends with a discussion of binocular vision. The second section (Books III-IV) treats reflection in plane, convex, concave, and compound mirrors. The last section (Book V) deals with refraction and includes
4095-422: The ability to make any predictions. The earliest person who attempted to merge these two approaches was Hipparchus , who produced geometric models that not only reflected the arrangement of the planets and stars but could be used to calculate celestial motions. Ptolemy, following Hipparchus, derived each of his geometrical models for the Sun, Moon, and the planets from selected astronomical observations done in
4186-472: The appearances and disappearances of stars over the course of the solar year. The Planisphaerium ( Greek : Ἅπλωσις ἐπιφανείας σφαίρας , lit. ' Flattening of the sphere ' ) contains 16 propositions dealing with the projection of the celestial circles onto a plane. The text is lost in Greek (except for a fragment) and survives in Arabic and Latin only. Ptolemy also erected an inscription in
4277-511: The bedrock. The carbonic acid that causes karst features is formed as rain passes through Earth's atmosphere picking up carbon dioxide (CO 2 ), which readily dissolves in the water. Once the rain reaches the ground, it may pass through soil that provides additional CO 2 produced by soil respiration . Some of the dissolved carbon dioxide reacts with the water to form a weak carbonic acid solution, which dissolves calcium carbonate . The primary reaction sequence in limestone dissolution
4368-403: The book on astrology and attributed it to Ptolemy". Historical confusion on this point can be inferred from Abu Ma'shar's subsequent remark: "It is sometimes said that the very learned man who wrote the book of astrology also wrote the book of the Almagest . The correct answer is not known." Not much positive evidence is known on the subject of Ptolemy's ancestry, apart from what can be drawn from
4459-450: The complexity of karst aquifers, and need to be supplemented with dye traces , measurement of spring discharges, and analysis of water chemistry. U.S. Geological Survey dye tracing has determined that conventional groundwater models that assume a uniform distribution of porosity are not applicable for karst aquifers. Linear alignment of surface features such as straight stream segments and sinkholes develop along fracture traces . Locating
4550-506: The data needed to compute the positions of the Sun, Moon and planets, the rising and setting of the stars, and eclipses of the Sun and Moon, making it a useful tool for astronomers and astrologers. The tables themselves are known through Theon of Alexandria 's version. Although Ptolemy's Handy Tables do not survive as such in Arabic or in Latin, they represent the prototype of most Arabic and Latin astronomical tables or zījes . Additionally,
4641-734: The details of his name, although modern scholars have concluded that Abu Ma'shar's account is erroneous. It is no longer doubted that the astronomer who wrote the Almagest also wrote the Tetrabiblos as its astrological counterpart. In later Arabic sources, he was often known as "the Upper Egyptian ", suggesting he may have had origins in southern Egypt . Arabic astronomers , geographers , and physicists referred to his name in Arabic as Baṭlumyus ( Arabic : بَطْلُمْيوس ). Ptolemy wrote in Koine Greek , and can be shown to have used Babylonian astronomical data . He might have been
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#17328631610904732-402: The earliest surviving table of refraction from air to water, for which the values (with the exception of the 60° angle of incidence) show signs of being obtained from an arithmetic progression. However, according to Mark Smith, Ptolemy's table was based in part on real experiments. Ptolemy's theory of vision consisted of rays (or flux) coming from the eye forming a cone, the vertex being within
4823-469: The elevation of the north celestial pole for a few cities. Although maps based on scientific principles had been made since the time of Eratosthenes ( c. 276 – c. 195 BC ), Ptolemy improved on map projections . The first part of the Geography is a discussion of the data and of the methods he used. Ptolemy notes the supremacy of astronomical data over land measurements or travelers' reports, though he possessed these data for only
4914-543: The emperor Claudius or the emperor Nero . The 9th century Persian astronomer Abu Ma'shar al-Balkhi mistakenly presents Ptolemy as a member of Ptolemaic Egypt's royal lineage , stating that the descendants of the Alexandrine general and Pharaoh Ptolemy I Soter were wise "and included Ptolemy the Wise, who composed the book of the Almagest ". Abu Ma'shar recorded a belief that a different member of this royal line "composed
5005-425: The empirical musical relations he identified by testing pitches against each other: He was able to accurately measure relative pitches based on the ratios of vibrating lengths two separate sides of the same single string , hence which were assured to be under equal tension, eliminating one source of error. He analyzed the empirically determined ratios of "pleasant" pairs of pitches, and then synthesised all of them into
5096-419: The eye, and the base defining the visual field. The rays were sensitive, and conveyed information back to the observer's intellect about the distance and orientation of surfaces. Size and shape were determined by the visual angle subtended at the eye combined with perceived distance and orientation. This was one of the early statements of size-distance invariance as a cause of perceptual size and shape constancy,
5187-557: The fissures. The enlarged fissures allow a larger quantity of water to enter which leads to a progressive enlargement of openings. Abundant small openings store a large quantity of water. The larger openings form a conduit system that drains the aquifer to springs. Characterization of karst aquifers requires field exploration to locate sinkholes, swallets , sinking streams , and springs in addition to studying geologic maps . Conventional hydrogeologic methods such as aquifer tests and potentiometric mapping are insufficient to characterize
5278-466: The global demand for drinkable water. Farming in karst areas must take into account the lack of surface water. The soils may be fertile enough, and rainfall may be adequate, but rainwater quickly moves through the crevices into the ground, sometimes leaving the surface soil parched between rains. The karst topography also poses peculiar difficulties for human inhabitants. Sinkholes can develop gradually as surface openings enlarge, but progressive erosion
5369-553: The history of science". One striking error noted by Newton was an autumn equinox said to have been observed by Ptolemy and "measured with the greatest care" at 2pm on 25 September 132, when the equinox should have been observed around 9:55am the day prior. In attempting to disprove Newton, Herbert Lewis also found himself agreeing that "Ptolemy was an outrageous fraud," and that "all those result capable of statistical analysis point beyond question towards fraud and against accidental error". The charges laid by Newton and others have been
5460-599: The introduction to the Handy Tables survived separately from the tables themselves (apparently part of a gathering of some of Ptolemy's shorter writings) under the title Arrangement and Calculation of the Handy Tables . The Planetary Hypotheses ( Greek : Ὑποθέσεις τῶν πλανωμένων , lit. ' Hypotheses of the Planets ' ) is a cosmological work, probably one of the last written by Ptolemy, in two books dealing with
5551-456: The karst groundwater flow rates from 0.5 to 7 miles per day (0.8 to 11.3 km/d). The rapid groundwater flow rates make karst aquifers much more sensitive to groundwater contamination than porous aquifers. Groundwater in karst areas is also just as easily polluted as surface streams, because Karst formations are cavernous and highly permeable, resulting in reduced opportunity for contaminant filtration. Well water may also be unsafe as
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#17328631610905642-525: The karst regions of the Balkans, Cvijić's 1893 publication Das Karstphänomen describes landforms such as karren, dolines and poljes . In a 1918 publication, Cvijić proposed a cyclical model for karst landscape development. Karst hydrology emerged as a discipline in the late 1950s and the early 1960s in France. Previously, the activities of cave explorers, called speleologists , had been dismissed as more of
5733-552: The last-named locality having been declared a site of special scientific interest in respect of it. Kegelkarst is a type of tropical karst terrain with numerous cone-like hills, formed by cockpits, mogotes , and poljes and without strong fluvial erosion processes. This terrain is found in Cuba, Jamaica, Indonesia, Malaysia, the Philippines, Puerto Rico, southern China, Myanmar, Thailand, Laos and Vietnam. Salt karst (or 'halite karst')
5824-412: The local South Slavic languages , all variations of the word are derived from a Romanized Illyrian base (yielding Latin : carsus , Dalmatian : carsus ), later metathesized from the reconstructed form * korsъ into forms such as Slovene : kras and Serbo-Croatian : krš , kras , first attested in the 18th century, and the adjective form kraški in the 16th century. As
5915-500: The mathematics of music should be based on only the one specific ratio of 3:2, the perfect fifth , and believed that tunings mathematically exact to their system would prove to be melodious, if only the extremely large numbers involved could be calculated (by hand). To the contrary, Ptolemy believed that musical scales and tunings should in general involve multiple different ratios arranged to fit together evenly into smaller tetrachords (combinations of four pitch ratios which together make
6006-555: The modern title is thought to be an Arabic corruption of the Greek name Hē Megistē Syntaxis (lit. "The greatest treatise"), as the work was presumably known in Late Antiquity . Because of its reputation, it was widely sought and translated twice into Latin in the 12th century , once in Sicily and again in Spain. Ptolemy's planetary models, like those of the majority of his predecessors, were geocentric and almost universally accepted until
6097-637: The most dramatic of these formations can be seen in Thailand 's Phangnga Bay and at Halong Bay in Vietnam . Calcium carbonate dissolved into water may precipitate out where the water discharges some of its dissolved carbon dioxide. Rivers which emerge from springs may produce tufa terraces, consisting of layers of calcite deposited over extended periods of time. In caves, a variety of features collectively called speleothems are formed by deposition of calcium carbonate and other dissolved minerals. Interstratal karst
6188-477: The motions of the Sun, Moon, planets, and stars. In 2023, archaeologists were able to read a manuscript which gives instructions for the construction of an astronomical tool called a meteoroscope ( μετεωροσκόπιον or μετεωροσκοπεῖον ). The text, which comes from an eighth-century manuscript which also contains Ptolemy's Analemma , was identified on the basis of both its content and linguistic analysis as being by Ptolemy. Ptolemy's second most well-known work
6279-461: The observations were taken at 12:30pm. The overall quality of Ptolemy's observations has been challenged by several modern scientists, but prominently by Robert R. Newton in his 1977 book The Crime of Claudius Ptolemy , which asserted that Ptolemy fabricated many of his observations to fit his theories. Newton accused Ptolemy of systematically inventing data or doctoring the data of earlier astronomers, and labelled him "the most successful fraud in
6370-704: The period. Sedimentation resumed and further limestone strata were deposited on an irregular karst surface, the cycle recurring several times in connection with fluctuating sea levels over prolonged periods. Pseudokarsts are similar in form or appearance to karst features but are created by different mechanisms. Examples include lava caves and granite tors —for example, Labertouche Cave in Victoria, Australia —and paleocollapse features. Mud Caves are an example of pseudokarst. Karst formations have unique hydrology, resulting in many unusual features. A karst fenster (karst window) occurs when an underground stream emerges onto
6461-401: The radius of the sphere of the fixed stars was 20 000 times the radius of the Earth. The work is also notable for having descriptions on how to build instruments to depict the planets and their movements from a geocentric perspective, much as an orrery would have done for a heliocentric one, presumably for didactic purposes. The Analemma is a short treatise where Ptolemy provides
6552-486: The reappearance of heliocentric models during the scientific revolution . Under the scrutiny of modern scholarship, and the cross-checking of observations contained in the Almagest against figures produced through backwards extrapolation, various patterns of errors have emerged within the work. A prominent miscalculation is Ptolemy's use of measurements that he claimed were taken at noon, but which systematically produce readings now shown to be off by half an hour, as if
6643-418: The right conditions. Subterranean drainage may limit surface water, with few to no rivers or lakes. In regions where the dissolved bedrock is covered (perhaps by debris) or confined by one or more superimposed non-soluble rock strata, distinctive karst features may occur only at subsurface levels and can be totally missing above ground. The study of paleokarst (buried karst in the stratigraphic column )
6734-757: The river flows into a cave in a formation known as the Madison Limestone and then rises again 800 m ( 1 ⁄ 2 mi) down the canyon in a placid pool. A turlough is a unique type of seasonal lake found in Irish karst areas which are formed through the annual welling-up of water from the underground water system. Main Article Aquifer#Karst Karst aquifers typically develop in limestone . Surface water containing natural carbonic acid moves down into small fissures in limestone. This carbonic acid gradually dissolves limestone thereby enlarging
6825-405: The secondary literature, while noting that issues with the accuracy of Ptolemy's observations had long been known. Other authors have pointed out that instrument warping or atmospheric refraction may also explain some of Ptolemy's observations at a wrong time. In 2022 the first Greek fragments of Hipparchus' lost star catalog were discovered in a palimpsest and they debunked accusations made by
6916-474: The spanning of more than 800 years; however, many astronomers have for centuries suspected that some of his models' parameters were adopted independently of observations. Ptolemy presented his astronomical models alongside convenient tables, which could be used to compute the future or past position of the planets. The Almagest also contains a star catalogue , which is a version of a catalogue created by Hipparchus . Its list of forty-eight constellations
7007-451: The spheres ). Although Ptolemy's Harmonics never had the influence of his Almagest or Geography , it is nonetheless a well-structured treatise and contains more methodological reflections than any other of his writings. In particular, it is a nascent form of what in the following millennium developed into the scientific method, with specific descriptions of the experimental apparatus that he built and used to test musical conjectures, and
7098-440: The structure of the universe and the laws that govern celestial motion . Ptolemy goes beyond the mathematical models of the Almagest to present a physical realization of the universe as a set of nested spheres, in which he used the epicycles of his planetary model to compute the dimensions of the universe. He estimated the Sun was at an average distance of 1 210 Earth radii (now known to actually be ~23 450 radii), while
7189-517: The subject of wide discussions and received significant push back from other scholars against the findings. Owen Gingerich , while agreeing that the Almagest contains "some remarkably fishy numbers", including in the matter of the 30-hour displaced equinox, which he noted aligned perfectly with predictions made by Hipparchus 278 years earlier, rejected the qualification of fraud. Objections were also raised by Bernard Goldstein , who questioned Newton's findings and suggested that he had misunderstood
7280-496: The supremacy of mathematical knowledge over other forms of knowledge. Like Aristotle before him, Ptolemy classifies mathematics as a type of theoretical philosophy; however, Ptolemy believes mathematics to be superior to theology or metaphysics because the latter are conjectural while only the former can secure certain knowledge. This view is contrary to the Platonic and Aristotelian traditions, where theology or metaphysics occupied
7371-625: The surface between layers of rock, cascades some distance, and then disappears back down, often into a sinkhole. Rivers in karst areas may disappear underground a number of times and spring up again in different places, even under a different name, like Ljubljanica , the "river of seven names". Another example of this is the Popo Agie River in Fremont County, Wyoming , where, at a site named "The Sinks" in Sinks Canyon State Park ,
7462-415: The surface, complex underground drainage systems (such as karst aquifers ) and extensive caves and cavern systems may form. Erosion along limestone shores, notably in the tropics , produces karst topography that includes a sharp makatea surface above the normal reach of the sea, and undercuts that are mostly the result of biological activity or bioerosion at or a little above mean sea level . Some of
7553-1002: The system ( pyrite or hydrogen sulfide ) to form sulfuric acid (H 2 SO 4 ). Sulfuric acid then reacts with calcium carbonate, causing increased erosion within the limestone formation. This chain of reactions is: This reaction chain forms gypsum . The karstification of a landscape may result in a variety of large- or small-scale features both on the surface and beneath. On exposed surfaces, small features may include solution flutes (or rillenkarren), runnels , limestone pavement (clints and grikes), kamenitzas collectively called karren or lapiez. Medium-sized surface features may include sinkholes or cenotes (closed basins), vertical shafts, foibe (inverted funnel shaped sinkholes), disappearing streams, and reappearing springs . Large-scale features may include limestone pavements , poljes , and karst valleys. Mature karst landscapes, where more bedrock has been removed than remains, may result in karst towers , or haystack/eggbox landscapes. Beneath
7644-573: The third part of the Geography , Ptolemy gives instructions on how to create maps both of the whole inhabited world ( oikoumenē ) and of the Roman provinces, including the necessary topographic lists, and captions for the maps. His oikoumenē spanned 180 degrees of longitude from the Blessed Islands in the Atlantic Ocean to the middle of China , and about 80 degrees of latitude from Shetland to anti-Meroe (east coast of Africa ); Ptolemy
7735-461: The water may have run unimpeded from a sinkhole in a cattle pasture, bypassing the normal filtering that occurs in a porous aquifer . Sinkholes have often been used as farmstead or community trash dumps . Overloaded or malfunctioning septic tanks in karst landscapes may dump raw sewage directly into underground channels. Geologists are concerned with these negative effects of human activity on karst hydrology which, as of 2007 , supplied about 25% of
7826-507: The western Highland Rim in the eastern United States is at the second-highest risk of karst sinkholes. In Canada, Wood Buffalo National Park , Northwest Territories contains areas of karst sinkholes. Mexico hosts important karst regions in the Yucatán Peninsula and Chiapas . The West of Ireland is home to The Burren , a karst limestone area. The South China Karst in the provinces of Guizhou , Guangxi , and Yunnan provinces
7917-461: Was Ptolemais Hermiou , a Greek city in the Thebaid region of Egypt (now El Mansha, Sohag Governorate ). This attestation is quite late, however, and there is no evidence to support it. It is known that Ptolemy lived in or around the city of Alexandria , in the Roman province of Egypt under Roman rule . He had a Latin name, Claudius, which is generally taken to imply he was a Roman citizen . He
8008-431: Was an Alexandrian mathematician , astronomer , astrologer , geographer , and music theorist who wrote about a dozen scientific treatises , three of which were important to later Byzantine , Islamic , and Western European science. The first was his astronomical treatise now known as the Almagest , originally entitled Mathematical Treatise ( Greek : Μαθηματικὴ Σύνταξις , Mathēmatikḗ Syntaxis ). The second
8099-614: Was familiar with Greek philosophers and used Babylonian observations and Babylonian lunar theory. In half of his extant works, Ptolemy addresses a certain Syrus, a figure of whom almost nothing is known but who likely shared some of Ptolemy's astronomical interests. Ptolemy died in Alexandria c. 168 . Ptolemy's Greek name , Ptolemaeus ( Πτολεμαῖος , Ptolemaîos ), is an ancient Greek personal name . It occurs once in Greek mythology and
8190-464: Was not based solely on data from Hipparchus’ Catalogue. ... These observations are consistent with the view that Ptolemy composed his star catalogue by combining various sources, including Hipparchus’ catalogue, his own observations and, possibly, those of other authors. The Handy Tables ( Greek : Πρόχειροι κανόνες ) are a set of astronomical tables, together with canons for their use. To facilitate astronomical calculations, Ptolemy tabulated all
8281-499: Was well aware that he knew about only a quarter of the globe, and an erroneous extension of China southward suggests his sources did not reach all the way to the Pacific Ocean. It seems likely that the topographical tables in the second part of the work (Books 2–7) are cumulative texts, which were altered as new knowledge became available in the centuries after Ptolemy. This means that information contained in different parts of
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