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91-484: Varenius was deeply influenced by the works of classical geographers such as Claudius Ptolemy and Strabo . Ptolemy's Geographia was particularly significant, as it provided a framework for mapping the known world using a coordinate system based on latitude and longitude, and the title of Geographia Generalis intentionally linked it to Ptolemy's text. Varenius aimed to build upon these classical foundations, integrating new discoveries and scientific principles, to create

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

364-805: A bestselling series titled the Respublicae (commonly known as the Republics or Petites Républiques ), the ancestor of the modern travel guide . Each of the thirty-five volumes in the series gave information on the geography, inhabitants, economy, and history of a country in Europe, Asia, Africa, or the Near East. Jean, son of Abraham, born in 1622, had since 1647 been in partnership with his father and uncle at Leiden, and when they died Daniel, son of Bonaventure, born in 1626, joined him. Their partnership did not last more than two years, and after its dissolution Jean carried on

455-470: 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

546-546: A decade of its publication. Varenius never lived to see this recognition as he died shortly after publishing the first edition at the age of 28. Geographia Generalis was among the first comprehensive attempts to systematize geographical knowledge. Varenius aimed to compile all known geographical information and theories into a single coherent framework. His work synthesized the geographical knowledge of his time, drawing from various sources, including classical texts, travel accounts, and contemporary scientific observations. The book

637-530: A figure of Minerva with owl, shield and olive tree, and the motto, Ne extra oleas . The earliest productions of the Elzevir press are marked with an angel bearing a hook and a scythe, and various other devices occur at different times. When the Elzevirs did not wish to put their name to their works they generally marked them with a sphere, but of course the mere fact that a work printed in the 17th century bears this mark

728-402: 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

819-492: 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

910-587: 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

1001-461: 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

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1092-407: A printing press at Leiden, where he carried on business to 1625; but none of his editions attained much fame. The last representatives of the Elzevir printers were Peter, grandson of Joost, who from 1667 to 1675 was a bookseller at Utrecht , and printed seven or eight volumes of little consequence; and Abraham, son of the first Abraham, who from 1681 to 1712 was university printer at Leiden. Some of

1183-507: A profound impact on the development of geography as a scientific discipline. It was widely read and used as a textbook for many years after its publication. English translations of the work were used in universities in both the United States and England and were widely read until the 1800s. The Russian translation was influential in the formation of the Russian tradition of geography, accelerating

1274-568: A response to the Cartesianism movement at Cambridge. The Jurin edition was still in the original Latin. In 1733, the Jurin edition was translated into English by Peter Shaw and Dugdale. The Dugdale-Shaw English translations excluded some content, and added material that reinforced the Newtonian perspective. This edition was released three more times in 1734, 1736, and 1765. Geographia Generalis had

1365-520: A sheaf of seven arrows, adorned with the motto Concordia res parvae crescunt . About 1620 the Leiden Elzevirs adopted a new device, known as le Solitaire , or the Hermit, and consisting of an elm tree , a fruitful vine and a man alone, with a motto Non solus (not alone). They also used another device, a palm tree with the motto, Assurgo pressa . The Elzevirs of Amsterdam used for their principal device

1456-506: A stint in Antwerp , and in 1565 his name can be found on the payroll of the great printer-publisher Plantin . In 1580, he made a final move to Leiden , where he seems to have worked first as a bookbinder, and later as a bookseller and publisher. An edition of Eutropius , which appeared in 1592, was long regarded as the earliest Elzevir publication, but the first is now known to be Drusii Ebraicarum quaestionum ac responsionum libri duo , which

1547-543: 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

1638-454: A theoretical foundation. Varenius considered geography to be a cross between science and pure mathematics, applied to quantifying things about the Earth. By applying mathematical principles and a systematic approach, he sought to demonstrate that geography could be studied with the same rigor as other established sciences. Due to the book's prominence, Varenius was known as " the geographer" within

1729-478: 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

1820-485: A trend of modernization in the discipline. Multiple versions have led to confusion, and criticism of the later versions has been attributed to the original. This was particularly noteworthy in Alexander von Humboldt 's discussion of the work, which referred to translations different from either the original or Newton's work. However, Newton's involvement in subsequent editions has made it continue to be relevant in discussing

1911-553: 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.,

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2002-572: 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;

2093-539: Is described as being rushed and incomplete. To keep up with demand, in 1664, the text was reprinted at the Elzevir Press with formatting changes. In 1671 and 1672, Elzevir press released publications based on the 1664 one. In 1672, Isaac Newton released an updated edition of the text, which included grammatical and typographical corrections, additional observations, corrections to calculations, and text restriction. These changes were substantial and on nearly every page of

2184-624: 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

2275-411: Is intended as an introductory textbook, and therefore the mathematical content is considered to be intermediate. Varenius divided the book into two main subsections: general geography and special geography. These two terms were likely borrowed from the work of Bartholomew Kecker. The main focus is general geography, which was further subdivided into three parts: the absolute part, the relative part, and

2366-578: 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

2457-622: 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

2548-462: 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

2639-562: 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

2730-728: The Aldines and the Estiennes , but their small editions in 12mo , 16mo and 24mo, for elegance of design, neatness, clearness and regularity of type, and beauty of paper, cannot be surpassed. Special mention ought to be made of their two editions of the New Testament in Greek, published in 1624 and 1633, of which the latter is the more beautiful and the more sought; the Psalterium Davidis , 1653; Virgilii opera , 1636; Terentii comediae , 1635; but

2821-662: 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

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2912-508: The Geographia Generalis by editors and translators. In the final translation of the text by James Jurin an Appendix containing many of these additions was included. This appendix contains citations to works published since the first edition of the book, figures, and tables. Several of these figures and tables were added by Isaac Newton . Geographia Generalis had several editions and translations, with several authors contributing to

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

3549-430: 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

3640-660: The Earth's shape and physical features. It is divided into six sections and contains 21 chapters. The first section contains two chapters discussing geometry and theory that are necessary to understand the rest of the book. The second section contains five chapters discussing the shape of the Earth, its size, its motion, and its composition. The third section contains four chapters and discusses physical geographic features, such as mountains, forests, and deserts. The fourth section contains six chapters and discusses water features, such as oceans, rivers, and lakes, as well as their motions. The fifth section contains one chapter titled "Concerning

3731-478: The Elzevir editions bear no other typographical mark than simply the words Apud Elzevirios , or Ex officina Elseviriana , under the rubrique of the town. But most bear one of their special devices, four of which are known to have been in common use. Louis Elzevir, the founder of the family, usually adopted the arms of the United Provinces , but with the lion swapped for an eagle on a cippus holding in its claws

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3822-485: 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

3913-425: The Greek term Tetrabiblos (lit. "Four Books") or by its Latin equivalent Quadripartitum . Its original title is unknown, but may have been a term found in some Greek manuscripts, Apotelesmatiká ( biblía ), roughly meaning "(books) on the Effects" or "Outcomes", or "Prognostics". As a source of reference, the Tetrabiblos is said to have "enjoyed almost the authority of a Bible among the astrological writers of

4004-497: 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

4095-455: 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

4186-422: 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

4277-500: The appearance of the Moon and Sun are discussed in these chapters. The comparative part contains ten chapters related to comparing places to each other and navigation. There are two chapters related to ship construction and cargo. These chapters serve to contextualize the nautical navigation information. These sections demonstrate how the theoretical aspects of geography can be practically applied. The outline of terrestrial geography contains

4368-472: 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

4459-403: 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

4550-547: The boundaries of a region, its latitude and longitude, mountains, mines, water features, animals, and the fertility of the land. The outline of celestial geography contains the relationship between a place and the equator and pole, the length of the day, the climate, and the observed motion of stars above the horizon. The outline of human geography contains the stature of a region's inhabitants, their food, customs, religions, languages, cities, historic events, and notable people. Several additions were made to later editions of

4641-664: The business alone until his death in 1661. In 1654 Daniel joined his cousin Louis (the third of that name and son of the second Louis), who was born in 1604, and had established a printing press at Amsterdam in 1638. From 1655 to 1666 they published a series of Latin classics in 8vo , cum notis variorum; Cicero in 4to ; the Etymologicon linguae Latinae ; and in 1663 a magnificent Corpus Juris Civilis in folio in two volumes. Louis died in 1670, and Daniel in 1680. Besides Bonaventure, another son of Matthieu, Isaac, born in 1593, established

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4732-420: The change of dry places into rainy ones." This section details the transitions between climate zones, discusses changes in landforms and land cover types over time, and speculates on the underlying mechanisms. The sixth section contains three chapters discussing the atmosphere and winds. The relative part contains nine chapters on the zones of the Earth caused by its shape. Light, heat, climate zones, seasons, and

4823-446: The comparative part. Special geography was further subdivided into three parts: terrestrial, celestial, and human. The subsections within special geography are outlined but not expanded on in the work. It is speculated that Verenius intended a complimentary book on special geography, but died before being able to complete it. Special geography is today considered to be regional geography . The absolute part contains information related to

4914-506: 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,

5005-734: 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

5096-402: 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

5187-469: 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

5278-543: 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

5369-425: 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

5460-419: 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,

5551-505: The highest honour. Despite being a minority position among ancient philosophers, Ptolemy's views were shared by other mathematicians such as Hero of Alexandria . There are several characters and items named after Ptolemy, including: House of Elzevir Elzevir is the name of a family of Dutch booksellers, publishers, and printers of the 17th and early 18th centuries. The duodecimo series of "Elzevirs" became very famous and very desirable among bibliophiles , who sought to obtain

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5642-540: The history of geography. The work was notable for its methodological rigor and systematic approach, setting a standard for future geographical studies. Through the mathematical quantification of space, the identification of universal spatial elements has been linked to spatial analysis . Ptolemy This is an accepted version of this page Claudius Ptolemy ( / ˈ t ɒ l ə m i / ; Ancient Greek : Πτολεμαῖος , Ptolemaios ; Latin : Claudius Ptolemaeus ; c.  100  – c.  170 AD)

5733-553: 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

5824-599: 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

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

6097-477: 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

6188-525: The name of the family was most often spelled Elsevier, or Elzevier, and their French editions mostly retain this name; but the name was gradually corrupted in English into Elzevir as a generic term for their books. The family originally came from Leuven , where Louis was born circa 1546. Although he worked in the book trade throughout his life, Louis seems to have worked mostly as a bookbinder in his early decades. He relocated with his family several times, including

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

6370-401: 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

6461-486: 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

6552-405: 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

6643-474: 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

6734-451: 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

6825-440: 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

6916-517: 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

7007-496: 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

7098-530: The tallest and freshest copies of these tiny books. Although it appears the family was involved with the book trade as early as the 16th century, it is only known for its work in some detail beginning with Lodewijk Elzevir (also called Louis). The family ceased printing in 1712, but a contemporary publisher, Elsevier (founded in 1880), took over, for marketing purposes, the name and logo of this early modern business, but without having any real historical connections to it. In an age of non-standardized spelling,

7189-516: The text over time. It is therefore necessary to check earlier versions against translations to determine what it originally contained, and the true authorship of the final product is ambiguous. The first edition of Geographia Generalis was published in 1650 at the Elzevir press in Amsterdam. The first edition was 786 pages in length, and written in Latin. The book was very popular but had several errors and

7280-520: The text titled Cosmography and geography in two parts. This translation was based on the Elzevir press editions, and had text from French cartographer Nicolas Sanson 's publication A Geographical Description of the World spliced into it. Blome's version of the text has been criticized for altering the meaning of sections, and for inconsistent tone. Many later translations and editions of the Geographia Generalis have been influenced by this version. In 1712,

7371-548: The text. Newton provided several figures and tables as well. Newton's additions mostly centered on mathematical content as it related to geographies, such as content related to projections, navigation, and cartography. In 1681, Newton released another updated edition of the text, including content related to shadows in the tropics. Newton also added the coordinates of Cambridge in the 1681 edition. The 1672 and 1681 editions were both published at Cambridge University Press . In 1682, Richard Blome published an English translation of

7462-573: 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

7553-445: The work was translated into Russian. This was influential to the development of Russian geography. In 1721, James Jurin, with help from Edmond Halley and Roger Cotes , released a revised edition of the text based on Isaac Newton's Cambridge editions. The most significant addition to this edition by Jurian is an appendix with forty-six citations, and thirteen diagrams. These additions were motivated in part to advance Newtonianism as

7644-663: The works that gave their press its chief celebrity are their collection of French authors on history and politics in 24mo, known under the name of the Petites Républiques , and their series of Latin, French and Italian classics in small 12mo. Also, they are noted for their publication in 1638 of Galileo 's last work, the Two New Sciences , at a time when the Roman Inquisition forbade the latter's writings. Between 1626 and 1649, Bonaventure and Abraham Elzevir published

7735-461: 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

7826-431: 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

7917-614: 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

8008-464: 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

8099-479: Was produced in 1583. In all Louis published about 150 works. He died on 4 February 1617. Of his seven sons, five, Matthieu/Matthijs, Louis, Gilles, Joost and Bonaventura, adopted their father's profession. Among them, Bonaventura Elzevir (1583–1652) is the most celebrated. He began business as a publisher in 1608, and in 1626 took into partnership Abraham Elzevir , his nephew by Matthijs, born at Leiden in 1592. In 1617 Isaac Elzevir (1596–1651), Matthijs' second son,

8190-437: Was the first in the family to acquire printing equipment, which then passed into the hands of the partnership of Bonaventura and Abraham in 1626 when he decided to exit the business. Abraham died on 14 August 1652, and Bonaventura about a month afterwards. The fame of the Elzevir editions rests chiefly on the works issued by the firm of Bonaventura and Abraham. Their Greek and Hebrew impressions are considered inferior to those of

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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