This is an accepted version of this page
119-448: The zodiac is a coordinate system of twelve "signs", based on twelve constellations used in astronomy and astrology. Zodiac may also refer to: Zodiac The zodiac is a belt-shaped region of the sky that extends approximately 8° north and south (as measured in celestial latitude ) of the ecliptic , the apparent path of the Sun across the celestial sphere over the course of
238-417: 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
357-601: 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
476-618: 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 is of Homeric form . It was common among the Macedonian upper class at the time of Alexander
595-470: 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
714-463: A complete list of the 36 Egyptian decans was placed among the hieroglyphs adorning the tomb of Seti I ; they figured again in the temple of Ramesses II , and characterize every Egyptian astrological monument. Both the famous zodiacs of Dendera display their symbols, identified by Karl Richard Lepsius . The division of the ecliptic into the zodiacal signs originates in Babylonian astronomy during
833-433: A digit from 0 to and including 11), degrees from 0 to 29, minutes, and seconds. Mughal king Jahangir issued an attractive series of coins in gold and silver depicting the twelve signs of the zodiac. What follows is a list of the signs of the modern zodiac (with the ecliptic longitudes of their first points), where 0° Aries is understood as the vernal equinox, with their Latin, Greek, Sanskrit, and Babylonian names. But
952-507: 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 is the Geography , which is a thorough discussion on maps and the geographic knowledge of
1071-566: A fourteen-sign system proposed by Steven Schmidt which adds Ophiuchus (see below) and Cetus (the IAU boundaries of which just graze by the ecliptic): The beginning of Aries is defined as the moment of vernal equinox , and all other dates shift accordingly. The precise Gregorian times and dates vary slightly from year to year as the Gregorian calendar shifts relative to the tropical year . These variations remain within less than two days' difference in
1190-402: 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
1309-492: 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
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#17328770347861428-596: 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 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
1547-587: 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
1666-461: 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
1785-611: A planet were not as important as the astrologically significant dates when the planet crossed from one zodiacal sign to the next. Knowledge of the Babylonian zodiac is said to be reflected in the Hebrew Bible ; E. W. Bullinger interpreted the creatures that appear in the book of Ezekiel ( 1:10 ) as the middle signs of the four quarters of the zodiac, with the Lion as Leo , the Bull as Taurus ,
1904-444: A rudimentary stage of evolution. They measured the position of a planet in reference to a set of "normal stars" close to the ecliptic (±9° of latitude). The normal stars were used as observational reference points to help position a planet within this ecliptic coordinate system. In Babylonian astronomical diaries , a planet position was generally given with respect to a zodiacal sign alone, though less often in specific degrees within
2023-408: A sign. When the degrees of longitude were given, they were expressed with reference to the 30° of the zodiacal sign, i.e., not with a reference to the continuous 360° ecliptic. In astronomical ephemerides , the positions of significant astronomical phenomena were computed in sexagesimal fractions of a degree (equivalent to minutes and seconds of arc ). For daily ephemerides, the daily positions of
2142-399: A takht. First, the astrologer would use an astrolabe to find the position of the sun, align the rule with the persons time of birth and then align the rete to establish the altitude of the sun on that date. Next, the astrologer would use an Ephemeris, a table denoting the mean position of the planets and stars within the sky at any given time. Finally, the astrologer would add the altitude of
2261-543: 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
2380-478: 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
2499-593: A very few years of 401 BC. Unlike modern astrologers, who place the beginning of the sign of Aries at the position of the Sun at the vernal equinox in the Northern Hemisphere ( March equinox ), Babylonian astronomers fixed the zodiac in relation to stars, placing the beginning of Cancer at the "Rear Twin Star" ( β Geminorum ) and the beginning of Aquarius at the "Rear Star of the Goat-Fish" ( δ Capricorni ). Due to
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#17328770347862618-553: 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.,
2737-522: 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;
2856-433: Is described in the 1st century BC astronomical text of Geminus of Rhodes. Geminus explains that Greek astronomers of his era associate the first degrees of the zodiac signs with the two solstices and the two equinoxes, in contrast to the older Chaldean (Babylonian) system, which placed these points within the zodiac signs. This illustrates that Ptolemy merely clarified the convention of Greek astronomers and did not originate
2975-622: 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
3094-399: Is one twelfth of a sidereal year , or 30.43 standard days . Due to Earth's slight orbital eccentricity , the duration of each sign varies appreciably, between about 29.4 days for Capricorn and about 31.4 days for Cancer (see Equation of time ). In addition, because the Earth's axis is at an angle, some signs take longer to rise than others, and the farther away from the equator the observer
3213-432: 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 was familiar with Greek philosophers and used Babylonian observations and Babylonian lunar theory. In half of his extant works, Ptolemy addresses
3332-410: Is situated, the greater the difference. Thus, signs are spoken of as "long" or "short" ascension . In tropical astrology , the zodiacal signs are distinct from the constellations associated with them, not only because of their drifting apart due to the precession of equinoxes but because the physical constellations take up varying widths of the ecliptic, so the Sun is not in each constellation for
3451-418: 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 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
3570-483: Is the diminutive of zōon ( ζῷον , "animal"). The name reflects the prominence of animals (and mythological hybrids ) among the twelve signs. The zodiac was in use by the Roman era , based on concepts inherited by Hellenistic astronomy from Babylonian astronomy of the Chaldean period (mid-1st millennium BC), which, in turn, derived from an earlier system of lists of stars along the ecliptic. The construction of
3689-466: Is the first known depiction of the classical zodiac of twelve signs. The earliest extant Greek text using the Babylonian division of the zodiac into 12 signs of 30 equal degrees each is the Anaphoricus of Hypsicles of Alexandria (fl. 190 BC). Particularly important in the development of Western horoscopic astrology was the astrologer and astronomer Ptolemy , whose work Tetrabiblos laid
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3808-626: 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
3927-413: 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
4046-504: 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 the emperor Claudius or the emperor Nero . The 9th century Persian astronomer Abu Ma'shar al-Balkhi mistakenly presents Ptolemy as
4165-662: 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
4284-410: 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
4403-749: 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 the Tetrábiblos , from the Koine Greek meaning "Four Books", or by its Latin equivalent Quadripartite . The Catholic Church promoted his work, which included
4522-784: 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
4641-457: 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
4760-588: The ecliptic and equator , which shifts in relation to the backdrop of fixed stars at a rate of 1° every 72 years, creating the phenomenon known as precession of the equinoxes. The Hindu zodiac, being sidereal, does not maintain this seasonal alignment, but there are still similarities between the two systems. The Hindu zodiac signs and corresponding Greek signs sound very different, being in Sanskrit and Greek respectively, but their symbols are nearly identical. For example, dhanu means "bow" and corresponds to Sagittarius,
4879-461: 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
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4998-519: 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
5117-421: The precession of the equinoxes , the time of year the Sun is in a given constellation has changed since Babylonian times, as the point of March equinox has moved from Aries into Pisces . Because the divisions were made into equal arcs of 30° each, they constituted an ideal system of reference for making predictions about a planet's longitude. However, Babylonian techniques of observational measurements were in
5236-487: The "archer", and kumbha means "water-pitcher" and corresponds to Aquarius, the "water-carrier". During the Abbasid era , Greek reference books were translated into Arabic , and Islamic astronomers then did their own observations, correcting Ptolemy's Almagest. One such book was Al-Sufi 's Book of Fixed Stars , which has pictorial depictions of 48 constellations. The book was divided into three sections: constellations of
5355-430: 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
5474-455: The 2nd century BC, as well as into developing the Hindu zodiac . Due to the precession of the equinoxes , the time of year that the Sun is in a given constellation has changed since Babylonian times, and the point of March equinox has moved from Aries into Pisces . The zodiac forms a celestial coordinate system , or more specifically an ecliptic coordinate system , which takes the ecliptic as
5593-518: 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 was Ptolemais Hermiou , a Greek city in the Thebaid region of Egypt (now El Mansha, Sohag Governorate ). This attestation
5712-453: The Earth's axis of rotation, rather than the plane of the planet's orbit around the Sun. 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) was an Alexandrian mathematician , astronomer , astrologer , geographer , and music theorist who wrote about
5831-485: 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
5950-564: 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 the Macedonian family's rule. The name Claudius is a Roman name, belonging to
6069-473: 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
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#17328770347866188-514: The Hellenistic world came to be so identified with astrology that "Chaldean wisdom" became among Greeks and Romans the synonym of divination through the planets and stars . Hellenistic astrology derived in part from Babylonian and Egyptian astrology . Horoscopic astrology first appeared in Ptolemaic Egypt (305 BC–30 BC). The Dendera zodiac , a relief dating to c. 50 BC ,
6307-657: The Man as Aquarius and the Eagle as a higher aspect of Scorpio. Some authors have linked the signs of the zodiac with the twelve tribes of Israel , and with the lunar Hebrew calendar , which has twelve lunar months in a lunar year . Martin and others have argued that the arrangement of the tribes around the Tabernacle (reported in the Book of Numbers ) corresponded to the order of the zodiac, with Judah , Reuben , Ephraim , and Dan representing
6426-424: The Sanskrit and the name equivalents (after c.500 BC) denote the constellations only, not the tropical zodiac signs. The "English translation" is not usually used by English speakers. The Latin names are standard English usage (except that "Capricorn" is used rather than "Capricornus"). These twelve signs have been arranged into a nursery rhyme as a mnemonic device: The ram, the bull, the heavenly twins, And next
6545-455: 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
6664-488: The Sun's planets have orbits that have only a slight inclination to the orbital plane of the Earth. Stars within the zodiac are subject to occultations by the Moon and other solar system bodies. These events can be useful, for example, to estimate the cross-sectional dimensions of a minor planet , or check a star for a close companion. The Sun's placement upon the vernal equinox, which occurs annually around 21 March, defines
6783-422: 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
6902-472: 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
7021-569: The astronomical constellations and the astrological signs is mistakenly reported in the popular press as a "change" to the list of traditional signs by some astronomical body like the IAU, NASA , or the Royal Astronomical Society . This happened in a 1995 report of the BBC Nine O'Clock News and various reports in 2011 and 2016. Some "parazodiacal" constellations are touched by the paths of
7140-554: The basis of the Western astrological tradition . Under the Greeks, and Ptolemy in particular, the planets, Houses, and signs of the zodiac were rationalized and their function set down in a way that has changed little to the present day. Ptolemy lived in the 2nd century AD, three centuries after the discovery of the precession of the equinoxes by Hipparchus around 130 BC. Hipparchus' lost work on precession never circulated very widely until it
7259-511: The best date for founding the new capital of Baghdad. Whilst horoscopes were generally widely accepted by society, many scholars condemned the use of astrology and divination, linking it to occult influences. Many theologians and scholars thought that it went against the tenets of Islam; as only God should be able to determine events rather than astrologers looking at the positions of the planets. In order to calculate someone's horoscope, an astrologer would use 3 tools: an astrolabe, ephemeris and
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#17328770347867378-504: The corresponding constellation. This alignment needs re calibrating every so often to keep the alignment in place. The ecliptic intersects with 13 constellations of Ptolemy 's Almagest , as well as of the more precisely delineated IAU designated constellations . In addition to the twelve constellations after which the twelve zodiac signs are named, the ecliptic intersects Ophiuchus , the bottom part of which interjects between Scorpius and Sagittarius. Occasionally this difference between
7497-459: The crab, the lion shines, The virgin and the scales, The scorpion, archer, and the goat, The man who holds the watering-pot, And fish with glittering scales. The following table compares the Gregorian dates on which the Sun enters a sign in the Ptolemaic tropical zodiac, and a sign in two sidereal systems: one proposed by Cyril Fagan , and
7616-506: 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,
7735-402: 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
7854-469: 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
7973-425: 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
8092-416: The end of the constellation Pisces, having been within that constellation since the 2nd century AD. The subsequent 30° of the ecliptic is nominally designated the zodiac sign Taurus, and so on through the twelve signs of the zodiac so that each occupies 1 ⁄ 12 th (30°) of the zodiac's great circle. Zodiac signs have never been used to determine the boundaries of astronomical constellations that lie in
8211-405: The end of the fifth century BC, Babylonian astronomers divided the ecliptic into 12 equal "signs", by analogy to 12 schematic months of 30 days each. Each sign contained 30° of celestial longitude , thus creating the first known celestial coordinate system. According to calculations by modern astrophysics, the zodiac was introduced between 409 and 398 BC, during Persian rule , and probably within
8330-538: The equation of Munjaala. The discovery of precession is attributed to Hipparchus around 130 BC. Ptolemy quotes from Hipparchus' now-lost work entitled "On the Displacement of the Solstitial and Equinoctial Points" in the seventh book of his 2nd century astronomical text, Almagest , where he describes the phenomenon of precession and estimates its value. Ptolemy clarified that the convention of Greek mathematical astronomy
8449-419: 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,
8568-574: The first half of the 1st millennium BC . The zodiac draws on stars in earlier Babylonian star catalogues , such as the MUL.APIN catalogue, which was compiled around 1000 BC. Some constellations can be traced even further back, to Bronze Age ( Old Babylonian Empire ) sources, including Gemini "The Twins", from Sumerian : 𒀯𒈦𒋰𒁀𒃲𒃲 , romanized: MAŠ.TAB.BA.GAL.GAL "The Great Twins"; Cancer "The Crab", from Sumerian : 𒀯𒀠𒇻 , romanized: AL.LUL "The Crayfish", among others. Around
8687-553: 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
8806-588: The influence that the stars have on events on the earth was important in Islamic civilization. As a rule, it was believed that the signs of the zodiac and the planets control the destiny not only of people but also of nations, and that the zodiac has the ability to determine a person's physical characteristics as well as intelligence and personal traits. The practice of astrology at this time could be divided into 4 broader categories: Genethlialogy, Catarchic Astrology, Interrogational Astrology and General Astrology. However
8925-599: 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
9044-500: 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
9163-458: The middle signs of Leo, Aquarius, Taurus, and Scorpio, respectively. Such connections were taken up by Thomas Mann , who in his novel Joseph and His Brothers , attributes characteristics of a sign of the zodiac to each tribe, in his rendition of the Blessing of Jacob . The Babylonian star catalogs entered Greek astronomy in the 4th century BC, via Eudoxus of Cnidus . Babylonia or Chaldea in
9282-555: 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
9401-490: The most common type of astrology was Genethlialogy, which examined all aspects of a person's life in relation to the planetary positions at their birth; more commonly known as our horoscope. Astrology services were offered widely across the empire, mainly in bazaars, where people could pay for a reading. Astrology was valued in the royal courts, for example, the Abbasid Caliph Al-Mansur used astrology to determine
9520-477: 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
9639-408: The natures of the signs from the theory of prognostication, or impossible to avoid error in then retaining and making use of them; as the regularity of their spaces and distances, upon which their influence depends, would then be invaded and broken in upon. Astronomically, the zodiac defines a belt of space extending 8° or 9° in celestial latitude to the north and south of the ecliptic , within which
9758-461: 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
9877-591: 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 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
9996-424: The orbits of the Moon and the principal planets remain. It is a feature of the ecliptic coordinate system – a celestial coordinate system centered upon the ecliptic (the plane of the Earth's orbit and the Sun's apparent path), by which celestial longitude is measured in degrees east of the vernal equinox (the ascending intersection of the ecliptic and equator). The zodiac is narrow in angular terms because most of
10115-526: The origin of latitude and the Sun's position at vernal equinox as the origin of longitude. In modern astronomy, the ecliptic coordinate system is still used for tracking Solar System objects. The English word zodiac derives from zōdiacus , the Latinized form of the Ancient Greek zōdiakòs kýklos ( ζῳδιακός κύκλος ), meaning "cycle or circle of little animals". Zōdion ( ζῴδιον )
10234-410: The paths of the planets corresponding to the band of about 8 arc degrees above and below the ecliptic. The zodiac of a given planet is the band that contains the path of that particular body; e.g., the "zodiac of the Moon" is the band of 5° above and below the ecliptic. By extension, the "zodiac of the comets" may refer to the band encompassing most short-period comets . As early as the 14th century BC
10353-464: The planets, leading to counts of up to 25 "constellations of the zodiac". The ancient Babylonian MUL.APIN catalog lists Orion , Perseus , Auriga , and Andromeda . Modern astronomers have noted that planets pass through Crater , Sextans , Cetus , Pegasus , Corvus , Hydra , Orion , and Scutum , with Venus very rarely passing through Aquila , Canis Minor , Auriga , and Serpens . Some other constellations are mythologically associated with
10472-410: The principle of the tropical zodiac, as is sometimes assumed. Ptolemy demonstrates that the principle of the tropical zodiac was well known to his predecessors within his astrological text, the Tetrabiblos , where he explains why it would be an error to associate the regularly spaced signs of the seasonally aligned zodiac with the irregular boundaries of the visible constellations: The beginnings of
10591-401: 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
10710-486: 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
10829-448: The recent past and the near-future, vernal equinox in UT always falling either on 20 or 21 March in the period of 1797 to 2043, falling on 19 March in 1796 the last time and in 2044 the next. The vernal equinox has fallen on 20 March UT since 2008, and will continue to do so until 2043. As each sign takes up exactly 30 degrees of the zodiac, the average duration of the solar stay in each sign
10948-476: The same amount of time. Thus, Virgo takes up 5 times as much ecliptic longitude as Scorpius . The zodiacal signs are an abstraction from the physical constellations, and each represent exactly 1 ⁄ 12 th of the full circle, but the time spent by the Sun in each sign varies slightly due to the eccentricity of the Earth's orbit . Sidereal astrology remedies this by assigning the zodiac sign approximately to
11067-449: The same names as the zodiac signs. According to mathematician-historian Montucla , the Hindu zodiac was adopted from the Greek zodiac through communications between ancient India and the Greek empire of Bactria . The Hindu zodiac uses the sidereal coordinate system , which makes reference to the fixed stars. The tropical zodiac (of Mesopotamian origin) is divided by the intersections of
11186-405: 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
11305-505: The serpent on the Dendera zodiac . The zodiac system was developed in Babylonia , some 2,500 years ago, during the " Age of Aries ". At the time, it is assumed, the precession of the equinoxes was unknown. Contemporary use of the coordinate system is presented with the choice of interpreting the system either as sidereal , with the signs fixed to the stellar background , or as tropical , with
11424-561: The signs fixed to the point ( vector of the Sun) at the March equinox . Western astrology takes the tropical approach, whereas Hindu astrology takes the sidereal one. This results in the originally unified zodiacal coordinate system drifting apart gradually, with a clockwise (westward) precession of 1.4 degrees per century. For the tropical zodiac used in Western astronomy and astrology, this means that
11543-454: The signs, and likewise those of the terms, are to be taken from the equinoctial and tropical points. This rule is not only clearly stated by writers on the subject, but is especially evident by the demonstration constantly afforded, that their natures, influences and familiarities have no other origin than from the tropics and equinoxes, as has been already plainly shown. And, if other beginnings were allowed, it would either be necessary to exclude
11662-474: 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
11781-451: 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
11900-405: The starting point for measurement, the first degree of which is historically known as the " first point of Aries ". The first 30° along the ecliptic is nominally designated as the zodiac sign Aries, which no longer falls within the proximity of the constellation Aries since the effect of precession is to move the vernal point through the backdrop of visible constellations. It is currently located near
12019-440: 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
12138-517: 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
12257-408: The sun taken from the astrolabe, with the mean position of the planets on the person's birthday, and add them together on the takht (also known as the dustboard). The dust board was merely a tablet covered in sand; on which the calculations could be made and erased easily. Once this had been calculated, the astrologer was then able to interpret the horoscope. Most of these interpretations were based on
12376-496: 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
12495-573: 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
12614-418: The time of the year by identifying each sign with the days of the year the Sun is in the respective sign. In Western astrology , and formerly astronomy , the time of each sign is associated with different attributes. The zodiacal system and its angular measurement in 360 sexagesimal degree (°) originated with Babylonian astronomy during the 1st millennium BC . It was communicated into Greek astronomy by
12733-577: The tropical sign of Aries currently lies somewhere within the constellation Pisces (" Age of Pisces "). The sidereal coordinate system takes into account the ayanamsa , ayan meaning "transit' or 'movement', and amsa meaning 'small part', i.e. movement of equinoxes in small parts. It is unclear when Indians became aware of the precession of the equinoxes, but Bhāskara II 's 12th-century treatise Siddhanta Shiromani gives equations for measurement of precession of equinoxes, and says his equations are based on some lost equations of Suryasiddhanta plus
12852-463: The vicinity of the zodiac, which are, and always have been, irregular in their size and shape. The convention of measuring celestial longitude within individual signs was still being used in the mid-19th century, but modern astronomy now numbers degrees of celestial longitude continuously from 0° to 360°, rather than 0° to 30° within each sign. This coordinate system is primary used by astronomers for observations of solar system objects. The use of
12971-554: The year. Also within this zodiac belt appear the Moon and the brightest planets , along their orbital planes. The zodiac is divided along the ecliptic into 12 equal parts ("signs") , each occupying 30° of celestial longitude . These signs roughly correspond to the astronomical constellations with the following modern names: Aries , Taurus , Gemini , Cancer , Leo , Virgo , Libra , Scorpio , Sagittarius , Capricorn , Aquarius , and Pisces . The signs have been used to determine
13090-513: The zodiac as a means to determine astronomical measurement remained the main method for defining celestial positions by Western astronomers until the Renaissance, at which time preference moved to the equatorial coordinate system, which measures astronomical positions by right ascension and declination rather than the ecliptic-based definitions of celestial longitude and celestial latitude . The orientation of equatorial coordinates are aligned with
13209-471: The zodiac in literature. For example, there were several manuals on how to interpret each zodiac sign, the treatise relating to each individual sign and what the characteristics of these zodiacs were. An example of the use of signs as astronomical coordinates may be found in the Nautical Almanac and Astronomical Ephemeris for the year 1767 . The "Longitude of the Sun" columns show the sign (represented as
13328-458: The zodiac is described in Ptolemy 's comprehensive 2nd century AD work, the Almagest . Although the zodiac remains the basis of the ecliptic coordinate system in use in astronomy besides the equatorial one, the term and the names of the twelve signs are today mostly associated with horoscopic astrology . The term "zodiac" may also refer to the region of the celestial sphere encompassing
13447-703: The zodiac, as found, e.g., in the Sefer Raziel HaMalakh . The zodiac is found in medieval stained glass as at Angers Cathedral , where the master glass maker, André Robin, made the ornate rosettes for the North and South transepts after the fire there in 1451. Astrology emerged in the 8th century AD as a distinct discipline in Islam, with a mix of Indian, Hellenistic Iranian and other traditions blended with Greek and Islamic astronomical knowledge, for example Ptolemy's work and Al-Sufi's Book of Fixed Stars. A knowledge of
13566-573: The zodiac, constellations north of the zodiac, and southern constellations. When Al-Sufi's book, and other works, were translated in the 11th century, there were mistakes made in the translations. As a result, some stars ended up with the names of the constellation they belong to (e.g. Hamal in Aries). The High Middle Ages saw a revival of interest in Greco-Roman magic , first in Kabbalism and later continued in Renaissance magic . This included magical uses of
13685-475: The zodiacal ones: Piscis Austrinus , The Southern Fish, is attached to Aquarius. In classical maps, it swallows the stream poured out of Aquarius' pitcher, but perhaps it formerly just swam in it. Aquila , The Eagle, was possibly associated with the zodiac by virtue of its main star, Altair . Hydra in the Early Bronze Age marked the celestial equator and was associated with Leo, which is shown standing on
13804-415: Was brought to prominence by Ptolemy, and there are few explanations of precession outside the work of Ptolemy until late Antiquity, by which time Ptolemy's influence was widely established. Ptolemy clearly explained the theoretical basis of the western zodiac as being a tropical coordinate system , by which the zodiac is aligned to the equinoxes and solstices, rather than the visible constellations that bear
13923-464: 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
14042-399: Was to commence the zodiac from the point of the vernal equinox and to always refer to this point as "the first degree" of Aries. This is known as the "tropical zodiac" (from the Greek word trópos, turn) because its starting point revolves through the circle of background constellations over time. The principle of the vernal point acting as the first degree of the zodiac for Greek astronomers
14161-499: 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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