Misplaced Pages

#529470

116-669: The Almagest ( / ˈ æ l m ə dʒ ɛ s t / AL -mə-jest ) is a 2nd-century mathematical and astronomical treatise on the apparent motions of the stars and planetary paths, written by Claudius Ptolemy ( c. AD 100 – c.  170 ) in Koine Greek . One of the most influential scientific texts in history, it canonized a geocentric model of the Universe that was accepted for more than 1,200 years from its origin in Hellenistic Alexandria , in

232-635: A 69-page preface. It has been described as "suffer[ing] from excessive literalness, particularly where the text is difficult" by Toomer, and as "very faulty" by Serge Jodra. The scanned books are available in full at the Gallica French National library. Greek mathematics Greek mathēmatikē ("mathematics") derives from the Ancient Greek : μάθημα , romanized :  máthēma , Attic Greek : [má.tʰɛː.ma] Koinē Greek : [ˈma.θi.ma] , from

348-565: A degree. Some errors may be due to atmospheric refraction causing stars that are low in the sky to appear higher than where they really are. A series of stars in Centaurus are off by a couple of degrees, including the star we call Alpha Centauri . These were probably measured by a different person or persons from the others, and in an inaccurate way. The star catalogue contains 48 constellations, which have different surface areas and numbers of stars. In Book VIII, Chapter 3, Ptolemy writes that

464-481: A device that historians of astronomy refer to as a "crank mechanism": he succeeded in creating models for the other planets, where Hipparchus had failed, by introducing a third device called the equant . Ptolemy wrote the Syntaxis as a textbook of mathematical astronomy. It explained geometrical models of the planets based on combinations of circles, which could be used to predict the motions of celestial objects. In

580-433: 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

696-539: A later book, the Planetary Hypotheses , Ptolemy explained how to transform his geometrical models into three-dimensional spheres or partial spheres. In contrast to the mathematical Syntaxis , the Planetary Hypotheses is sometimes described as a book of cosmology . Ptolemy's comprehensive treatise of mathematical astronomy superseded most older texts of Greek astronomy. Some were more specialized and thus of less interest; others simply became outdated by

812-631: 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 ,

928-444: 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

1044-408: 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

1160-516: A subset of star coordinates in the Almagest can indeed be traced back to Hipparchus, but not that the complete star catalogue was simply "copied". Rather, Hipparchus' major errors are no longer present in the Almagest and, on the other hand, Hipparchus' star catalogue had some stars that are entirely absent from the Almagest. It can be concluded that Hipparchus' star catalogue, while forming the basis, has been reobserved and revised. The figure he used

1276-399: 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

SECTION 10

#1732765408530

1392-660: 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

1508-521: Is a close paraphrase of Ptolemy's own words from Toomer's translation. The layout of the catalogue has always been tabular. Ptolemy writes explicitly that the coordinates are given as (ecliptical) "longitudes" and "latitudes", which are given in columns, so this has probably always been the case. It is significant that Ptolemy chooses the ecliptical coordinate system because of his knowledge of precession, which distinguishes him from all his predecessors. Hipparchus' celestial globe had an ecliptic drawn in, but

1624-497: Is an accepted version of this page 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 the year. Also within this zodiac belt appear the Moon and the brightest planets , along their orbital planes. The zodiac

1740-451: Is based on Hipparchus' own estimate for precession, which was 1° in 100 years, instead of the correct 1° in 72 years. Dating attempts through proper motion of the stars also appear to date the actual observation to Hipparchus' time instead of Ptolemy. Many of the longitudes and latitudes have been corrupted in the various manuscripts. Most of these errors can be explained by similarities in the symbols used for different numbers. For example,

1856-680: Is customarily attributed to the Pythagoreans, including the discovery of irrationals, attributed to Hippasus (c. 530–450 BC) and Theodorus (fl. 450 BC). The greatest mathematician associated with the group, however, may have been Archytas (c. 435-360 BC), who solved the problem of doubling the cube , identified the harmonic mean , and possibly contributed to optics and mechanics . Other mathematicians active in this period, not fully affiliated with any school, include Hippocrates of Chios (c. 470–410 BC), Theaetetus (c. 417–369 BC), and Eudoxus (c. 408–355 BC). Greek mathematics also drew

1972-550: 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 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

2088-433: 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

2204-433: 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 the time of the year by identifying each sign with

2320-457: Is number" and were keen in looking for mathematical relations between numbers and things. Pythagoras himself was given credit for many later discoveries, including the construction of the five regular solids . However, Aristotle refused to attribute anything specifically to Pythagoras and only discussed the work of the Pythagoreans as a group. Almost half of the material in Euclid 's Elements

2436-413: Is simply wrong, and that the Almagest should be seen as a great, if not indeed the first, scientific treatise." He continued, "Newton’s work does focus critical attention on the many difficulties and inconsistencies apparent in the fine structure of the Almagest. In particular, his conclusion that the Almagest is not a historical account of how Ptolemy actually derived his models and parameters is essentially

SECTION 20

#1732765408530

2552-472: 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

2668-529: Is therefore possible to draw the stick figures in the modern sense so that they fit the description in the Almagest. These constellations form the basis for the modern constellations that were formally adopted by the International Astronomical Union in 1922, with official boundaries that were agreed in 1928. Of the stars in the catalogue, 108 (just over 10%) were classified by Ptolemy as 'unformed', by which he meant lying outside

2784-661: Is thought to be the first Arabic translator. No Latin translation was made before the 12th century. Henry Aristippus made the first Latin translation directly from a Greek copy, but it was not as influential as a later translation into Latin made in Spain by the Italian scholar Gerard of Cremona from the Arabic (finished in 1175). Gerard translated the Arabic text while working at the Toledo School of Translators , although he

2900-479: 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 the paths of the planets corresponding to the band of about 8 arc degrees above and below

3016-459: The Almagest . Hence the Almagest could not have been completed before about 150, a quarter-century after Ptolemy began observing. The name comes from Arabic اَلْمَجِسْطِيّ al-majisṭī , with اَلـ al- meaning ' the ' and majisṭī being a corruption of Greek μεγίστη megístē 'greatest'. The Arabic name was popularized by a Latin translation known as Almagestum made in

3132-951: The Antikythera mechanism , the accurate measurement of the circumference of the Earth by Eratosthenes (276–194 BC), and the mathematical and mechanical works of Heron (c. 10–70 AD). Several centers of learning appeared during the Hellenistic period, of which the most important one was the Mouseion in Alexandria , Egypt , which attracted scholars from across the Hellenistic world (mostly Greek, but also Egyptian , Jewish , Persian , among others). Although few in number, Hellenistic mathematicians actively communicated with each other; publication consisted of passing and copying someone's work among colleagues. Later mathematicians in

3248-521: The Dedekind cut , developed by Richard Dedekind , who acknowledged Eudoxus as inspiration. Euclid , who presumably wrote on optics, astronomy, and harmonics, collected many previous mathematical results and theorems in the Elements , a canon of geometry and elementary number theory for many centuries. Menelaus , a later geometer and astronomer, wrote a standard work on spherical geometry in

3364-483: 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 the origin of latitude and the Sun's position at vernal equinox as

3480-459: 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

3596-569: The Seven Wise Men of Greece . According to Proclus , he traveled to Babylon from where he learned mathematics and other subjects, coming up with the proof of what is now called Thales' Theorem . An equally enigmatic figure is Pythagoras of Samos (c. 580–500 BC), who supposedly visited Egypt and Babylon, and ultimately settled in Croton , Magna Graecia , where he started a kind of brotherhood. Pythagoreans supposedly believed that "all

Almagest - Misplaced Pages Continue

3712-530: The Syntaxis were written by Theon of Alexandria (extant), Pappus of Alexandria (only fragments survive), and Ammonius Hermiae (lost). 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 example is Ptolemy's use of measurements said to have been taken at noon, but which systematically produce readings that are off by half an hour, as if

3828-532: The cosmos together rather than physical or mechanical forces. Aristotle (c. 384–322 BC), the founder of the Peripatetic school , often used mathematics to illustrate many of his theories, as when he used geometry in his theory of the rainbow and the theory of proportions in his analysis of motion. Much of the knowledge about ancient Greek mathematics in this period is thanks to records referenced by Aristotle in his own works. The Hellenistic era began in

3944-593: 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,

4060-421: 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

4176-492: 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

4292-468: The 12th century from an Arabic translation, which would endure until original Greek copies resurfaced in the 15th century. The work was originally called Μαθηματικὴ Σύνταξις ( Mathēmatikḕ Sýntaxis ) in Koine Greek , and was also known as Syntaxis Mathematica in Latin . The treatise was later called Ἡ Μεγάλη Σύνταξις ( Hē Megálē Sýntaxis ), "The Great Treatise"; Latin: Magna Syntaxis ), and

4408-404: The 2nd millennium BC. While these civilizations possessed writing and were capable of advanced engineering, including four-story palaces with drainage and beehive tombs , they left behind no mathematical documents. Though no direct evidence is available, it is generally thought that the neighboring Babylonian and Egyptian civilizations had an influence on the younger Greek tradition. Unlike

4524-422: 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. John Phillips Britton, Visiting Fellow at Yale University, wrote of R.R. Newton, "I think that his main conclusion with respect to Ptolemy’s stature and achievements as an astronomer

4640-561: The Circle ), and a proof that the area enclosed by a parabola and a straight line is 4/3 times the area of a triangle with equal base and height ( Quadrature of the Parabola ). Archimedes also showed that the number of grains of sand filling the universe was not uncountable, devising his own counting scheme based on the myriad , which denoted 10,000 ( The Sand-Reckoner ). The most characteristic product of Greek mathematics may be

4756-426: 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 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

Almagest - Misplaced Pages Continue

4872-494: The Greek letters Α and Δ were used to mean 1 and 4 respectively, but because these look similar copyists sometimes wrote the wrong one. In Arabic manuscripts, there was confusion between for example 3 and 8 (ج and ح). (At least one translator also introduced errors. Gerard of Cremona , who translated an Arabic manuscript into Latin around 1175, put 300° for the latitude of several stars. He had apparently learned from Moors , who used

4988-414: The Hellenistic and early Roman periods , and much of the work represented by authors such as Euclid (fl. 300 BC), Archimedes (c. 287–212 BC), Apollonius (c. 240–190 BC), Hipparchus (c. 190–120 BC), and Ptolemy (c. 100–170 AD) was of a very advanced level and rarely mastered outside a small circle. Examples of applied mathematics around this time include the construction of analogue computers like

5104-467: 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 ,

5220-870: 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 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

5336-674: 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

5452-868: The Roman era include Diophantus (c. 214–298 AD), who wrote on polygonal numbers and a work in pre-modern algebra ( Arithmetica ), Pappus of Alexandria (c. 290–350 AD), who compiled many important results in the Collection , Theon of Alexandria (c. 335–405 AD) and his daughter Hypatia (c. 370–415 AD), who edited Ptolemy's Almagest and other works, and Eutocius of Ascalon ( c. 480–540 AD), who wrote commentaries on treatises by Archimedes and Apollonius. Although none of these mathematicians, save perhaps Diophantus, had notable original works, they are distinguished for their commentaries and expositions. These commentaries have preserved valuable extracts from works which have perished, or historical allusions which, in

5568-424: 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

5684-492: 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

5800-481: The Sun. Ptolemy's authority was preferred by most medieval Islamic and late medieval European astronomers. Ptolemy inherited from his Greek predecessors a geometrical toolbox and a partial set of models for predicting where the planets would appear in the sky. Apollonius of Perga ( c.  262  – c.  190 BC ) had introduced the deferent and epicycle and the eccentric deferent to astronomy. Hipparchus (2nd century BC) had crafted mathematical models of

5916-500: The absence of original documents, are precious because of their rarity. Most of the mathematical texts written in Greek survived through the copying of manuscripts over the centuries. While some fragments dating from antiquity have been found above all in Egypt , as a rule they do not add anything significant to our knowledge of Greek mathematics preserved in the manuscript tradition. Greek mathematics constitutes an important period in

SECTION 50

#1732765408530

6032-545: The attention of philosophers during the Classical period . Plato (c. 428–348 BC), the founder of the Platonic Academy , mentions mathematics in several of his dialogues. While not considered a mathematician, Plato seems to have been influenced by Pythagorean ideas about number and believed that the elements of matter could be broken down into geometric solids. He also believed that geometrical proportions bound

6148-563: 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

6264-511: 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

6380-473: The constellations should be outlined on a globe, but it is unclear exactly how he means this: should surrounding polygons be drawn or should the figures be sketched or even line figures be drawn? This is not stated. Although no line figures have survived from antiquity, the figures can be reconstructed on the basis of the descriptions in the star catalogue: The exact celestial coordinates of the figures' heads, feet, arms, wings and other body parts are recorded. It

6496-445: The coordinates were equatorial. Since Hipparchus' star catalogue has not survived in its original form, but was absorbed into the Almagest star catalogue (and heavily revised in the 265 years in between), the Almagest star catalogue is the oldest one in which complete tables of coordinates and magnitudes have come down to us. As mentioned, Ptolemy includes a star catalog containing 1022 stars. He says that he "observed as many stars as it

6612-479: 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 the sidereal system proposed by Cyril Fagan . The beginning of Aries

6728-430: The data of earlier astronomers, and labelled him "the most successful fraud in 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 at 9:54am the day prior. Herbert Lewis, who had reworked some of Ptolemy's calculations, agreed with Newton that "Ptolemy

6844-414: 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 the 2nd century BC, as well as into developing

6960-530: The dedication of George's work, and Regiomontanus's translation had the upper hand for over 100 years. During the 16th century, Guillaume Postel , who had been on an embassy to the Ottoman Empire , brought back Arabic disputations of the Almagest , such as the works of al-Kharaqī , Muntahā al-idrāk fī taqāsīm al-aflāk ("The Ultimate Grasp of the Divisions of Spheres", 1138–39). Commentaries on

7076-483: The early years of printing, there were considerable differences between various editions of the same text, as the process of transcription was highly personal. An example illustrating how the Syntaxis was organized is given below; it is a Latin edition printed in 1515 at Venice by Petrus Lichtenstein. The cosmology of the Syntaxis includes five main points, each of which is the subject of a chapter in Book I. What follows

SECTION 60

#1732765408530

7192-461: The eccentricity of the Earth's orbit . Sidereal astrology remedies this by assigning the zodiac sign approximately to 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

7308-406: 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 a complete list of the 36 Egyptian decans was placed among the hieroglyphs adorning

7424-416: 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

7540-405: 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

7656-550: 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

7772-404: The flourishing of Greek literature in the span of 800 to 600 BC, not much is known about Greek mathematics in this early period—nearly all of the information was passed down through later authors, beginning in the mid-4th century BC. Greek mathematics allegedly began with Thales of Miletus (c. 624–548 BC). Very little is known about his life, although it is generally agreed that he was one of

7888-419: The history of mathematics : fundamental in respect of geometry and for the idea of formal proof . Greek mathematicians also contributed to number theory , mathematical astronomy , combinatorics , mathematical physics , and, at times, approached ideas close to the integral calculus . Eudoxus of Cnidus developed a theory of proportion that bears resemblance to the modern theory of real numbers using

8004-593: 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

8120-424: The instigation of the Greek churchman Cardinal Bessarion . Around the same time, George of Trebizond made a full translation accompanied by a commentary that was as long as the original text. George's translation, done under the patronage of Pope Nicholas V , was intended to supplant the old translation. The new translation was a great improvement; the new commentary was not, and aroused criticism. The Pope declined

8236-929: The lack of original manuscripts, the dates for some Greek mathematicians are more certain than the dates of surviving Babylonian or Egyptian sources because a number of overlapping chronologies exist, though many dates remain uncertain. Netz (2011) has counted 144 ancient authors in the mathematical or exact sciences, from whom only 29 works are extant in Greek: Aristarchus , Autolycus , Philo of Byzantium , Biton , Apollonius , Archimedes , Euclid , Theodosius , Hypsicles , Athenaeus , Geminus , Heron , Apollodorus , Theon of Smyrna , Cleomedes , Nicomachus , Ptolemy , Gaudentius , Anatolius , Aristides Quintilian , Porphyry , Diophantus , Alypius , Damianus , Pappus , Serenus , Theon of Alexandria , Anthemius , and Eutocius . The following works are extant only in Arabic translations: Zodiac This

8352-517: 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 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

8468-765: The late 4th century BC, following Alexander the Great's conquest of the Eastern Mediterranean , Egypt , Mesopotamia , the Iranian plateau , Central Asia , and parts of India , leading to the spread of the Greek language and culture across these regions. Greek became the lingua franca of scholarship throughout the Hellenistic world, and the mathematics of the Classical period merged with Egyptian and Babylonian mathematics to give rise to Hellenistic mathematics. Greek mathematics reached its acme during

8584-522: The letter س (sin) for 300 (like the Hebrew ש (shin) ), but the manuscript he was translating came from the East, where س was used for 60, like the Hebrew ס (samekh) .) Even without the errors introduced by copyists, and even accounting for the fact that the longitudes are more appropriate for 58 AD than for 137 AD, the latitudes and longitudes are not fully accurate, with errors as great as large fractions of

8700-604: The medieval Byzantine and Islamic worlds, and in Western Europe through the Middle Ages and early Renaissance until Copernicus . It is also a key source of information about ancient Greek astronomy . Ptolemy set up a public inscription at Canopus, Egypt , in 147 or 148. N. T. Hamilton found that the version of Ptolemy's models set out in the Canopic Inscription was earlier than the version in

8816-463: 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

8932-500: 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

9048-479: The motion of the Sun and Moon. Hipparchus had some knowledge of Mesopotamian astronomy , and he felt that Greek models should match those of the Babylonians in accuracy. He was unable to create accurate models for the remaining five planets. The Syntaxis adopted Hipparchus' solar model, which consisted of a simple eccentric deferent. For the Moon, Ptolemy began with Hipparchus' epicycle-on-deferent, then added

9164-408: 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

9280-481: The newer models. As a result, the older texts ceased to be copied and were gradually lost. Much of what we know about the work of astronomers like Hipparchus comes from references in the Syntaxis . The first translations into Arabic were made in the 9th century, with two separate efforts, one sponsored by the caliph Al-Ma'mun , who received a copy as a condition of peace with the Byzantine emperor. Sahl ibn Bishr

9396-506: The observations were taken at 12:30pm. However, an explanation for this error was found in 1969. The overall quality of Claudius Ptolemy's scholarship and place as "one of the most outstanding scientists of antiquity" has been challenged by several modern writers, most prominently by Robert R. Newton in the 1977 book The Crime of Claudius Ptolemy , which asserted that the scholar fabricated his observations to fit his theories. Newton accused Ptolemy of systematically inventing data or doctoring

9512-424: 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

9628-477: 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 ) is the diminutive of zōon ( ζῷον , "animal"). The name reflects

9744-417: The physical constellations take up varying widths of the ecliptic, so the Sun is not in each constellation for 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

9860-468: 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

9976-595: 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 the zodiac is described in Ptolemy 's comprehensive 2nd century AD work,

10092-482: The recognized constellation figures. These were later absorbed into their surrounding constellations or in some cases used to form new constellations. Ptolemy assigned the following order to the planetary spheres , beginning with the innermost: Other classical writers suggested different sequences. Plato ( c.  427  – c.  347 BC ) placed the Sun second in order after the Moon. Martianus Capella (5th century AD) put Mercury and Venus in motion around

10208-614: The same as mine, although our reasons for this conclusion and our inferences from it differ radically." The Almagest under the Latin title Syntaxis mathematica , was edited by J. L. Heiberg in Claudii Ptolemaei opera quae exstant omnia , vols. 1.1 and 1.2 (1898, 1903). Three translations of the Almagest into English have been published. The first, by R. Catesby Taliaferro of St. John's College in Annapolis, Maryland ,

10324-504: 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

10440-515: 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

10556-573: 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

10672-454: 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

10788-460: The stars of a given zodiac constellation in the catalog fall in the 30-degree range designated by the same name (the so-called 'zodiac sign'). The ecliptic longitudes are about 26° lower than those of AD 2000 (the J2000 epoch). Ptolemy says that the ecliptic longitudes are for the beginning of the reign of Antoninus Pius (138 AD) and that he found that the longitudes had increased by 2° 40′ since

10904-405: 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

11020-573: The style of the Elements , the Spherics , arguably considered the first treatise in non-Euclidean geometry . Archimedes made use of a technique dependent on a form of proof by contradiction to reach answers to problems with an arbitrary degree of accuracy, while specifying the limits within which the answers lay. Known as the method of exhaustion , Archimedes employed it in several of his works, including an approximation to π ( Measurement of

11136-408: 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

11252-583: The superlative form of this (Greek: μεγίστη megístē , 'greatest') lies behind the Arabic name from which the English name Almagest derives. Written possibly around 150 CE the text survives as copies, the oldest being from the 9th century when Arabic scholars started to translate the text, which in turn have survived in copies from the 11th and 13th century. The Syntaxis Mathematica consists of thirteen sections, called books. As with many medieval manuscripts that were handcopied or, particularly, printed in

11368-470: The theory of conic sections , which was largely developed in the Hellenistic period , starting with the work of Menaechmus and perfected primarily under Apollonius in his work Conics . The methods employed in these works made no explicit use of algebra , nor trigonometry , the latter appearing around the time of Hipparchus . Ancient Greek mathematics was not limited to theoretical works but

11484-637: The time of Hipparchus which was 265 years earlier (Alm. VII, 2). But calculations show that his ecliptic longitudes correspond more closely to around the middle of the first century CE (+48 to +58). Since Tycho Brahe found this offset, astronomers and historians investigated this problem and suggested several causes: Subtracting the systematic error leaves other errors that cannot be explained by precession. Of these errors, about 18 to 20 are also found in Hipparchus' star catalogue (which can only be reconstructed incompletely). From this it can be concluded that

11600-501: 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 the first half of the 1st millennium BC . The zodiac draws on stars in earlier Babylonian star catalogues , such as

11716-577: 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

11832-399: The twelve constellations after which the twelve zodiac signs are named, the ecliptic intersects Ophiuchus , the bottom part of which interjects between Scorpio and Sagittarius. Occasionally this difference between 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

11948-564: The verb manthanein , "to learn". Strictly speaking, a máthēma could be any branch of learning, or anything learnt; however, since antiquity certain mathēmata (mainly arithmetic, geometry, astronomy, and harmonics) were granted special status. The origins of Greek mathematics are not well documented. The earliest advanced civilizations in Greece and Europe were the Minoan and later Mycenaean civilizations, both of which flourished during

12064-463: 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

12180-519: 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

12296-479: 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

12412-720: 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

12528-700: 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

12644-483: 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

12760-455: Was also used in other activities, such as business transactions and in land mensuration, as evidenced by extant texts where computational procedures and practical considerations took more of a central role. Although the earliest Greek mathematical texts that have been found were written after the Hellenistic period, most are considered to be copies of works written during and before the Hellenistic period. The two major sources are Despite

12876-532: Was an outrageous fraud", and that "all those results capable of statistical analysis point beyond question towards fraud and against accidental error". Although some have described the charges laid by Newton as "erudite and imposing", others have disagreed with the findings. Bernard R. Goldstein wrote, "Unfortunately, Newton’s arguments in support of these charges are marred by all manner of distortions, misunderstandings, and excesses of rhetoric due to an intensely polemical style." Owen Gingerich , while agreeing that

12992-415: 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

13108-773: Was included in volume 16 of the Great Books of the Western World in 1952. The second, by G. J. Toomer , Ptolemy's Almagest in 1984, with a second edition in 1998. The third was a partial translation by Bruce M. Perry in The Almagest: Introduction to the Mathematics of the Heavens in 2014. A direct French translation from the Greek text was published in two volumes in 1813 and 1816 by Nicholas Halma , including detailed historical comments in

13224-432: Was possible to perceive, even to the sixth magnitude". The ecliptic longitudes are given in terms of a zodiac sign and a number of degrees and fractions of a degree. The zodiac signs each represent exactly 30°, starting with Aries representing longitude 0° to 30°. The degrees are added to the lower limit of the 30-degree range to obtain the longitude. Unlike the situation with the zodiac of modern-day astrology , most of

13340-399: 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

13456-474: Was unable to translate many technical terms such as the Arabic Abrachir for Hipparchus. In the 13th century a Spanish version was produced, which was later translated under the patronage of Alfonso X . In the 15th century, a Greek version appeared in Western Europe. The German astronomer Johannes Müller (known as Regiomontanus , after his birthplace of Königsberg ) made an abridged Latin version at

#529470