The Almagest (/ˈælməˌdʒɛst/) is a 2nd-century Greek-language mathematical and astronomical treatise on the apparent motions of the stars and planetary paths, written by Claudius Ptolemy (c. AD 100 – c. 170). One of the most influential scientific texts of all time, its geocentric model was accepted for more than 1200 years from its origin in Hellenistic Alexandria, in the medieval Byzantine and Islamic worlds, and in Western Europe through the Middle Ages and early Renaissance until Copernicus.

The Almagest is the critical source of information on ancient Greek astronomy. It has also been valuable to students of mathematics because it documents the ancient Greek mathematician Hipparchus's work, which has been lost. Hipparchus wrote about trigonometry, but because his works appear to have been lost, mathematicians use Ptolemy's book as their source for Hipparchus's work and ancient Greek trigonometry in general.

Claudius Ptolemaeus, Almagestum, 1515.djvu&page=309
An edition in Latin of the Almagestum in 1515

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 the Almagest. Hence it cannot have been completed before about 150, a quarter-century after Ptolemy began observing.[1]

Geometric construction used by Hipparchus in his determination of the distances to the Sun and Moon


The work was originally titled "Μαθηματικὴ Σύνταξις" (Mathēmatikē Syntaxis) in Ancient Greek, and also called Syntaxis Mathematica or Almagestum in Latin. The treatise was later titled Hē Megalē Syntaxis (Ἡ Μεγάλη Σύνταξις, "The Great Treatise"; Latin: Magna Syntaxis), and the superlative form of this (Ancient Greek: μεγίστη, megiste, "greatest") lies behind the Arabic name al-majisṭī (المجسطي), from which the English name Almagest derives. The Arabic name is important due to the popularity of a Latin re-translation made in the 12th century from an Arabic translation, which would endure until original Greek copies resurfaced in the 15th century.



The Syntaxis Mathematica consists of thirteen sections, called books. As with many medieval manuscripts that were handcopied or, particularly, printed in 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.[2]

  • Book I contains an outline of Aristotle's cosmology: on the spherical form of the heavens, with the spherical Earth lying motionless as the center, with the fixed stars and the various planets revolving around the Earth. Then follows an explanation of chords with table of chords; observations of the obliquity of the ecliptic (the apparent path of the Sun through the stars); and an introduction to spherical trigonometry.
  • Book II covers problems associated with the daily motion attributed to the heavens, namely risings and settings of celestial objects, the length of daylight, the determination of latitude, the points at which the Sun is vertical, the shadows of the gnomon at the equinoxes and solstices, and other observations that change with the spectator's position. There is also a study of the angles made by the ecliptic with the vertical, with tables.
  • Book III covers the length of the year, and the motion of the Sun. Ptolemy explains Hipparchus' discovery of the precession of the equinoxes and begins explaining the theory of epicycles.
  • Books IV and V cover the motion of the Moon, lunar parallax, the motion of the lunar apogee, and the sizes and distances of the Sun and Moon relative to the Earth.
  • Book VI covers solar and lunar eclipses.
  • Books VII and VIII cover the motions of the fixed stars, including precession of the equinoxes. They also contain a star catalogue of 1022 stars, described by their positions in the constellations, together with ecliptic longitude and latitude. Ptolemy states that the longitudes (which increase due to precession) are for the beginning of the reign of Antoninus Pius (138 AD), whereas the latitudes do not change with time. (But see below, under The star catalog.) The constellations north of the zodiac and the northern zodiac constellations (Aries through Virgo) are in the table at the end of Book VII, while the rest are in the table at the beginning of Book VIII. The brightest stars were marked first magnitude (m = 1), while the faintest visible to the naked eye were sixth magnitude (m = 6). Each numerical magnitude was considered twice the brightness of the following one, which is a logarithmic scale. (The ratio was subjective as no photodetectors existed.) This system is believed to have originated with Hipparchus. The stellar positions too are of Hipparchan origin, despite Ptolemy's claim to the contrary.
Ptolemy identified 48 constellations: The 12 of the zodiac, 21 to the north of the zodiac, and 15 to the south.[3]
  • Book IX addresses general issues associated with creating models for the five naked eye planets, and the motion of Mercury.
  • Book X covers the motions of Venus and Mars.
  • Book XI covers the motions of Jupiter and Saturn.
  • Book XII covers stations and retrograde motion, which occurs when planets appear to pause, then briefly reverse their motion against the background of the zodiac. Ptolemy understood these terms to apply to Mercury and Venus as well as the outer planets.
  • Book XIII covers motion in latitude, that is, the deviation of planets from the ecliptic.

Ptolemy's cosmos

The cosmology of the Syntaxis includes five main points, each of which is the subject of a chapter in Book I. What follows is a close paraphrase of Ptolemy's own words from Toomer's translation.[4]

  • The celestial realm is spherical, and moves as a sphere.
  • The Earth is a sphere.
  • The Earth is at the center of the cosmos.
  • The Earth, in relation to the distance of the fixed stars, has no appreciable size and must be treated as a mathematical point.[5]
  • The Earth does not move.

The star catalog

As mentioned, Ptolemy includes a star catalog containing 1022 stars. He says that he "observed as many stars as it was possible to perceive, even to the sixth magnitude", and that the ecliptic longitudes are for the beginning of the reign of Antoninus Pius (138 AD). But calculations show that his ecliptic longitudes correspond more closely to around 58 AD. He states that he found that the longitudes had increased by 2° 40′ since the time of Hipparchos. This is the amount of axial precession that occurred between the time of Hipparchos and 58 AD. It appears therefore that Ptolemy took a star catalog of Hipparchos and simply added 2° 40′ to the longitudes.[6]

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, 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 the letter "sin" for 300, but the manuscript he was translating came from the East, where "sin" was used for 60.)[7]

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 very accurate, with errors of large fractions of 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.[8] A series of stars in Centaurus are off by a couple 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.[9]

Ptolemy's planetary model

16th-century representation of Ptolemy's geocentric model in Peter Apian's Cosmographia, 1524

Ptolemy assigned the following order to the planetary spheres, beginning with the innermost:

  1. Moon
  2. Mercury
  3. Venus
  4. Sun
  5. Mars
  6. Jupiter
  7. Saturn
  8. Sphere of fixed stars

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 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 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 a device that historians of astronomy refer to as a "crank mechanism":[10] 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 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 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.

Ptolemy 16century
Ptolemy's Almagest became an authoritative work for many centuries.

The first translations into Arabic were made in the 9th century, with two separate efforts, one sponsored by the caliph Al-Ma'mun. Sahl ibn Bishr is thought to be the first Arabic translator. By this time, the Syntaxis was lost in Western Europe, or only dimly remembered. 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 by Gerard of Cremona from the Arabic (finished in 1175).[11] Gerard translated the Arabic text while working at the Toledo School of Translators, although he was unable to translate many technical terms such as the Arabic Abrachir for Hipparchus. In the 12th century a Spanish version was produced, which was later translated under the patronage of Alfonso X.

Almagest 1.jpeg
Picture of George of Trebizond's Latin translation of the Syntaxis Mathematica or Almagest

In the 15th century, a Greek version appeared in Western Europe. The German astronomer Johannes Müller (known, from his birthplace of Königsberg, as Regiomontanus) made an abridged Latin version at the instigation of the Greek churchman Johannes, 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 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", 1138/9).[12]

Commentaries on the Syntaxis were written by Theon of Alexandria (extant), Pappus of Alexandria (only fragments survive), and Ammonius Hermiae (lost).

Modern editions

The Almagest 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, 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.[4] The third was a partial translation by Bruce M. Perry in The Almagest: Introduction to the Mathematics of the Heavens in 2014.[13]

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 a 69-page preface. The scanned books are available in full at the Gallica French national library.[14][15]


Ptolemy's cataloque of stars.djvu&page=9

Ptolemy's catalogue of stars; a revision of the Almagest by Christian Heinrich Friedrich Peters and Edward Ball Knobel, 1915

Epytoma Ioannis de Monte Regio in Almagestum Ptolomei.djvu&page=9

Epytoma Ioannis de Monte Regio in Almagestum Ptolomei, Latin, 1496

Claudius Ptolemaeus, Almagestum, 1515.djvu&page=2

Almagestum, Latin, 1515

See also


  1. ^ NT Hamilton, N. M. Swerdlow, G. J. Toomer. "The Canobic Inscription: Ptolemy's Earliest Work". In Berggren and Goldstein, eds., From Ancient Omens to Statistical Mechanics. Copenhagen: University Library, 1987.
  2. ^ "Almagestum (1515)". Universität Wien. Retrieved 31 May 2014.
  3. ^ Ley, Willy (December 1963). "The Names of the Constellations". For Your Information. Galaxy Science Fiction. pp. 90–99.
  4. ^ a b Toomer, G. J. (1998), Ptolemy's Almagest (PDF), Princeton University Press, ISBN 0-691-00260-6
  5. ^ Ptolemy. Almagest., Book I, Chapter 5.
  6. ^ Christian Peters and Edward Knobel (1915). Ptolemy's Catalogue of the Stars – A Revision of the Almagest. p. 15.
  7. ^ Peters and Knobel, pp. 9-14.
  8. ^ Peters and Knobel, p. 14.
  9. ^ Peters and Knobel, p. 112.
  10. ^ Michael Hoskin. The Cambridge Concise History of Astronomy. Chapter 2, page 44.
  11. ^ See p. 3 of Introduction of the Toomis translation.
  12. ^ Islamic science and the making of European Renaissance, by George Saliba, p. 218 ISBN 978-0-262-19557-7
  13. ^ Perry, Bruce M. (2014), The Almagest: Introduction to the Mathematics of the Heavens, Green Lion Press, ISBN 978-188800943-9
  14. ^ Halma, Nicolas (1813). Composition mathématique de Claude Ptolémée, traduite pour la première fois du grec en français, sur les manuscrits originaux de la bibliothèque impériale de Paris, tome 1 (in French). Paris: J. Hermann. p. 608.
  15. ^ Halma, Nicolas (1816). Composition mathématique de Claude Ptolémée, ou astronomie ancienne, traduite pour la première fois du grec en français sur les manuscrits de la bibliothèque du roi, tome 2 (in French). Paris: H. Grand. p. 524.


  • James Evans (1998) The History and Practice of Ancient Astronomy, Oxford University Press ISBN 0-19-509539-1
  • Michael Hoskin (1999) The Cambridge Concise History of Astronomy, Cambridge University Press ISBN 0-521-57291-6
  • Olaf Pedersen (1974) A Survey of the Almagest, Odense University Press ISBN 87-7492-087-1.
  • Alexander Jones & Olaf Pedersen (2011) A Survey of the Almagest, Springer ISBN 9780387848259
  • Olaf Pedersen (1993) Early Physics and Astronomy: A Historical Introduction, 2nd edition, Cambridge University Press ISBN 0-521-40340-5

External links

Abu al-Wafa' Buzjani

Abū al-Wafāʾ, Muḥammad ibn Muḥammad ibn Yaḥyā ibn Ismāʿīl ibn al-ʿAbbās al-Būzjānī or Abū al-Wafā Būzhjānī (Persian: ابوالوفا بوزجانی or بوژگانی‎) (10 June 940 – 15 July 998) was a Persian mathematician and astronomer who worked in Baghdad. He made important innovations in spherical trigonometry, and his work on arithmetics for businessmen contains the first instance of using negative numbers in a medieval Islamic text.

He is also credited with compiling the tables of sines and tangents at 15 ' intervals. He also introduced the secant and cosecant functions, as well studied the interrelations between the six trigonometric lines associated with an arc. His Almagest was widely read by medieval Arabic astronomers in the centuries after his death. He is known to have written several other books that have not survived.

Agrippa (astronomer)

Agrippa (Greek: Ἀγρίππας; fl. 92 AD) was a Greek astronomer. The only thing that is known about him regards an astronomical observation that he made in 92 AD, which is cited by Ptolemy (Almagest, VII, 3). Ptolemy writes that in the twelfth year of the reign of Domitian, on the seventh day of the Bithynian month Metrous, Agrippa observed the occultation of a part of the Pleiades by the southernmost part of the Moon.

The purpose of Agrippa's observation was probably to check the precession of the equinoxes, which was discovered by Hipparchus.

The lunar crater Agrippa is named after him.


Abū Muḥammad 'Abd al-Jabbār al-Kharaqī, also Al-Kharaqī was a Persian astronomer and mathematician of the 12th century, born in Kharaq near Merv. He was in the service of Sultan Sanjar at the Persian Court. Al-Kharaqī challenged the astronomical theory of Ptolemy in the Almagest, and established an alternative theory of the spheres, imagining huge material spheres in which the planets moved inside tubes.During his travels to the Ottoman Empire in 1536, Guillaume Postel acquired an astronomical work by al-Kharaqī, Muntahā al-idrāk fī taqāsīm al-aflāk ("The Ultimate Grassp of the Divisions of Spheres"), annotated it, and brought it back to Europe.Al-Kharaqī also wrote mathematical treatises, now lost, Al-Risala al-Shāmila ("Comprehensive Treatise") and Al-Risala al-Maghribiyya ("The North African Treatise", related to the calculus of dirham and dinar).

Almagest (journal)

Almagest is a peer-reviewed academic journal that publishes contributions evaluating scientific developments. Almagest addresses the philosophical assumptions behind scientific ideas and developments and the reciprocal influence between historical context and these phenomena. The journal is abstracted in the Philosophy Research Index, STEP - Science and Technology in the European Periphery and LibTOC.

Ancient Greek astronomy

Greek astronomy is astronomy written in the Greek language in classical antiquity. Greek astronomy is understood to include the ancient Greek, Hellenistic, Greco-Roman, and Late Antiquity eras. It is not limited geographically to Greece or to ethnic Greeks, as the Greek language had become the language of scholarship throughout the Hellenistic world following the conquests of Alexander. This phase of Greek astronomy is also known as Hellenistic astronomy, while the pre-Hellenistic phase is known as Classical Greek astronomy. During the Hellenistic and Roman periods, much of the Greek and non-Greek astronomers working in the Greek tradition studied at the Musaeum and the Library of Alexandria in Ptolemaic Egypt.

The development of astronomy by the Greek and Hellenistic astronomers is considered, by historians, to be a major phase in the history of astronomy. Greek astronomy is characterized from the start by seeking a rational, physical explanation for celestial phenomena. Most of the constellations of the northern hemisphere derive from Greek astronomy, as are the names of many stars, asteroids, and planets. It was influenced by Egyptian and especially Babylonian astronomy; in turn, it influenced Indian, Arabic-Islamic and Western European astronomy.

Book of Fixed Stars

The Book of Fixed Stars (Arabic: كتاب صور الكواكب‎ kitāb suwar al-kawākib) is an astronomical text written by Abd al-Rahman al-Sufi (Azophi) around 964. The book was written in Arabic, although the author himself was Persian. It was an attempt to create a synthesis of the comprehensive star catalogue in Ptolemy’s Almagest (books VII and VIII) with the indigenous Arabic astronomical traditions on the constellations.

The book was thoroughly illustrated along with observations and descriptions of the stars, their positions (copied from Ptolemy's Almagest with the longitudes increased by 12° 42' to account for the precession), their magnitudes (brightness) and their color. His results, as in Ptolemy's Almagest, were set out constellation by constellation. For each constellation, he provided two drawings, one from the outside of a celestial globe, and the other from the inside.

The work was highly influential and survives in numerous manuscripts and translations. The oldest manuscript, kept in the Bodleian Library, dates to 1009 and is the work of the author's son. There is a thirteenth-century copy in the British Library (Or. 5323).

He has the earliest known descriptions and illustrations of what he called "a little cloud", which is actually the Andromeda Galaxy. He mentions it as lying before the mouth of a Big Fish, an Arabic constellation. This "cloud" was apparently commonly known to the Isfahan astronomers, very probably before 905.

The first recorded mention of the Large Magellanic Cloud was also given in the Book of Fixed Stars. These were the first galaxies other than the Milky Way to be observed from Earth. The Great Andromeda Nebula he observed was also the first true nebula to be observed, as distinct from a star cluster.He probably also cataloged the Omicron Velorum star cluster as a "nebulous star", and an additional "nebulous object" in Vulpecula, a cluster now variously known as Al-Sufi's Cluster, the "Coathanger asterism", Brocchi's Cluster or Collinder 399. Moreover, he mentions the two Magellanic Clouds, and that they are not visible from Iraq nor Najd, but visible from Tihama, and that they are called al-Baqar (the cows).

There has not been a published English translation of the book, though it was translated into French by Hans Schjellerup in 1874. As of March 2012, one is in preparation by Ihsan Hafez of James Cook University, Townsville.

Callippic cycle

For astronomy and calendar studies, the Callippic cycle (or Calippic) is a particular approximate common multiple of the year (specifically the tropical year) and the synodic month, that was proposed by Callippus during 330 BC. It is a period of 76 years, as an improvement of the 19-year Metonic cycle.

A century before Callippus, Meton had discovered the cycle in which 19 years equals 235 lunations. If we assume a year is about ​365 1⁄4 days, 19 years total about 6940 days, which exceeds 235 lunations by almost a third of a day, and 19 tropical years by four tenths of a day. It implicitly gave the solar year a duration of ​6940⁄19 = 365 + ​5⁄19 = 365 + ​1⁄4 + ​1⁄76 days = 365 d 6 h 18 min 56 s. Callippus accepted the 19-year cycle, but held that the duration of the year was more closely ​365 1⁄4 days (= 365 d 6 h), so he multiplied the 19-year cycle by 4 to obtain an integer number of days, and then omitted 1 day from the last 19-year cycle. Thus, he computed a cycle of 76 years that consists of 940 lunations and 27,759 days, which has been named the Callippic cycle after him.Although the cycle's error has been computed as one full day in 553 years, or 4.95 parts per million, in actuality 27,759 days in 76 years has a mean year of exactly ​365 1⁄4 days, which relative to the mean northward equinoctial year is about 11 minutes too long per year, in other words the cycle drifts another day late per ​130 10⁄11 years, which is considerably worse than the drift of the unrounded Metonic cycle. If the Callippic cycle is considered as closer to its unrounded length of ​27,758 3⁄4 days (based on 940 lunations) then its accuracy is essentially the same as the unrounded Metonic cycle (within a few seconds per year). If it is considered as 940 lunations less one day then the Callippic mean year will be shortened by ​1⁄76 of a day (18 minutes 57 seconds), making it grossly too short, and it will also grossly drift ahead with respect to the mean lunar cycle at the rate of ​1⁄940 of a day (1 minute 31 seconds) per lunar month. If the cycle length is truncated to 27,758 days then the mean year is 365 days 5 hours 41 minutes 3 seconds, or almost 8 minutes too brief per year, and it will drift ahead of the mean lunar cycle by about ​(​3⁄4)⁄940 day (1 minute 9 seconds) per lunar month. Altogether, the purported accuracy of this cycle is not impressive, but it is of historical interest.The first year of the first Callippic cycle began at the summer solstice of 330 BC (28 June in the proleptic Julian calendar), and was subsequently used by later astronomers. In Ptolemy's Almagest, for example, he cites (Almagest VII 3, H25) observations by Timocharis during the 47th year of the first Callippic cycle (283 BC), when on the eighth of Anthesterion, the Pleiades star cluster was occulted by the Moon.The Callippic calendar originally used the names of months from the Attic calendar. Later astronomers, such as Hipparchus, preferred other calendars, including the ancient Egyptian calendar. Also Hipparchus invented his own Hipparchic calendar cycle as an improvement upon the Callippic cycle. Ptolemy's Almagest provided some conversions between the Callippic and Egyptian calendars, such as that Anthesterion 8, 47th year of the first Callippic period was equivalent to day 29 of the month of Athyr, during year 465 of Nabonassar. However, the original, complete form of the Callippic calendar is no longer known.


A constellation is a group of stars that forms an imaginary outline or pattern on the celestial sphere, typically representing an animal, mythological person or creature, a god, or an inanimate object.The origins of the earliest constellations likely go back to prehistory. People used them to relate stories of their beliefs, experiences, creation, or mythology. Different cultures and countries adopted their own constellations, some of which lasted into the early 20th century before today's constellations were internationally recognized. Adoption of constellations has changed significantly over time. Many have changed in size or shape. Some became popular, only to drop into obscurity. Others were limited to single cultures or nations.

The 48 traditional Western constellations are Greek. They are given in Aratus' work Phenomena and Ptolemy's Almagest, though their origin probably predates these works by several centuries. Constellations in the far southern sky were added from the 15th century until the mid-18th century when European explorers began traveling to the Southern Hemisphere. Twelve ancient constellations belong to the zodiac (straddling the ecliptic, which the Sun, Moon, and planets all traverse). The origins of the zodiac remain historically uncertain; its astrological divisions became prominent c. 400 BC in Babylonian or Chaldean astronomy, probably dates back to prehistory.

In 1928, the International Astronomical Union (IAU) formally accepted 88 modern constellations, with contiguous boundaries that together cover the entire celestial sphere. Any given point in a celestial coordinate system lies in one of the modern constellations. Some astronomical naming systems include the constellation where a given celestial object is found to convey its approximate location in the sky. The Flamsteed designation of a star, for example, consists of a number and the genitive form of the constellation name.

Other star patterns or groups called asterisms are not constellations per se but are used by observers to navigate the night sky. Asterisms often refer to several stars within a constellation or may share stars with several constellations. Examples include the Pleiades and Hyades within the constellation Taurus and the False Cross split between the southern constellations Carina and Vela, or Venus' Mirror in the constellation of Orion.

Gerald J. Toomer

Gerald James Toomer (born 23 November 1934) is a historian of astronomy and mathematics who has written numerous books and papers on ancient Greek and medieval Islamic astronomy. In particular, he translated Ptolemy's Almagest into English.

Formerly a fellow of Corpus Christi College, Cambridge University, he moved to Brown University as a special student in 1959 to study "the history of mathematics in antiquity and the transmission of these systems through Arabic into medieval Europe." He joined the History of Mathematics department in 1963, became an associate professor in 1965, and was the chairman from 1980 to 1986.

Gerard of Cremona

Gerard of Cremona (Latin: Gerardus Cremonensis; c. 1114 – 1187) was an Italian translator of scientific books from Arabic into Latin. He worked in Toledo, Kingdom of Castile and obtained the Arabic books in the libraries at Toledo. Some of the books had been originally written in Greek and were unavailable in Greek or Latin in Europe at the time. Gerard of Cremona is the most important translator among the Toledo School of Translators who invigorated medieval Europe in the twelfth century by transmitting the Arab's and ancient Greek's knowledge in astronomy, medicine and other sciences, by making the knowledge available in the Latin language. One of Gerard's most famous translations is of Ptolemy's Almagest from Arabic texts found in Toledo.

Confusingly there appear to have been two translators of Arabic text into Latin known as Gerard of Cremona, one active in the 12th century who concentrated on astronomy and other scientific works, the other active in the 13th century who concentrated on medical works.


Hipparchus of Nicaea (; Greek: Ἵππαρχος, Hipparkhos; c. 190 – c. 120 BC) was a Greek astronomer, geographer, and mathematician. He is considered the founder of trigonometry but is most famous for his incidental discovery of precession of the equinoxes.Hipparchus was born in Nicaea, Bithynia (now İznik, Turkey), and probably died on the island of Rhodes. He is known to have been a working astronomer at least from 162 to 127 BC. Hipparchus is considered the greatest ancient astronomical observer and, by some, the greatest overall astronomer of antiquity. He was the first whose quantitative and accurate models for the motion of the Sun and Moon survive. For this he certainly made use of the observations and perhaps the mathematical techniques accumulated over centuries by the Babylonians and by Meton of Athens (5th century BC), Timocharis, Aristyllus, Aristarchus of Samos and Eratosthenes, among others. He developed trigonometry and constructed trigonometric tables, and he solved several problems of spherical trigonometry. With his solar and lunar theories and his trigonometry, he may have been the first to develop a reliable method to predict solar eclipses. His other reputed achievements include the discovery and measurement of Earth's precession, the compilation of the first comprehensive star catalog of the western world, and possibly the invention of the astrolabe, also of the armillary sphere, which he used during the creation of much of the star catalogue.

History of science in the Renaissance

During the Renaissance, great advances occurred in geography, astronomy, chemistry, physics, mathematics, manufacturing, anatomy and engineering. The rediscovery of ancient scientific texts was accelerated after the Fall of Constantinople in 1453, and the invention of printing democratized learning and allowed a faster propagation of new ideas. But, at least in its initial period, some see the Renaissance as one of scientific backwardness. Historians like George Sarton and Lynn Thorndike have criticized how the Renaissance affected science, arguing that progress was slowed for some amount of time. Humanists favored human-centered subjects like politics and history over study of natural philosophy or applied mathematics. Others have focused on the positive influence of the Renaissance, pointing to factors like the rediscovery of lost or obscure texts and the increased emphasis on the study of language and the correct reading of texts.

Marie Boas Hall coined the term Scientific Renaissance to designate the early phase of the Scientific Revolution, 1450–1630. More recently, Peter Dear has argued for a two-phase model of early modern science: a Scientific Renaissance of the 15th and 16th centuries, focused on the restoration of the natural knowledge of the ancients; and a Scientific Revolution of the 17th century, when scientists shifted from recovery to innovation.


Hypatia (born c. 350–370; died 415 AD) was a Hellenistic Neoplatonist philosopher, astronomer, and mathematician, who lived in Alexandria, Egypt, then part of the Eastern Roman Empire. She was a prominent thinker of the Neoplatonic school in Alexandria, where she taught philosophy and astronomy. She is the first female mathematician whose life is reasonably well recorded. Hypatia was renowned in her own lifetime as a great teacher and a wise counselor. She is known to have written a commentary on Diophantus's thirteen-volume Arithmetica, which may survive in part, having been interpolated into Diophantus's original text, and another commentary on Apollonius of Perga's treatise on conic sections, which has not survived. Many modern scholars also believe that Hypatia may have edited the surviving text of Ptolemy's Almagest, based on the title of her father Theon's commentary on Book III of the Almagest.

Hypatia is known to have constructed astrolabes and hydrometers, but did not invent either of these, which were both in use long before she was born. Although she herself was a pagan, she was tolerant towards Christians and taught many Christian students, including Synesius, the future bishop of Ptolemais. Ancient sources record that Hypatia was widely beloved by pagans and Christians alike and that she established great influence with the political elite in Alexandria. Towards the end of her life, Hypatia advised Orestes, the Roman prefect of Alexandria, who was in the midst of a political feud with Cyril, the bishop of Alexandria. Rumors spread accusing her of preventing Orestes from reconciling with Cyril and, in March 415 AD, she was murdered by a mob of Christians led by a lector named Peter.Hypatia's death shocked the empire and transformed her into a "martyr for philosophy", leading future Neoplatonists such as Damascius to become increasingly fervent in their opposition to Christianity. During the Middle Ages, Hypatia was co-opted as a symbol of Christian virtue and scholars believe she was part of the basis for the legend of Saint Catherine of Alexandria. During the Age of Enlightenment, she became a symbol of opposition to Catholicism. In the nineteenth century, European literature, especially Charles Kingsley's 1853 novel Hypatia, romanticized her as "the last of the Hellenes". In the twentieth century, Hypatia became seen as an icon for women's rights and a precursor to the feminist movement. Since the late twentieth century, some portrayals have associated Hypatia's death with the destruction of the Library of Alexandria, despite the historical fact that the library no longer existed during Hypatia's lifetime.

Ishaq ibn Hunayn

Abū Yaʿqūb Isḥāq ibn Ḥunayn (Arabic: إسحاق بن حنين‎) (c. 830 Baghdad, – c. 910-1) was an influential Arab physician and translator, known for writing the first biography of physicians in the Arabic language. He is also known for his translations of Euclid's Elements and Ptolemy's Almagest. He is the son of the famous translator Hunayn Ibn Ishaq.

Jabir ibn Aflah

Abū Muḥammad Jābir ibn Aflaḥ (Arabic: أبو محمد جابر بن أفلح‎, Latin: Geber/Gebir; 1100–1150) was an Arab Muslim astronomer and mathematician from Seville, who was active in 12th century al-Andalus. His work Iṣlāḥ al-Majisṭi (Correction of the Almagest) influenced Islamic, Jewish, and Christian astronomers.


Claudius Ptolemy (; Koine Greek: Κλαύδιος Πτολεμαῖος, Klaúdios Ptolemaîos [kláwdios ptolɛmɛ́os]; Latin: Claudius Ptolemaeus; c. AD 100 – c.  170) was a Greco-Roman mathematician, astronomer, geographer and astrologer. He lived in the city of Alexandria in the Roman province of Egypt, wrote in Koine Greek, and held Roman citizenship. The 14th-century astronomer Theodore Meliteniotes gave his birthplace as the prominent Greek city Ptolemais Hermiou (Greek: Πτολεμαΐς ‘Ερμείου) in the Thebaid (Greek: Θηβαΐδα [Θηβαΐς]). This attestation is quite late, however, and, according to Gerald Toomer, the translator of his Almagest into English, there is no reason to suppose he ever lived anywhere other than Alexandria. He died there around AD 168.Ptolemy wrote several scientific treatises, three of which were of importance to later Byzantine, Islamic and European science. The first is the astronomical treatise now known as the Almagest, although it was originally entitled the Mathematical Treatise (Μαθηματικὴ Σύνταξις, Mathēmatikē Syntaxis) and then known as the Great Treatise (Ἡ Μεγάλη Σύνταξις, Hē Megálē Syntaxis). The second is the Geography, which is a thorough discussion of the geographic knowledge of the Greco-Roman world. The third is the astrological treatise in which he attempted to adapt horoscopic astrology to the Aristotelian natural philosophy of his day. This is sometimes known as the Apotelesmatika (Ἀποτελεσματικά) but more commonly known as the Tetrabiblos from the Greek (Τετράβιβλος) meaning "Four Books" or by the Latin Quadripartitum.

Theon of Alexandria

Theon of Alexandria (; Ancient Greek: Θέων ὁ Ἀλεξανδρεύς; c. AD 335 – c. 405) was a Greek scholar and mathematician who lived in Alexandria, Egypt. He edited and arranged Euclid's Elements and wrote commentaries on works by Euclid and Ptolemy. His daughter Hypatia also won fame as a mathematician.

Triquetrum (astronomy)

The triquetrum (derived from the Latin tri- ["three"] and quetrum ["cornered"]) was the medieval name for an ancient astronomical instrument first described by Ptolemy (c. 90–c. 168) in the Almagest (V. 12). Also known as Parallactic Rulers, it was used for determining altitudes of heavenly bodies. Ptolemy calls it a "parallactic instrument" and seems to have used it to determine the zenith distance and parallax of the Moon.

Tusi couple

The Tusi couple is a mathematical device in which a small circle rotates inside a larger circle twice the diameter of the smaller circle. Rotations of the circles cause a point on the circumference of the smaller circle to oscillate back and forth in linear motion along a diameter of the larger circle. The Tusi couple is a 2-cusped hypocycloid.

The couple was first proposed by the 13th-century Persian astronomer and mathematician Nasir al-Din al-Tusi in his 1247 Tahrir al-Majisti (Commentary on the Almagest) as a solution for the latitudinal motion of the inferior planets, and later used extensively as a substitute for the equant introduced over a thousand years earlier in Ptolemy's Almagest.

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