The Almagest // 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, it canonized a geocentric model of the Universe that 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. 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 the Almagest. Hence the Almagest could not have been completed before about 150, a quarter-century after Ptolemy began observing. [ pages needed ]
The work was originally titled "Μαθηματικὴ Σύνταξις" (Mathēmatikē Syntaxis) in Ancient Greek, and also called Syntaxis Mathematica 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 translation known as Almagestum 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.
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.
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.However, the figure he used seems to have been based on Hipparchos' 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 Hipparchos' 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, 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 (like the Hebrew "shin"), but the manuscript he was translating came from the East, where "sin" was used for 60, like the Hebrew "samech".)
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.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.
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 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":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.
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 is thought to be the first Arabic translator.
No Latin translation was made in the Ancient Rome nor the Medieval West 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 by Gerard of Cremona from the Arabic (finished in 1175).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 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, 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.[ citation needed ] The Pope declined the dedication of George's work,[ citation needed ] 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).
Commentaries on the Syntaxis were written by Theon of Alexandria (extant), Pappus of Alexandria (only fragments survive), and Ammonius Hermiae (lost).
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, 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 a 69-page preface. The scanned books are available in full at the Gallica French national library.
Around AD 150, Ptolemy wrote his great handbook of astronomy called Mathematike Syntaxis...
Hipparchus of Nicaea 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, and probably died on the island of Rhodes, Greece. He is known to have been a working astronomer between 162 and 127 BC.
Claudius Ptolemy was a mathematician, astronomer, geographer, and astrologer who wrote about a dozen scientific treatises, three of which were of importance to later Byzantine, Islamic, and Western European science. The first is the astronomical treatise now known as the Almagest, although it was originally entitled the Mathēmatikē Syntaxis, and later known as The Greatest Treatise. 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 Apotelesmatiká but more commonly known as the Tetrábiblos, from the Koine Greek meaning "Four Books," or by its Latin equivalent Quadripartitum.
The zodiac is an area of the sky that extends approximately 8° north or south of the ecliptic, the apparent path of the Sun across the celestial sphere over the course of the year. The paths of the Moon and visible planets are also within the belt of the zodiac.
Eudoxus of Cnidus was an ancient Greek astronomer, mathematician, scholar, and student of Archytas and Plato. All of his works are lost, though some fragments are preserved in Hipparchus' commentary on Aratus's poem on astronomy. Sphaerics by Theodosius of Bithynia may be based on a work by Eudoxus.
In astronomy, axial precession is a gravity-induced, slow, and continuous change in the orientation of an astronomical body's rotational axis. In particular, it can refer to the gradual shift in the orientation of Earth's axis of rotation in a cycle of approximately 26,000 years. This is similar to the precession of a spinning top, with the axis tracing out a pair of cones joined at their apices. The term "precession" typically refers only to this largest part of the motion; other changes in the alignment of Earth's axis—nutation and polar motion—are much smaller in magnitude.
In astronomy, the geocentric model is a superseded description of the Universe with Earth at the center. Under the geocentric model, the Sun, Moon, stars, and planets all orbit Earth. The geocentric model was the predominant description of the cosmos in many ancient civilizations, such as those of Aristotle in Classical Greece and Ptolemy in Roman Egypt.
In the Hipparchian, Ptolemaic, and Copernican systems of astronomy, the epicycle was a geometric model used to explain the variations in speed and direction of the apparent motion of the Moon, Sun, and planets. In particular it explained the apparent retrograde motion of the five planets known at the time. Secondarily, it also explained changes in the apparent distances of the planets from the Earth.
Timocharis of Alexandria was a Greek astronomer and philosopher. Likely born in Alexandria, he was a contemporary of Euclid.
The celestial spheres, or celestial orbs, were the fundamental entities of the cosmological models developed by Plato, Eudoxus, Aristotle, Ptolemy, Copernicus, and others. In these celestial models, the apparent motions of the fixed stars and planets are accounted for by treating them as embedded in rotating spheres made of an aetherial, transparent fifth element (quintessence), like jewels set in orbs. Since it was believed that the fixed stars did not change their positions relative to one another, it was argued that they must be on the surface of a single starry sphere.
Equant is a mathematical concept developed by Claudius Ptolemy in the 2nd century AD to account for the observed motion of the planets. The equant is used to explain the observed speed change in different stages of the planetary orbit. This planetary concept allowed Ptolemy to keep the theory of uniform circular motion alive by stating that the path of heavenly bodies was uniform around one point and circular around another point.
The fixed stars compose the background of astronomical objects that appear not to move relative to each other in the night sky compared to the foreground of Solar System objects that do. Generally, the fixed stars are taken to include all stars other than the Sun. Nebulae and other deep-sky objects may also be counted among the fixed stars.
The term Great Year has two major meanings. It is defined by scientific astronomy as "The period of one complete cycle of the equinoxes around the ecliptic, or about 25,800 years". A more precise figure of 25,772 years is currently accepted. The position of the Earth's axis in the northern night sky currently almost aligns with the star Polaris, the North Star. This is a passing coincidence and has not been so in the past and will not be so again until a Great Year has passed.
The Copernican Revolution was the paradigm shift from the Ptolemaic model of the heavens, which described the cosmos as having Earth stationary at the center of the universe, to the heliocentric model with the Sun at the center of the Solar System. This revolution consisted of two phases; the first being extremely mathematical in nature and the second phase starting in 1610 with the publication of a pamphlet by Galileo. Beginning with the publication of Nicolaus Copernicus’s De revolutionibus orbium coelestium, contributions to the “revolution” continued until finally ending with Isaac Newton’s work over a century later.
Nur ad-Din al-Bitruji was an Iberian-Arab astronomer and a Qadi in al-Andalus. Al-Biṭrūjī was the first astronomer to present a non-Ptolemaic astronomical system as an alternative to Ptolemy's models, with the planets borne by geocentric spheres. Another original aspect of his system was that he proposed a physical cause of celestial motions. His alternative system spread through most of Europe during the 13th century.
Trepidation, in now-obsolete medieval theories of astronomy, refers to hypothetical oscillation in the precession of the equinoxes. The theory was popular from the 9th to the 16th centuries.
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 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.
Early study of triangles can be traced to the 2nd millennium BC, in Egyptian mathematics and Babylonian mathematics. Trigonometry was also prevalent in Kushite mathematics. Systematic study of trigonometric functions began in Hellenistic mathematics, reaching India as part of Hellenistic astronomy. In Indian astronomy, the study of trigonometric functions flourished in the Gupta period, especially due to Aryabhata, who discovered the sine function. During the Middle Ages, the study of trigonometry continued in Islamic mathematics, by mathematicians such as Al-Khwarizmi and Abu al-Wafa. It became an independent discipline in the Islamic world, where all six trigonometric functions were known. Translations of Arabic and Greek texts led to trigonometry being adopted as a subject in the Latin West beginning in the Renaissance with Regiomontanus. The development of modern trigonometry shifted during the western Age of Enlightenment, beginning with 17th-century mathematics and reaching its modern form with Leonhard Euler (1748).
Copernican heliocentrism is the name given to the astronomical model developed by Nicolaus Copernicus and published in 1543. This model positioned the Sun at the center of the Universe, motionless, with Earth and the other planets orbiting around it in circular paths, modified by epicycles, and at uniform speeds. The Copernican model displaced the geocentric model of Ptolemy that had prevailed for centuries, which had placed Earth at the center of the Universe. Copernican heliocentrism is often regarded as the launching point to modern astronomy and the Scientific Revolution.
Gerald James Toomer 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.
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