Seeing the light of day almost 19 centuries ago, it was first published in Russian translation only in 1998. In late antiquity, this work was referred to as the greatest. The body of astronomical knowledge for many centuries, right up to Copernicus and Tycho Brahe, was a reference book for astronomers. There is no other book except the Bible that has had such a long and turbulent life.
Ptolemy lived and worked in Egypt, near Alexandria, his work "Mathematical construction in 13 books"(later known as "Big Essay") was completed in the middle of the 2nd century. AD The book came to Medieval Europe from the Arabs, through Spain. The first translation from Greek was made in Persia a hundred years after the appearance of the original, and from the 9th century. Numerous Arabic translations began to appear, one of which was translated into Latin in Toledo in 1175 and printed in Venice in 1515. The Greek text of the Almagest was published in 1538 in Basel, and in 1813-1816. a French translation has appeared. Finally, at the beginning of this century, a scientific edition of the Greek text was published, which became the basis for translation into German and English in 1952-1984. , as well as for Russian translation.
The manuscript of this translation was prepared by the famous mathematician and historian of science I.N. Veselovsky in the 60s. Then the publication did not take place, as reported in the comments to the current edition, due to the fact that the “great luminary of science” back in 1935 called Ptolemy’s world system “dilapidated.” It is, indeed, long outdated, but the book in which it is presented is immortal, and its publication in Russian is an event in the history of Russian culture and a real holiday for historians of science. Enormous credit for this belongs to the scientific editor of the translation, G.E. Kurtik; M.M. Rozhanskaya, G.P. Matvievskaya, M.Yu. Shevchenko, S.V. Zhitomirsky and V.A. Bronshten also participated in the work on the book.
The significance of the Almagest is enormous and enduring. More than a hundred astronomical observations, from the 7th century. BC. to 141, the Catalog of Constellations, the only one preserved from ancient times, still serves science. Of course, most of Ptolemy’s constructions are not original and are based on the work of previous generations of Greek astronomers, but he systematized them, and thanks to him they have come to us.
Of particular interest is the Ptolemaic world system, based on numerous observations of the motion of planets relative to stars. We have known for a long time that this system is incorrect, but how well it represented the observations! True, not all. For the success of a scientific hypothesis, it is almost always necessary to be able to forget about some facts that it does not explain, to be able to turn to them, as the British say, “with a blind eye.” One could even say that a theory that explains too much is most often not trustworthy even in a narrower area than the system of the universe...
So, Ptolemy created his concept of the world system. The motionless spherical Earth rests in the center of the universe, its dimensions are negligible in comparison with the distance to the sphere of the fixed stars. They are only motionless relative to the others, and all together make a revolution around the Earth per day, just like the internal spheres on which the wandering luminaries are located - the Moon, Mercury, Venus, the Sun, Mars, Jupiter and Saturn (in order of distance from the Earth), endowed and other movements. The true movements of perfect celestial bodies should be uniform and circular, but they do not seem like that to us (the planets even make loop-like movements along the celestial sphere) because it is not the planets themselves that move in circles with a center in the Earth (deferents), but the centers of smaller circles ( epicycles). In the 13th century King Alfonso X of Castile expressed the heretical thought that if he had been present at the creation of the world, he would have advised the Lord to have a simpler model...
Ptolemy's theory predicted the positions of the planets quite well, but problems remained. Thus, as the Moon moves along the epicycle, its apparent dimensions should periodically change by half. Ptolemy apparently noticed this contradiction with observational data, since in his theory of eclipses he used not theoretical, but observed angular dimensions of the Moon. Given the distances he obtained, Mercury, located directly behind the Moon, should have a completely measurable diurnal parallax. However, Ptolemy notes that none of the planets has parallax. Following “more ancient mathematicians,” he places the sphere of the Sun between the spheres of Venus and Mars on the grounds that such a position “more naturally separates the planets that can be located at any distance from it, and those for which this is not the case” (p. 277). And to this day, Mercury and Venus are called the lower planets, and the rest - the upper.
In 1997, A.K. Dambis and Yu.N. Efremov approached this problem as the inverse of the classical problem of stellar astronomy. For more than two centuries, astronomers have been determining the proper movements of stars based on known coordinates in different eras of observation; here, the era at the turn of the 1st and 2nd centuries was considered unknown. BC. The main contribution to the solution is made by the fifty fastest stars - the involvement of others no longer reduces the error. Let us recall that the confidently dated observations of Hipparchus (declinations of 18 stars) date back to 130 BC! A link to this result managed to get into the book under review (p. 577).
So, contrary to his own statement, Ptolemy himself did not determine the coordinates of the stars in the catalog? True, he wrote “we observed” and not “determined the coordinates.” But why is it not said that the coordinates were taken from Hipparchus? Indeed, throughout the Almagest there is evidence of the greatest reverence that Ptolemy felt for his predecessor. Could it be that Ptolemy himself determined the coordinates of only the bright stars, and for most of the stars he took the coordinates of Hipparchus, who was a more skilled observer? A hint of this is given by the stars’ own movements, leading to slightly later epochs for other bright stars, and by the words of Ptolemy himself: “In this way, by the distances from the Moon, we determine the position of each individual bright star” (p. 215).
In the English translation, the idea of our own determination of the coordinates of bright stars is expressed more clearly: “And so we determined the position of each of the bright stars by their distances from the Moon.” There is also another phrase indicating one’s own definitions of the coordinates of the bright stars of the zodiac belt. We are talking about determining the magnitude of precession, and in this case new observations are needed.
In conclusion, let's say a few words about the features of Russian translation. The main one is the preservation of the original, literal meaning of phrases, which have long been customary to be replaced by the corresponding terms. So, instead of “ecliptic” we read “a circle passing through the middles of the zodiacal constellations”, and "celestial equator"- this is the “equinox circle”. This closeness to the original conveys the flavor of the era, but still complicates the text. The development of science is inextricably linked with the introduction of terminology and the emergence of new concepts. The type designation 23;47 should be understood as 23 ° 47" (23 degrees 47 min) - it turns out that this is accepted among historians of astronomy and is explained only in the notes (p. 468). Work I.N. Veselovsky the translation was not completed. The team, headed by G.E. Kurtik, clarified many places in the translation, using modern editions of the Almagest and numerous works devoted to its interpretation. "Almagest" is not an easy read, so the circulation is 1000 copies. seems justified. The long-awaited publication of the Russian edition is a great event in the history of Russian culture. Our country is now among those five or six whose population can get acquainted with the immortal creation of Ptolemy in their native language.
Bronshten V.A. Claudius Ptolemy. M., 1988. P.99.
Newton R. The Crime of Claudius Ptolemy. M., 1985.
See: Efremov Yu.N. // Vestn. RFBR. 1998. N 3. P. 37.
Toomer G. Ptolemy's Almagest. London, 1984. P.328.
Claudius Ptolemy occupies one of the most honorable places in the history of world science. His works played a huge role in the development of astronomy, mathematics, optics, geography, chronology, and music. The literature dedicated to him is truly enormous. And yet his image remains unclear and contradictory to this day. Among the figures of science and culture of long-gone eras it is hardly possible to name many about whom such contradictory judgments were expressed and such fierce debates took place among specialists as about Ptolemy.
This is explained, on the one hand, by the most important role that his works played in the history of science, and on the other, by the extreme paucity of biographical information about him.
Ptolemy owns a number of outstanding works on the main areas of ancient natural science. The largest of them, and the one that also left the greatest mark in the history of science, is the astronomical work published in this edition, usually called the “Almagest”.
"Almagest" is a compendium of ancient mathematical astronomy, which reflects almost all of its most important directions. Over time, this work supplanted the earlier works of ancient authors on astronomy and thus became a unique source on many important issues of its history. For centuries, right up to the era of Copernicus, the Almagest was considered an example of a strictly scientific approach to solving astronomical problems. Without this work it is impossible to imagine the history of medieval Indian, Persian, Arab and European astronomy. Copernicus’s famous work “On Rotations,” which laid the foundation for modern astronomy, was in many respects a continuation of the “Almagest.”
Other works of Ptolemy, such as “Geography”, “Optics”, “Harmonics”, etc., also had a great influence on the development of the corresponding fields of knowledge, sometimes no less than the “Almagest” on astronomy. In any case, each of them marked the beginning of a tradition of presentation of a scientific discipline that has been preserved for centuries. In terms of the breadth of scientific interests, combined with the depth of analysis and rigor of presentation of the material, few can be placed next to Ptolemy in the history of world science.
However, Ptolemy paid the greatest attention to astronomy, to which, in addition to the Almagest, he devoted other works. In “Planetary Hypotheses” he developed a theory of the movement of planets as an integral mechanism within the framework of the geocentric system of the world he adopted; in “Handy Tables” he gave a collection of astronomical and astrological tables with explanations, necessary for a practicing astronomer in his daily work. He dedicated a special treatise “The Four Books”, in which great importance was also attached to astronomy, to astrology. Several of Ptolemy's works are lost and are known only by their titles.
Such a variety of scientific interests gives every reason to classify Ptolemy as one of the most outstanding scientists known to the history of science. World fame, and most importantly - the rare fact that his works have been perceived for centuries as timeless sources of scientific knowledge, testify not only to the breadth of the author's horizons, the rare generalizing and systematizing power of his mind, but also to the high skill of presenting the material. In this regard, the works of Ptolemy, and above all the Almagest, became a model for many generations of scientists.
Very little is known reliably about the life of Ptolemy. What little has been preserved in ancient and medieval literature on this issue is presented in the work of F. Boll. The most reliable information concerning the life of Ptolemy is contained in his own writings. In the Almagest he cites a number of his observations, which date back to the reign of the Roman emperors Hadrian (117-138) and Antoninus Pius (138-161): at the earliest - March 26, 127 AD, and at the latest - February 2 141 AD In addition, the Canopic Inscription, dating back to Ptolemy, mentions the 10th year of the reign of Antoninus, i.e. 147/148 AD When trying to assess the limits of Ptolemy’s life, it is also necessary to keep in mind that after the Almagest he wrote several more large works, different in subject matter, of which at least two (“Geography” and “Optics”) are of an encyclopedic nature, which the most conservative estimates should have taken at least twenty years. Therefore, it can be assumed that Ptolemy was still alive under Marcus Aurelius (161-180), as later sources report. According to Olympiodor, Alexandrian philosopher of the 6th century. AD, Ptolemy worked as an astronomer in the city of Kanop (now Abukir), located in the western part of the Nile Delta, for 40 years. This message, however, is contradicted by the fact that all of Ptolemy's observations given in the Almagest were made in Alexandria. The name Ptolemy itself indicates the Egyptian origin of its owner, who probably belonged to the Greeks, adherents of Hellenistic culture in Egypt, or came from Hellenized local residents. The Latin name "Claudius" suggests that he had Roman citizenship. Ancient and medieval sources also contain a lot of less reliable evidence about the life of Ptolemy, which can neither be confirmed nor refuted.
Almost nothing is known about Ptolemy's scientific environment. “Almagest” and a number of his other works (except for “Geography” and “Harmonics”) are dedicated to a certain Sir (Σύρος). This name was quite common in Hellenistic Egypt during the period under review. We have no other information about this person. It is not even known whether he studied astronomy. Ptolemy also uses planetary observations of a certain Theon (book ΙΧ, chapter 9; book X, chapter 1), carried out in the period 127-132. AD He reports that these observations were “left” to him by “the mathematician Theon” (Book X, Ch. 1, p. 316), which apparently suggests personal contact. Perhaps Theon was Ptolemy's teacher. Some scientists identify him with Theon of Smyrna (first half of the 2nd century AD), a Platonist philosopher who paid attention to astronomy [NAMA, pp. 949-950].
Ptolemy undoubtedly had employees who assisted him in making observations and calculating tables. The volume of calculations that were required to construct the astronomical tables in the Almagest is truly enormous. During the time of Ptolemy, Alexandria was still a major scientific center. It operated several libraries, of which the largest was located in the Alexandrian Museion. There were apparently personal contacts between the library staff and Ptolemy, as often happens now in scientific work. Someone helped Ptolemy in selecting literature on issues of interest to him, brought manuscripts or led him to the shelves and niches where the scrolls were kept.
Until recently, it was assumed that the Almagest was the earliest astronomical work of Ptolemy that has come down to us. However, recent research has shown that the Canopic Inscription preceded the Almagest. Mentions of the “Almagest” are contained in the “Planetary Hypotheses”, “Tables at Hand”, “The Four Books” and “Geography”, which makes their later writing undoubted. This is also evidenced by the analysis of the content of these works. In the "Handy Tables" many tables are simplified and improved compared to similar tables in the "Almagest". The “Planetary Hypotheses” uses a different system of parameters to describe the movements of the planets and solves a number of issues in a new way, for example, the problem of planetary distances. In Geography, the prime meridian is moved to the Canary Islands instead of Alexandria, as is customary in the Almagest. “Optics” was also created, apparently, later than “Almagest”; it examines astronomical refraction, which does not play a significant role in the Almagest. Since the “Geography” and “Harmonics” do not contain a dedication to Sir, it can be argued with a certain degree of risk that these works were written later than other works of Ptolemy. We do not have other more accurate landmarks that would allow us to chronologically record the works of Ptolemy that have come down to us.
To appreciate Ptolemy's contribution to the development of ancient astronomy, it is necessary to clearly understand the main stages of its previous development. Unfortunately, most of the works of Greek astronomers dating back to the early period (V-III centuries BC) have not reached us. We can judge their content only from quotations in the works of later authors and, above all, from Ptolemy himself.
At the origins of the development of ancient mathematical astronomy lie four features of the Greek cultural tradition, clearly expressed already in the early period: a tendency towards a philosophical understanding of reality, spatial (geometric) thinking, commitment to observations and the desire to reconcile the speculative image of the world and observed phenomena.
In the early stages, ancient astronomy was closely connected with the philosophical tradition, from where it borrowed the principle of circular and uniform motion as the basis for describing the visible uneven movements of the luminaries. The earliest example of the application of this principle in astronomy was the theory of homocentric spheres of Eudoxus of Cnidus (c. 408-355 BC), improved by Callippus (IV century BC) and accepted with certain modifications by Aristotle (Metaphysics. XII, 8).
This theory qualitatively reproduced the features of the movement of the Sun, Moon and five planets: the daily rotation of the celestial sphere, the movements of the luminaries along the ecliptic from west to east at different speeds, changes in latitude and retrograde movements of the planets. The movements of the luminaries in it were controlled by the rotation of the celestial spheres to which they were attached; the spheres revolved around a single center (the Center of the World), coinciding with the center of the motionless Earth, had the same radius, zero thickness and were considered to consist of ether. Visible changes in the brightness of luminaries and associated changes in their distances relative to the observer could not be satisfactorily explained within the framework of this theory.
The principle of circular and uniform motion was also successfully applied in spherics - a section of ancient mathematical astronomy, in which problems related to the daily rotation of the celestial sphere and its most important circles, primarily the equator and ecliptic, the rising and setting of luminaries, zodiac signs relative to the horizon at various latitudes were solved . These problems were solved using spherical geometry methods. In the time preceding Ptolemy, a number of treatises on spherics appeared, including Autolycus (c. 310 BC), Euclid (second half of the 4th century BC), Theodosius (second half of the 2nd century BC AD), Hypsicles (2nd century BC), Menelaus (1st century AD) and others [Matvievskaya, 1990, p.27-33].
An outstanding achievement of ancient astronomy was the theory of heliocentric planetary motion, proposed by Aristarchus of Samos (c. 320-250 BC). However, this theory, as far as our sources allow us to judge, did not have any noticeable impact on the development of mathematical astronomy proper, i.e. did not lead to the creation of an astronomical system that has not only philosophical, but also practical significance and makes it possible to determine the positions of the luminaries in the sky with the required degree of accuracy.
An important step forward was the invention of eccentrics and epicycles, which made it possible to qualitatively explain at the same time, on the basis of uniform and circular movements, the observed irregularities in the movement of luminaries and changes in their distances relative to the observer. The equivalence of the epicyclic and eccentric models for the case of the Sun was proven by Apollonius of Perga (III-II centuries BC). He also used the epicyclic model to explain the retrograde motions of the planets. New mathematical tools made it possible to move from a qualitative to a quantitative description of the movements of luminaries. For the first time, apparently, this problem was successfully solved by Hipparchus (II century BC). He created, based on eccentric and epicyclic models, theories of the movement of the Sun and Moon, which made it possible to determine their current coordinates for any moment in time. However, he was unable to develop a similar theory for planets due to lack of observations.
Hipparchus also owns a number of other outstanding achievements in astronomy: the discovery of precession, the creation of a star catalogue, the measurement of lunar parallax, the determination of distances to the Sun and Moon, the development of the theory of lunar eclipses, the design of astronomical instruments, in particular the armillary sphere, carrying out a large number of observations that have not been lost partly of its significance to the present day, and much more. The role of Hipparchus in the history of ancient astronomy is truly enormous.
Observations constituted a special direction in ancient astronomy long before Hipparchus. In the early period, observations were mainly qualitative. With the development of kinematic-geometric modeling, observations are mathematized. The main purpose of the observations is to determine the geometric and speed parameters of the adopted kinematic models. In parallel, astronomical calendars are being developed that make it possible to record the dates of observations and determine the intervals between observations based on a linear uniform time scale. During the observation, the positions of the luminaries were recorded relative to the selected points of the kinematic model at the current moment, or the time of passage of the luminary through the selected point of the diagram was determined. Such observations include: determination of the moments of the equinoxes and solstices, the altitude of the Sun and Moon when passing through the meridian, the temporal and geometric parameters of eclipses, the dates of the Moon covering the stars and planets, the positions of the planets relative to the Sun, Moon and stars, the coordinates of stars, etc. The earliest observations of this kind date back to the 5th century. BC. (Meton and Euctemon in Athens); Ptolemy was also aware of the observations of Aristillus and Timocharis, carried out in Alexandria at the beginning of the 3rd century. BC, Hipparchus in Rhodes in the second half of the 2nd century. BC, Menelaus and Agrippa, respectively, in Rome and Bithynia at the end of the 1st century. BC, Theon in Alexandria at the beginning of the 2nd century. AD Greek astronomers also had at their disposal (already, apparently, in the 2nd century BC) the results of observations of Mesopotamian astronomers, including lists of lunar eclipses, planetary configurations, etc. The Greeks were also familiar with lunar and planetary periods, accepted in Mesopotamian astronomy of the Seleucid period (IV-I centuries BC). They used this data to test the accuracy of the parameters of their own theories. The observations were accompanied by the development of theory and the construction of astronomical instruments.
A special direction in ancient astronomy was the observation of stars. Greek astronomers identified about 50 constellations in the sky. It is not known exactly when this work was done, but by the beginning of the 4th century. BC. it was apparently already completed; there is no doubt that Mesopotamian tradition played an important role in this.
Descriptions of constellations constituted a special genre in ancient literature. The starry sky was depicted visually on celestial globes. Tradition associates the earliest examples of this kind of globes with the names of Eudoxus and Hipparchus. However, ancient astronomy went much further than a simple description of the shape of the constellations and the location of the stars in them. An outstanding achievement was the creation by Hipparchus of the first star catalog containing ecliptic coordinates and brightness estimates for each star included in it. According to some sources, the number of stars in the catalog did not exceed 850; according to another version, it included about 1022 stars and was structurally similar to Ptolemy's catalogue, differing from it only in the longitudes of the stars.
The development of ancient astronomy occurred in close connection with the development of mathematics. The solution of astronomical problems was largely determined by the mathematical tools that astronomers had at their disposal. The works of Eudoxus, Euclid, Apollonius, and Menelaus played a special role in this. The appearance of the “Almagest” would have been impossible without the previous development of logistics methods - a standard system of rules for carrying out calculations, without planimetry and the fundamentals of spherical geometry (Euclid, Menelaus), without plane and spherical trigonometry (Hipparchus, Menelaus), without the development of kinematic-geometric modeling methods movements of the luminaries using the theory of eccentrics and epicycles (Apollonius, Hipparchus), without developing methods for specifying functions of one, two and three variables in tabular form (Mesopotamian astronomy, Hipparchus?). For its part, astronomy directly influenced the development of mathematics. Such, for example, sections of ancient mathematics as trigonometry of chords, spherical geometry, stereographic projection, etc. developed only because they were given special importance in astronomy.
In addition to geometric methods for modeling the movements of luminaries, ancient astronomy also used arithmetic methods of Mesopotamian origin. Greek planetary tables have reached us, calculated on the basis of Mesopotamian arithmetic theory. Antique astronomers apparently used the data from these tables to substantiate the epicyclic and eccentric models. In the time preceding Ptolemy, approximately from the 2nd century. BC, a whole class of special astrological literature became widespread, including lunar and planetary tables, which were calculated based on the methods of both Mesopotamian and Greek astronomy.
Ptolemy's work was originally entitled "Mathematical work in 13 books" (Μαθηματικής Συντάξεως βιβλία ϊγ). In late antiquity it was referred to as the “great” (μεγάλη) or “greatest (μεγίστη) work”, as opposed to the “Small Astronomical Collection” (ό μικρός αστρονομούμενος) - a collection of small treatises on spherics and others sections of ancient astronomy. In the 9th century. when translating the “Mathematical Essay” into Arabic Greek wordή μεγίστη was reproduced in Arabic as “al-majisti”, from which the currently accepted Latinized form of the title of this work “Almagest” comes from.
The Almagest consists of thirteen books. The division into books undoubtedly belongs to Ptolemy himself, while the division into chapters and their names were introduced later. It can be stated with certainty that during the time of Pappus of Alexandria at the end of the 4th century. AD This kind of division already existed, although it differed significantly from the currently accepted one.
The Greek text that has reached us also contains a number of later interpolations that did not belong to Ptolemy, but were introduced by scribes for various reasons [RA, pp. 5-6].
"Almagest" is a textbook mainly on theoretical astronomy. It is intended for an already prepared reader familiar with Euclidean geometry, spherics and logistics. The main theoretical problem solved in the Almagest is the pre-calculation of the visible positions of the luminaries (Sun, Moon, planets and stars) on the celestial sphere at an arbitrary moment in time with an accuracy corresponding to the capabilities of visual observations. Another important class of problems solved in the Almagest is the pre-calculation of dates and other parameters of special astronomical phenomena associated with the movement of luminaries - lunar and solar eclipses, heliacal risings and setting of planets and stars, determination of parallax and distances to the Sun and Moon, and etc. In solving these problems, Ptolemy follows a standard methodology that includes several stages.
1. Based on preliminary rough observations, it becomes clear characteristics in the motion of the luminary, and a kinematic model is selected that best corresponds to the observed phenomena. The procedure for selecting one model from several equally possible ones must satisfy the “principle of simplicity”; Ptolemy writes about this: “We consider it appropriate to explain phenomena using the simplest assumptions, unless observations contradict the hypothesis put forward” (Book III, Chapter 1, p. 79). Initially, the choice is made between a simple eccentric and a simple epicyclic model. At this stage, questions are resolved about the correspondence of the circles of the model to certain periods of the movement of the luminary, about the direction of movement of the epicycle, about the places of acceleration and deceleration of movement, about the position of apogee and perigee, etc.
2. Based on the accepted model and using observations, both his own and his predecessors, Ptolemy determines the periods of motion of the luminary with the highest possible accuracy, the geometric parameters of the model (epicycle radius, eccentricity, apogee longitude, etc.), the moments of passage of the luminary through the selected points of the kinematic diagram to tie the movement of the luminary to the chronological scale.
This technique works most simply when describing the movement of the Sun, where a simple eccentric model is sufficient. When studying the motion of the Moon, however, Ptolemy had to modify the kinematic model three times in order to find a combination of circles and lines that would best fit the observations. Significant complications also had to be introduced into kinematic models to describe the movements of the planets in longitude and latitude.
A kinematic model that reproduces the movements of the luminary must satisfy the “principle of uniformity” of circular movements. “We believe,” writes Ptolemy, “that for a mathematician the main task is ultimately to show that celestial phenomena are obtained with the help of uniform circular motions” (Book III, Chapter 1, p. 82). This principle, however, is not strictly followed. He refuses it whenever (without, however, explicitly stipulating this) when observations require it, for example, in lunar and planetary theories. Violation of the principle of uniformity of circular motions in a number of models later became the basis for criticism of the Ptolemaic system in the astronomy of Islamic countries and medieval Europe.
3. After determining the geometric, speed and time parameters of the kinematic model, Ptolemy proceeds to constructing tables with the help of which the coordinates of the luminary at an arbitrary moment in time should be calculated. Such tables are based on the idea of a linear, homogeneous time scale, the beginning of which is taken to be the beginning of the era of Nabonassar (-746, February 26, true noon). Any value recorded in the table is obtained as a result of complex calculations. At the same time, Ptolemy shows masterly mastery of Euclid's geometry and the rules of logistics. In conclusion, rules for using tables are given, and sometimes also examples of calculations.
The presentation in the Almagest is strictly logical in nature. At the beginning of Book I we consider general issues relating to the structure of the world as a whole, its most general mathematical model. Here the sphericity of the sky and the Earth, the central position and immobility of the Earth, the insignificance of the size of the Earth compared to the size of the sky are proven, two main directions on the celestial sphere are identified - the equator and the ecliptic, parallel to which the daily rotation of the celestial sphere and the periodic movements of the luminaries occur, respectively. The second half of Book I introduces chord trigonometry and spherical geometry - ways of solving triangles on a sphere using Menelaus' theorem.
Book II is entirely devoted to questions of spherical astronomy, which do not require knowledge of the coordinates of the luminaries as a function of time for their solution; it examines the problems of determining the times of sunrise, sunset and passage through the meridian of arbitrary arcs of the ecliptic at various latitudes, day length, length of the gnomon shadow, angles between the ecliptic and the main circles of the celestial sphere, etc.
In Book III, a theory of the movement of the Sun is developed, which contains the determination of the duration of the solar year, the selection and justification of the kinematic model, the determination of its parameters, and the construction of tables for calculating the longitude of the Sun. The final section explores the concept of the equation of time. The theory of the Sun is the basis for studying the movement of the Moon and stars. The longitudes of the Moon at the moments of lunar eclipses are determined from the known longitude of the Sun. The same goes for determining the coordinates of stars.
Books IV-V are devoted to the theory of the movement of the Moon in longitude and latitude. The movement of the Moon is studied approximately according to the same scheme as the movement of the Sun, with the only difference that Ptolemy, as we have already noted, successively introduces here three kinematic models. An outstanding achievement was Ptolemy's discovery of the second inequality in the motion of the Moon, the so-called evection, associated with the Moon being in quadrature. In the second part of Book V, the distances to the Sun and Moon are determined and the theory of solar and lunar parallax, necessary for the pre-calculation of solar eclipses, is constructed. The parallel tables (book V, chapter 18) are perhaps the most complex of all those contained in the Almagest.
Book VI is devoted entirely to the theory of lunar and solar eclipses.
Books VII and VIII contain a star catalog and discuss a number of other issues concerning the fixed stars, including the theory of precession, the construction of a celestial globe, heliacal risings and settings of stars, etc.
Books IX-XIII present the theory of planetary motion in longitude and latitude. In this case, the movements of the planets are analyzed independently of each other; movements in longitude and latitude are also considered independently. In describing the movements of the planets along longitude, Ptolemy uses three kinematic models, differing in detail, respectively for Mercury, Venus and the upper planets. They implemented an important improvement known as equant, or eccentricity bisection, which made it possible to increase the accuracy of determining the longitudes of planets by approximately three times compared to a simple eccentric model. In these models, however, the principle of uniformity of circular rotations is formally violated. Kinematic models for describing the motion of planets along latitude are particularly complex. These models are formally incompatible with the kinematic models of longitude motion accepted for the same planets. Discussing this problem, Ptolemy expresses several important methodological points that characterize his approach to modeling the movements of luminaries. In particular, he writes: “And let no one... consider these hypotheses too artificial; human concepts should not be applied to the divine... But to celestial phenomena we should try to adapt as simple assumptions as possible... Their connection and mutual influence in various movements seem to us very artificial in the models we arrange, and it is difficult to make sure that the movements do not interfere each other, but in the sky none of these movements will encounter obstacles from such a connection. It would be better to judge the very simplicity of heaven not on the basis of what seems so to us...” (Book XIII, Chapter 2, p. 401). Book XII analyzes the retrograde movements and magnitudes of maximum elongations of the planets; at the end of Book XIII, heliacal risings and setting of planets are considered, which require knowledge of both the longitude and latitude of the planets for their determination.
The theory of planetary motion, set out in the Almagest, belongs to Ptolemy himself. In any case, there are no serious grounds indicating that anything similar existed in the time preceding Ptolemy.
In addition to the Almagest, Ptolemy also wrote a number of other works on astronomy, astrology, geography, optics, music, etc., which were very famous in antiquity and the Middle Ages, including:
"The Canopic Inscription"
"Handy tables"
"Planetary Hypotheses"
"Analemma"
"Planispherium"
"The Four Books"
"Geography",
"Optics",
“Harmonics”, etc. For the time and order of writing these works, see section 2 of this article. Let's briefly look at their contents.
The "Canopic Inscription" is a list of the parameters of Ptolemy's astronomical system, which was carved on a stele dedicated to the Savior God (possibly Serapis) in the city of Canopus in the 10th year of the reign of Antoninus (147/148 AD). The stele itself has not survived, but its contents are known from three Greek manuscripts. Most of the parameters adopted in this list coincide with those used in the Almagest. However, there are discrepancies not related to copyist errors. A study of the text of the Canopic Inscription showed that it dates back to a time earlier than the time of the creation of the Almagest.
“Handy Tables” (Πρόχειροι κανόνες), the second largest astronomical work of Ptolemy after the “Almagest”, is a collection of tables for calculating the positions of the luminaries on the sphere at an arbitrary moment and for pre-calculating some astronomical phenomena, especially eclipses. The tables are preceded by Ptolemy's "Introduction", which explains the basic principles of their use. The “Tables at Hand” have come down to us in Theon of Alexandria’s arrangement, but it is known that Theon changed little in them. He also wrote two commentaries on them - the “Great Commentary” in five books and the “Small Commentary”, which were supposed to replace Ptolemy’s “Introduction”. “Handy Tables” are closely related to the “Almagest”, but also contain a number of innovations that are both theoretical and practical. For example, they adopted other methods for calculating the latitudes of planets, and a number of parameters of kinematic models were changed. The era of Philip (-323) is taken as the initial era of the tables. The tables contain a star catalog of about 180 stars in the vicinity of the ecliptic, in which longitudes are measured sidereally, with Regulus ( α Leo) is taken as the origin of sidereal longitude. There is also a list of about 400 “Major Cities” with geographic coordinates. The “Tables at Hand” also contains the “Royal Canon” - the basis of Ptolemy’s chronological calculations (see Appendix “Calendar and Chronology in the Almagest”). In most tables, function values are given with an accuracy of minutes, and the rules for their use are simplified. These tables undoubtedly had an astrological purpose. Subsequently, the “Tables at Hand” enjoyed great popularity in Byzantium, Persia and the medieval Muslim East.
“Planetary Hypotheses” (Ύποτέσεις τών πλανωμένων) is a small but important work in the history of astronomy by Ptolemy, consisting of two books. Only part of the first book survives in Greek; however, a complete Arabic translation of this work has reached us, belonging to Thabit ibn Koppe (836-901), as well as a translation into Hebrew in the 14th century. The book is devoted to the description of the astronomical system as a whole. “Planetary Hypotheses” differ from the “Almagest” in three respects: a) they use a different system of parameters to describe the movements of the stars; b) kinematic models have been simplified, in particular the model for describing the motion of planets along latitude; c) the approach to the models themselves has been changed, which are considered not as geometric abstractions designed to “save phenomena”, but as parts of a single mechanism that is physically realized. The parts of this mechanism are built from ether, the fifth element of Aristotelian physics. The mechanism that controls the movements of the stars is a combination of a homocentric model of the world with models built on the basis of eccentrics and epicycles. The movement of each luminary (Sun, Moon, planets and stars) occurs inside a special spherical ring of a certain thickness. These rings are sequentially nested into each other in such a way that there is no space left for emptiness. The centers of all rings coincide with the center of the stationary Earth. Inside the spherical ring, the star moves according to the kinematic model adopted in the Almagest (with minor changes).
In the Almagest, Ptolemy determines absolute distances (in units of the radius of the Earth) only to the Sun and Moon. This cannot be done for planets due to their lack of noticeable parallax. In the Planetary Hypotheses, however, he finds absolute distances for planets as well, based on the assumption that the maximum distance of one planet is equal to the minimum distance of the planet next to it. The accepted sequence of arrangement of luminaries: Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn, fixed stars. The Almagest defines the maximum distance to the Moon and the minimum distance to the Sun from the center of the spheres. Their difference closely corresponds to the total thickness of the spheres of Mercury and Venus, obtained independently. This coincidence in the eyes of Ptolemy and his followers confirmed the correct location of Mercury and Venus in the interval between the Moon and the Sun and testified to the reliability of the system as a whole. At the end of the treatise, the results of Hipparchus’ determination of the apparent diameters of the planets are presented, on the basis of which their volumes are calculated. The "planetary hypotheses" enjoyed great popularity in late antiquity and the Middle Ages. The planetary mechanism developed in them was often depicted graphically. These images (Arabic and Latin) served as a visual expression of the astronomical system, which was usually defined as the “Ptolemaic system”.
“Phases of the Fixed Stars” (Φάσεις απλανών αστέρων) is a small work by Ptolemy in two books devoted to weather predictions based on observations of the dates of the synodic phenomena of stars. Only Book II has reached us, containing a calendar in which a weather prediction is given for each day of the year on the assumption that it was on this day that one of four possible synodic phenomena occurred (heliac sunrise or sunset, acronic sunrise, cosmic sunset). For example:
Thoth 1 141/2 hours: [star] in the tail of Leo (ß Leo) rises;
according to Hipparchus, the north winds end; according to Eudoxus,
rain, thunderstorm, north winds end.
Ptolemy uses only 30 stars of the first and second magnitude and gives predictions for five geographical climates for which the maximum
The length of the day varies from 13 1/2 h to 15 1/2 h every 1/2 h. Dates are given in the Alexandrian calendar. The dates of the equinoxes and solstices are also indicated (I, 28; IV, 26; VII, 26; XI, 1), which allows us to approximately date the time of writing the work as 137-138. AD Weather predictions based on observations of star rises obviously reflect a pre-scientific stage in the development of ancient astronomy. However, Ptolemy introduces an element of science into this not entirely astronomical area.
“Analemma” (Περί άναλήμματος) is a treatise that describes a method for finding by geometric construction in a plane arcs and angles that fix the position of a point on a sphere relative to selected great circles. Fragments of the Greek text and a complete Latin translation of this work, made by Willem of Moerbeke (XIII century AD), have been preserved. In it, Ptolemy solves the following problem: determine the spherical coordinates of the Sun (its altitude and azimuth), if the geographic latitude of the place φ, the longitude of the Sun λ and the time of day are known. To fix the position of the Sun on the sphere, he uses a system of three orthogonal axes forming an octant. Angles on the sphere are measured relative to these axes, which are then determined in the plane by construction. The method used is close to those currently used in descriptive geometry. The main area of its application in ancient astronomy was the design sundial. A presentation of the contents of the Analemma is contained in the works of Vitruvius (On Architecture IX, 8) and Heron of Alexandria (Dioptra 35), who lived half a century earlier than Ptolemy. But although the basic idea of the method was known long before Ptolemy, his solution is distinguished by completeness and beauty, which we do not find in any of his predecessors.
"Planispherium" (probable Greek name: "Άπλωσις επιφανείας σφαίρας) - a small work by Ptolemy devoted to the use of the theory of stereographic projection in solving astronomical problems. Survived only in Arabic; the Spanish-Arabic version of this work, owned by Maslama al-Majriti (Χ -ΧΙ centuries . AD), was translated into Latin language Hermann from Carinthia in 1143. The idea of stereographic projection is as follows: the points of a ball are projected from any point on its surface onto a plane tangent to it, while circles drawn on the surface of the ball turn into circles on the plane and the angles retain their magnitude. The basic properties of stereographic projection were already known, apparently, two centuries before Ptolemy. In “Planisphery” Ptolemy solves two problems: (1) to construct in a plane, using the stereographic projection method, displays of the main circles of the celestial sphere and (2) to determine the rising times of the ecliptic arcs in the straight and oblique spheres (i.e. at ψ = O and ψ ≠ O respectively) purely geometrically. This work is also related in its content to the problems currently being solved in descriptive geometry. The methods developed there served as the basis for the creation of the astrolabe, an instrument that played an important role in the history of ancient and medieval astronomy.
“The Quadruple” (Τετράβιβλος or “Αποτελεσματικά”, i.e. “Astrological influences”) is the main astrological work of Ptolemy, also known under the Latinized name “Quadripartitum”. It consists of four books.
During the time of Ptolemy, belief in astrology was widespread. Ptolemy was no exception in this regard. He views astrology as a necessary complement to astronomy. Astrology predicts earthly events, taking into account the influence of celestial bodies; astronomy provides information about the positions of luminaries necessary for making predictions. Ptolemy, however, was not a fatalist; He considers the influence of celestial bodies to be only one of the factors determining events on Earth. In works on the history of astrology, four types of astrology, common in the Hellenistic period, are usually distinguished - world (or general), genetlialogy, catarchen and interrogative. In Ptolemy's work, only the first two types are considered. Book I gives general definitions basic astrological concepts. Book II is entirely devoted to world astrology, i.e. methods of predicting events concerning large earth regions, countries, peoples, cities, large social groups, etc. Issues of so-called “astrological geography” and weather predictions are discussed here. Books III and IV are devoted to methods of predicting individual human destinies. Ptolemy's work is characterized by a high mathematical level, which distinguishes it favorably from other astrological works of the same period. This is probably why the “Four Books” enjoyed enormous authority among astrologers, despite the fact that it lacked catharchen astrology, i.e. methods for determining the favorability or unfavorability of the chosen moment for any business. In the Middle Ages and the Renaissance, Ptolemy's fame was sometimes determined by this work rather than by his astronomical works.
Ptolemy's Geography, or Geographical Guide (Γεωγραφική ύφήγεσις) in eight books, was extremely popular. In terms of volume, this work is not much inferior to the Almagest. It contains a description of the part of the world known in the time of Ptolemy. However, Ptolemy's work differs significantly from similar works of his predecessors. The actual descriptions take up little space in it; the main attention is paid to the problems of mathematical geography and cartography. Ptolemy reports that he borrowed all the factual material from the geographical work of Marinus of Tire (dating approximately to the year 2000 AD), which was, apparently, a topographical description of regions indicating directions and distances between points. The main task of mapping is to display the spherical surface of the Earth on a flat map surface with minimal distortion.
In Book I, Ptolemy critiques the projection method used by Marinus of Tire, the so-called cylindrical projection, and rejects it. He proposes two other methods—equidistant conic and pseudoconic projections. He takes the dimensions of the world in longitude to be equal to 180°, counting the longitude from the prime meridian passing through the Isles of the Blessed (Canary Islands), from west to east, in latitude - from 63° north to 16;25° south of the equator (which corresponds to parallels through Thule and through a point located symmetrically to Meroe relative to the equator).
Books II-VII provide a list of cities indicating geographic longitude and latitude and brief descriptions. In its compilation, apparently, lists of places with the same day length, or places located at a certain distance from the prime meridian, were used, which were possibly part of the work of Marinus of Tire. Lists of a similar type are contained in Book VIII, where a division of the world map into 26 regional maps is also given. Ptolemy's work also included the maps themselves, which, however, have not reached us. The cartographic material usually associated with Ptolemy's Geography is actually of later origin. Ptolemy's "Geography" played an outstanding role in the history of mathematical geography, no less than the "Almagest" in the history of astronomy.
Ptolemy's "Optics" in five books has reached us only in a Latin translation of the 12th century. from Arabic, and the beginning and end of this work have been lost. It is written in line with the ancient tradition, represented by the works of Euclid, Archimedes, Heron and others, but, as always, Ptolemy’s approach is original. Books I (which has not survived) and II discuss the general theory of vision. It is based on three postulates: a) the process of vision is determined by rays that emanate from the human eye and, as it were, feel the object; b) color is a quality inherent in the objects themselves; c) color and light are equally necessary to make an object visible. Ptolemy also states that the process of vision occurs in a straight line. Books III and IV discuss the theory of reflection from mirrors - geometric optics, or catoptrics, to use the Greek term. The presentation is carried out with mathematical rigor. Theoretical provisions are proven experimentally. The problem of binocular vision is also discussed here, mirrors of various shapes are considered, including spherical and cylindrical. Book V is about refraction; it studies refraction when light passes through air-water, water-glass, air-glass media using an instrument specially designed for this purpose. The results obtained by Ptolemy correspond quite well to Snell's law of refraction - sin α / sin β = n 1 / n 2, where α is the angle of incidence, β is the angle of refraction, n 1 and n 2 are the refractive indices in the first and second media, respectively. At the end of the surviving part of Book V, astronomical refraction is discussed.
Harmonics (Αρμονικά) is a small work by Ptolemy in three books devoted to musical theory. It deals with the mathematical intervals between notes according to various Greek schools. Ptolemy compares the teachings of the Pythagoreans, who, in his opinion, emphasized the mathematical aspects of theory at the expense of experience, and the teachings of Aristoxenus (IV century AD), who acted in the opposite way. Ptolemy himself strives to create a theory that combines the advantages of both directions, i.e. strictly mathematical and at the same time taking into account experimental data. Book III, which has not reached us in full, examines the applications of musical theory in astronomy and astrology, including, apparently, the musical harmony of the planetary spheres. According to Porphyry (3rd century AD), Ptolemy borrowed the content of the Harmonics mostly from the works of the Alexandrian grammarian of the second half of the 1st century. AD Didyma.
A number of lesser-known works are also associated with the name of Ptolemy. These include a treatise on philosophy “On the abilities of judgment and decision-making” (Περί κριτηρίον και ηγεμονικού), which sets out the ideas of mainly Peripatetic and Stoic philosophy, a small astrological work “Fruit” (Καρπός), known in Latin translation e called "Centiloquium "or "Fructus", which included one hundred astrological positions, a treatise on mechanics in three books, from which two fragments have been preserved - "Gravities" and "Elements", as well as two purely mathematical works, in one of which the postulate of parallel and in another, that there are no more than three dimensions in space. Pappus of Alexandria, in his commentary on Book V of the Almagest, attributes to Ptolemy the creation of a special instrument called a “meteoroscope”, similar to an armillary sphere.
Thus, we see that there is, perhaps, not a single area in ancient mathematical science where Ptolemy did not make a very significant contribution.
Ptolemy's work had a huge influence on the development of astronomy. The fact that its significance was immediately appreciated is evidenced by the appearance already in the 4th century. AD commentaries - essays devoted to explaining the content of the Almagest, but often having independent significance.
The first known commentary was written around 320 by one of the most prominent representatives of the Alexandrian scientific school, Pappus. Most of this work has not reached us - only commentaries on books V and VI of the Almagest have survived.
The second commentary, compiled in the 2nd half of the 4th century. AD Theon of Alexandria, has come down to us in a more complete form (books I-IV). The Almagest was also commented on by Theon’s daughter, the illustrious Hypatia (c. 370-415 AD).
In the 5th century Neoplatonist Proclus Diadochos (412-485), who headed the Academy in Athens, wrote an essay on astronomical hypotheses, which was an introduction to the astronomy of Hipparchus and Ptolemy.
The closure of the Athens Academy in 529 and the resettlement of Greek scientists to the countries of the East contributed to the rapid spread of ancient science here. The teachings of Ptolemy were mastered and significantly influenced the astronomical theories that were being formed in Syria, Iran and India.
In Persia, at the court of Shapur I (241-171), the Almagest apparently became known already around 250 AD. and then he was translated into Pahlavi. There was also a Persian version of Ptolemy's Tables at Hand. Both of these works had a great influence on the content of the main Persian astronomical work of the pre-Islamic period, the so-called Shah-i-Zij.
The Almagest was apparently translated into Syriac at the beginning of the 6th century. AD Sergius of Reshain (d. 536), famous physicist and philosopher, student of Philoponus. In the 7th century A Syriac version of Ptolemy's Tables at Hand was also in use.
From the beginning of the 9th century. The Almagest also became widespread in Islamic countries - in Arabic translations and commentaries. It is listed among the first works of Greek scholars to be translated into Arabic. The translators used not only the Greek original, but also the Syriac and Pahlavi versions.
The most popular name among astronomers in Islamic countries was the name “Great Book,” which sounded in Arabic as “Kitab al-Majisti.” Sometimes, however, this work was called “The Book of Mathematical Sciences” (“Kitab at-ta’alim”), which more accurately corresponded to its original Greek title “Mathematical Work”.
There were several Arabic translations and many adaptations of the Almagest, performed at different times. Their approximate list, which numbered 23 names in 1892, is gradually being refined. At present, the main issues related to the history of Arabic translations of the Almagest have been generally clarified. According to P. Kunitsch, “Almagest” in Islamic countries in the 9th-12th centuries. was known in at least five different versions:
1) Syriac translation, one of the earliest (not preserved);
2) a translation for al-Ma'mun of the early 9th century, apparently from Syriac; its author was al-Hasan ibn Quraysh (not preserved);
3) another translation for al-Ma'mun, made in 827/828 by al-Hajjaj ibn Yusuf ibn Matar and Sarjun ibn Khiliya ar-Rumi, apparently also from Syriac;
4) and 5) translation by Ishaq ibn Hunayn al-Ibadi (830-910), the famous translator of Greek scientific literature, made in 879-890. directly from Greek; came to us in the processing of the greatest mathematician and astronomer Thabit ibn Korra al-Harrani (836-901), but in the 12th century. was also known as an independent work. According to P. Kunitsch, later Arabic translations more accurately conveyed the content of the Greek text.
Currently, many Arabic works have been thoroughly studied, which essentially represent comments on the Almagest or its adaptations made by astronomers from Islamic countries, taking into account the results of their own observations and theoretical research [Matvievskaya, Rosenfeld, 1983]. Among the authors are outstanding scientists, philosophers and astronomers of the medieval East. Astronomers from Islamic countries made changes of greater or lesser importance to almost all sections of the Ptolemaic astronomical system. First of all, they clarified its main parameters: the angle of inclination of the ecliptic to the equator, the eccentricity and longitude of the apogee of the Sun’s orbit, the average speeds of the Sun, Moon and planets. They replaced tables of chords with sines and also introduced a whole set of new trigonometric functions. They developed more accurate methods for determining the most important astronomical quantities, such as parallax, the equation of time, etc. Old astronomical instruments were improved and new ones were developed, on which observations were regularly made that were significantly superior in accuracy to the observations of Ptolemy and his predecessors.
A significant part of the Arabic-language astronomical literature was made up of zijs. These were collections of tables - calendar, mathematical, astronomical and astrological, which astronomers and astrologers used in their daily work. The ZJs included tables that made it possible to chronologically record observations and find geographical coordinates places, determine the moments of sunrise and sunset, calculate the positions of luminaries on the celestial sphere for any moment in time, pre-calculate lunar and solar eclipses, determine parameters of astrological significance. The zijs contained rules for using tables; sometimes more or less detailed theoretical proofs of these rules were also included.
Ziji VIII-XII centuries. were created under the influence, on the one hand, of Indian astronomical works, and on the other, of Ptolemy’s “Almagest” and “Tables at Hand”. The astronomical tradition of pre-Muslim Iran also played an important role. Ptolemaic astronomy in this period was represented by the “Verified Zij” of Yahya ibn Abi Mansur (IX century AD), two Zijs of Habash al-Khasib (IX century AD), “Sabean Zij” of Muhammad al-Battani (c. 850-929), “Comprehensive Zij” by Kushyar ibn Labban (c. 970-1030), “Canon of Mas’ud” by Abu Rayhan al-Biruni (973-1048), “Sanjar Zij” by al-Khazini (first half of the 12th century .) and other works. Of particular note is the “Book on the Elements of the Science of the Stars” by Ahmad al-Fargani (IX century), containing a presentation of the astronomical system of Ptolemy.
In the 11th century The Almagest was translated by al-Biruni from Arabic into Sanskrit.
During Late Antiquity and the Middle Ages, Greek manuscripts of the Almagest continued to be preserved and copied in regions under the rule of the Byzantine Empire. The earliest surviving Greek manuscripts of the Almagest date back to the 9th century AD. . Although astronomy in Byzantium did not enjoy the same popularity as in Islamic countries, the love for ancient science did not fade away. Byzantium therefore became one of the two sources from which information about the Almagest penetrated into Europe.
Ptolemaic astronomy initially became known in Europe through the translations of Zij al-Farghani and al-Battani into Latin. Individual quotations from the Almagest can be found in the works of Latin authors already in the first half of the 12th century. However, this work became available in full to scholars of medieval Europe only in the second half of the 12th century.
In 1175, the eminent translator Gerardo of Cremona, working in Toledo in Spain, completed a Latin translation of the Almagest, using the Arabic versions of Hajjaj, Ishaq ibn Hunayn and Thabit ibn Qorra. This translation has gained great popularity. It is known in numerous manuscripts and was already printed in Venice in 1515. In parallel or a little later (c. 1175-1250), an abbreviated version of the Almagest (“Almagestum parvum”) appeared, which was also very popular.
Two (or even three) other medieval Latin translations of the Almagest, made directly from the Greek text, remain less well known. The first of these (the name of the translator is unknown), entitled "Almagesti geometria" and preserved in several manuscripts, is based on a Greek manuscript of the 10th century, which was brought in 1158 from Constantinople to Sicily. The second translation, also anonymous and even less popular in the Middle Ages, is known in a single manuscript.
A new Latin translation of the “Almagest” from the Greek original was carried out only in the 15th century, when, from the beginning of the Renaissance, a keen interest in the ancient philosophical and natural scientific heritage showed in Europe. On the initiative of one of the propagandists of this heritage, Pope Nicholas V, his secretary George of Trebizond (1395-1484) translated the Almagest in 1451. The translation, very imperfect and full of errors, was nevertheless published in 1528 in print in Venice and was reprinted in Basel in 1541 and 1551.
The shortcomings of the translation of George of Trebizond, known from the manuscript, caused sharp criticism from astronomers who needed a full-fledged text of Ptolemy’s major work. The preparation of a new edition of the Almagest is associated with the names of two major German mathematicians and astronomers of the 15th century. - Georg Purbach (1423-1461) and his student Johann Muller, known as Regiomontanus (1436-1476). Purbach intended to publish the Latin text of the Almagest, corrected from the Greek original, but did not have time to complete the work. Regiomontanus was also unable to complete it, although he spent a lot of effort studying Greek manuscripts. But he published Purbach’s work “The New Theory of Planets” (1473), which explained the main points of Ptolemy’s planetary theory, and he himself compiled a brief summary of the “Almagest”, published in 1496. These publications, published before the appearance of the printed edition of the translation of George of Trebizond, played a role vital role in popularizing the teachings of Ptolemy. It was through them that Nicolaus Copernicus became acquainted with this teaching [Veselovsky, Bely, pp.83-84].
The Greek text of the Almagest was first published in print in Basel in 1538.
Let us also note the Wittenberg edition of Book I of the Almagest as presented by E. Reingold (1549), which served as the basis for its translation into Russian in the 80s of the 17th century. unknown translator. The manuscript of this translation was recently discovered by V.A. Bronshten in the library of Moscow University [Bronshten, 1996; 1997].
A new edition of the Greek text together with a French translation was carried out in 1813-1816. N. Alma. In 1898-1903. An edition of the Greek text by I. Heiberg was published, satisfying modern scientific requirements. It served as the basis for all subsequent translations of the Almagest into European languages: German, which was published in 1912-1913. K. Manicius [NA I, II; 2nd ed., 1963], and two English ones. The first of them belongs to R. Tagliaferro and is of low quality, the second - to J. Toomer [RA]. The commentary edition of the Almagest in English by J. Toomer is currently considered the most authoritative among historians of astronomy. During its creation, in addition to the Greek text, a number of Arabic manuscripts were also used in the versions of Hajjaj and Ishaq-Sabit [RA, pp. 3-4].
The translation by I.N. is also based on the publication by I. Geiberg. Veselovsky, published in this edition. I.N. Veselovsky, in the introduction to his comments to the text of N. Copernicus’s book “On the Rotations of the Celestial Spheres,” wrote: “To compile comments to “De Revolutionibus,” it was necessary to translate the text of Ptolemy’s “Megale Syntaxis” from Greek; I had at my disposal an edition by Abbot Alma (Halma) with notes by Delambre (Paris, 1813-1816)” [Copernicus, 1964, p. 469]. It seems to follow from this that the translation of I.N. Veselovsky was based on an outdated edition by N. Alm. However, in the archives of the Institute of the History of Natural Science and Technology of the Russian Academy of Sciences, where the translation manuscript is kept, a copy of the edition of the Greek text by I. Heiberg, which belonged to I.N., was also discovered. Veselovsky. Direct comparison of the translation text with the editions of N. Alm and I. Geiberg shows that his preliminary translation by I.N. Veselovsky later revised it in accordance with the text by I. Geiberg. This is indicated, for example, by the accepted numbering of chapters in books, designations in drawings, the form in which tables are given, and many other details. In his translation, in addition, I.N. Veselovsky took into account most corrections made to the Greek text by C. Manitsius.
Of particular note is also the critical English edition of Ptolemy's star catalogue, published in 1915, undertaken by H. Peters and E. Noble [R. - TO.].
A large amount of scientific literature, both astronomical and historical-astronomical in nature, is associated with the Almagest. It reflected, first of all, the desire to comprehend and explain the theory of Ptolemy, as well as attempts to improve it, which were repeatedly undertaken in antiquity and the Middle Ages and culminated in the creation of the teachings of Copernicus.
Over time, the interest in the history of the emergence of the Almagest and in the personality of Ptolemy himself, which has manifested itself since ancient times, has not diminished - and perhaps even increased. It is impossible to give any satisfactory overview of the literature on the Almagest in a short article. This is a large independent work that goes beyond the scope of this study. Here we have to limit ourselves to indicating a small number of works, mostly modern, that will help the reader navigate the literature about Ptolemy and his work.
First of all, mention should be made of the largest group of studies (articles and books) devoted to the analysis of the content of the Almagest and determining its role in the development of astronomical science. These problems are considered in works on the history of astronomy, starting with the oldest, for example, in the two-volume “History of Astronomy in Antiquity” published in 1817 by J. Delambre, “Studies on the History of Ancient Astronomy” by P. Tannery, “History of Planetary Systems from Thales before Kepler” by J. Dreyer, in the major work of P. Duhem “Systems of the World”, in the masterfully written book by O. Neugebauer “Exact Sciences in Antiquity” [Neugebauer, 1968]. The content of the Almagest is also studied in works on the history of mathematics and mechanics. Among the works of Russian scientists, special mention should be made of the works of I.N. Idelson, dedicated to the planetary theory of Ptolemy [Idelson, 1975], I.N. Veselovsky and Yu.A. Bely [Veselovsky, 1974; Veselovsky, Bely, 1974], V.A. Bronshten [Bronshten, 1988; 1996] and M.Yu. Shevchenko [Shevchenko, 1988; 1997].
The results of numerous studies carried out by the beginning of the 70s concerning the Almagest and the history of ancient astronomy in general are summarized in two fundamental works: “History of Ancient Mathematical Astronomy” by O. Neugebauer [NAMA] and “Review of the Almagest” by O. Pedersen . Anyone who wishes to seriously study the Almagest will not be able to do without these two outstanding works. A large number of valuable comments concerning various aspects of the content of the Almagest - the history of the text, computational procedures, Greek and Arabic manuscript traditions, the origin of parameters, tables, etc., can be found in German [HA I, II] and English [RA] editions of the translation of the Almagest.
Research on “Almagest” continues today with no less intensity than in the previous period, in several main areas. The greatest attention is paid to the origin of the parameters of Ptolemy’s astronomical system, the kinematic models and computational procedures he adopted, and the history of the star catalogue. Much attention is also paid to studying the role of Ptolemy's predecessors in the creation of the geocentric system, as well as the fate of Ptolemy's teachings in the medieval Muslim East, Byzantium and Europe.
In this regard, see also. A detailed analysis in Russian of biographical data about the life of Ptolemy is presented in [Bronshten, 1988, pp. 11-16].
See book XI, chapter 5, p. 352 and book IX, chapter 7, p. 303, respectively.
A number of manuscripts indicate the 15th year of Antoninus's reign, which corresponds to 152/153 AD. .
Cm. .
It is reported, for example, that Ptolemy was born in Hermian Ptolemais, located in Upper Egypt, and that this explains his name “Ptolemy” (Theodore of Miletus, XIV century AD); according to another version, he was from Pelusium, a border city east of the Nile Delta, but this statement is most likely the result of an erroneous reading of the name “Claudius” in Arabic sources [NAMA, p. 834]. In late antiquity and the Middle Ages, Ptolemy was also credited with royal origin [NAMA, p. 834, p. 8; Toomer, 1985].
The opposite point of view is also expressed in the literature, namely, that in the time preceding Ptolemy there already existed a developed heliocentric system based on epicycles, and that the Ptolemy system is only a reworking of this earlier system [Idelson, 1975, p. 175; Rawlins, 1987]. However, in our opinion, such assumptions do not have sufficient basis.
On this issue, see [Neugebauer, 1968, p. 181; Shevchenko, 1988; Vogt, 1925], as well as [Newton, 1985, Chapter IX].
More detailed review methods of pre-Ptolemaic astronomy, see.
Or in other words: “Mathematical collection (construction) in 13 books.”
The existence of “Little Astronomy” as a special direction in ancient astronomy is recognized by all historians of astronomy with the exception of O. Neugenbauer. See on this issue [NAMA, pp. 768-769].
See on this issue [Idelson, 1975, pp. 141-149].
For the Greek text, see (Heiberg, 1907, S.149-155]; for the French translation, see; for descriptions and studies, see [NAMA, pp. 901,913-917; Hamilton etc., 1987; Waerden, 1959, Col. 1818- 1823; 1988(2), S.298-299].
The only more or less complete edition of the “Tables at Hand” belongs to N. Alma; For the Greek text of Ptolemy's Introduction, see ; For research and descriptions, see .
For Greek text, translation and commentary, see.
For Greek text see ; a parallel German translation, including those parts that have been preserved in Arabic, see [ibid., S.71-145]; Greek text and parallel translation into French see; Arabic text with English translation of the part missing in the German translation, see ; For research and commentary, see [NAMA, pp. 900-926; Hartner, 1964; Murschel, 1995; SA, pp. 391-397; Waerden, 1988(2), p.297-298]; description and analysis of Ptolemy’s mechanical model of the world in Russian, see [Rozhanskaya, Kurtik, p. 132-134].
For the Greek text of the surviving part, see ; for Greek text and French translation see ; For research and commentary, see .
For fragments of the Greek text and Latin translation, see; research see .
The Arabic text has not yet been published, although several manuscripts of this work are known, earlier than the era of al-Majriti.; for Latin translation see ; translation into German see ; For research and commentary, see [NAMA, pp. 857-879; Waerden, 1988(2), S.301-302; Matvievskaya, 1990, pp. 26-27; Neugebauer, 1968, pp. 208-209].
For Greek text see ; for Greek text and parallel translation into English see ; For a complete translation into Russian from English, see [Ptolemy, 1992]; translation into Russian from ancient Greek of the first two books, see [Ptolemy, 1994, 1996); For an essay on the history of ancient astrology, see [Kurtik, 1994]; For research and commentary, see .
For a description and analysis of Ptolemy's cartographic projection methods, see [Neugebauer, 1968, pp. 208-212; NAMA, p.880-885; Toomer, 1975, pp. 198-200].
For Greek text see ; collection of ancient maps see; translation into English see ; for translation of individual chapters into Russian, see [Bodnarsky, 1953; Latyshev, 1948]; For a more detailed bibliography concerning Ptolemy's Geography, see [NAMA; Toomer, 1975, p. 205], see also [Bronshten, 1988, p. 136-153]; about the geographical tradition in the countries of Islam, dating back to Ptolemy, see [Krachkovsky, 1957].
For a critical edition of the text, see ; for descriptions and analysis see [NAMA, pp. 892-896; Bronshten, 1988, p. 153-161]. For a more complete bibliography, see.
For Greek text see ; German translation with commentary see ; For astronomical aspects of Ptolemy’s musical theory, see [NAMA, pp. 931-934]. Brief essay for the musical theory of the Greeks, see [Zhmud, 1994, pp. 213-238].
For Greek text see ; more detailed description cm. . For a detailed analysis of Ptolemy's philosophical views, see.
For Greek text see ; however, according to O. Neugebauer and other researchers, there are no serious grounds for attributing this work to Ptolemy [NAMA, p.897; Haskins, 1924, p.68 et seq.].
For Greek text and German translation see ; translation into French see .
The version of Hajjaj ibn Matar is known in two Arabic manuscripts, of which the first (Leiden, cod. or. 680, complete) dates back to the 11th century. AD, the second (London, British Library, Add.7474), partially preserved, dates back to the 13th century. . Ishaq-Sabit's version came to us in more copies of varying completeness and preservation, of which we note the following: 1) Tunis, Bibl. Nat. 07116 (XI century, complete); 2) Teheran, Sipahsalar 594 (XI century, beginning of book 1, tables and catalog of stars are missing); 3) London, British Library, Add.7475 (early XIII century, books VII-XIII); 4) Paris, Bibl. Nat.2482 (beginning of the 13th century, books I-VI). Full list For currently known Arabic manuscripts of the Almagest, see. For a comparative analysis of the content of various versions of the Almagest translations into Arabic, see.
For an overview of the contents of the most famous jijas of astronomers from Islamic countries, see.
The Greek text in J. Heiberg's edition is based on seven Greek manuscripts, of which the most important are the following four: A) Paris, Bibl. Nat., gr.2389 (complete, 9th century); B) Vaticanus, gr.1594 (complete, 9th century); C) Venedig, Marc, gr.313 (complete, 10th century); D) Vaticanus gr.180 (complete, 10th century). Letter designations for manuscripts were introduced by I. Geiberg.
In this regard, the works of R. Newton have become very famous [Newton, 1985, etc.], who accuses Ptolemy of falsifying astronomical observation data and concealing the astronomical (heliocentric?) system that existed before him. Most historians of astronomy reject R. Newton's global conclusions, while recognizing that some of his observational results cannot but be considered fair.
Ptolemy , and completely - Claudius Ptolemy (Claudius Ptolemaeus) was born between 127-145. AD in Alexandria (Egypt), an ancient astronomer, geographer and mathematician who considered the Earth to be the center of the universe (the “Ptolemaic system”). Unfortunately, very little is currently known about his life. (Except that the Ptolemaic dynasty established itself in Egypt as a result of the conquests of Alexander the Great, who gave Egypt as a reward to one of his outstanding military leaders. The famous Egyptian queen Cleopatra also bore the surname Ptolemy. - S.A. Astakhov.)
The results of his work on astronomy were preserved in his large book "Mathematics syntax" ("Mathematical Collection"), which eventually becomes known as "Ho megas astronomos" ("The Great Astronomer"). However, to refer to this book in the 9th century, Arab astronomers used the Greek term "Megiste" ("excellent"). When the Arabic definite article "al" (another meaning is "as", in English - "like") was written together, the name became known as "Almagest", which is still used today.
The Almagest is divided into 13 separate volumes, each of which considers a specific astronomical concept related to the stars and objects of the solar system (the Earth and all other celestial bodies related to the solar system). Without any doubt, the Almagest is an encyclopedia of nature, which has made it so useful for many generations of astronomers and had a profound influence on them. In essence, this is a synthesis of the results obtained by Ancient Greek astronomy, as well as the main source of information about the work of Hipparchus, apparently the greatest astronomer of antiquity. In the book it is often difficult to determine which information belongs to Ptolemy and which to Hipparchus, because Ptolemy significantly supplemented Hipparchus's data with his own observations, apparently using similar or similar instruments. For example, if Hipparchus compiled his star catalog (the first of its type) based on data on 850 stars, then Ptolemy expanded the number of stars in his own catalog to 1,022.
Ptolemy repeated observations of the movements of the Sun, Moon and planets of the solar system again and again and corrected Hipparchus' data - this time in order to formulate his own geocentric theory, which is currently known as the Ptolemaic model of the structure of the solar system. In the first book of the Almagest Ptolemy describes this geocentric system in detail and tries to prove, using various arguments, that there must be a stationary Earth at the center of the universe. It is necessary to note his very consistent proof that in the case of the Earth’s movement, as previously assumed by some of the Greek philosophers, over time, certain phenomena will appear and should be detected in the starry sky, in particular the parallaxes of stars. On the other side, Ptolemy argued that since all bodies fall to the center of the universe, it is the Earth that should be located there in accordance with the directions of freely falling drops of water. Moreover, if the Earth is not the center, then it must rotate with a period of 24 hours, and, therefore, bodies thrown vertically upward should not fall on the same place, as is the case in practice. Ptolemy was able to prove that by that time not a single observation contradicting these arguments had been obtained. As a result, the geocentric system became the absolute truth for Western Christendom until the 15th century, when it was supplanted by the heliocentric system developed by the great Polish astronomer Nicolaus Copernicus.
Ptolemy established the following order for the objects of the solar system: Earth (center), Moon, Mercury, Venus, Sun, Mars, Jupiter and Saturn. To explain the irregularities in the motion of these celestial bodies, he, just like Hipparchus, needed a system of trims and epicycles or one of the moving eccentrics (both systems developed by Apollo of Pergamon, a Greek geometer of the 3rd century BC) to describe their movements only and exclusively with the help of uniform movement in circles.
In the Ptolemaic system, the trims are large circles centered on the Earth, and the epicycles are circles of smaller diameter, the centers of which move uniformly along the circles of the trims. At the same time, the Sun, Moon and planets move along the circles of their own epicycles. Or, for a moving eccenter, there is a circle with a center shifted relative to the Earth towards the planet moving around this circle. Both schemes are mathematically equivalent. But even with the introduction of these concepts, not all observed elements of planetary motion could be explained. By introducing another concept into astronomy, Ptolemy showed his genius brilliantly. He proposed that the Earth should be located at some distance from the center of trim for each planet and that the center of the planetary trim and epicycle for assumed uniform cyclic motion was an imaginary point lying between the location of the Earth and another imaginary point, which he called the equant. In this case, the Earth and the equant lie on the same diameter of the corresponding planetary trim. In addition, he believed that the distance from the Earth to the center of trim should be equal to the distance from the center of trim to the equant. With this hypothesis Ptolemy was able to explain much more accurately many of the observed elements of planetary motions.
In the Ptolemaic system the ecliptic plane is a clear solar annual path against the background of stars. It should be assumed that the planets' trim planes are inclined at small angles relative to the ecliptic plane, but the planes of their epicycles must be inclined at the same angles relative to the trims so that the epicycle planes are always parallel to the ecliptic plane. The trim planes of Mercury and Venus were chosen to ensure the oscillations of these planets relative to the ecliptic plane (above - below), and, therefore, the planes of their epicycles were selected to ensure the corresponding oscillations relative to their trims.
However, it was still necessary to explain the so-called retrograde (reverse) motion, which was periodically observed in the form of obvious reverse loops of the trajectories of the outer planets against the background of stars (for Mars, Jupiter and Saturn).
Although Ptolemy and understood that the planets were located much closer to the Earth than the "fixed" or "fixed" stars, he apparently believed in the physical existence of "crystalline spheres" to which - as they then said - all celestial bodies were attached. Beyond the sphere of the fixed stars, Ptolemy assumed the existence of other spheres, ending in connection with the “primum mobile” (“prime mover” - maybe God?), which had the necessary power to ensure the movement of the remaining spheres that make up the entire observable universe.
As, first of all, a geometer, Ptolemy performed several important mathematical works. He presented the new geometric theorems and proofs he developed in a book called "Analemma" (“Peri analemmatos” - Greek, “De analemmate” - Latin), where he discussed in detail the properties of projections of points onto the celestial sphere (an imaginary sphere expanding outward from the Earth for infinity, onto the surface of which objects located in space are projected), in particular , into three planes located among themselves according to the rule of the right screw (“gimlet”, if we proceed from the school physics textbook) at right angles to each other - the horizon, the meridian, and the primary vertical. In another book - "Planisphaerium" - Ptolemy deals with stereographic projection - drawing projections of a solid body onto a plane - however, here too he used the south pole of the celestial sphere as the center of his projections. (The point where projection lines intersect is used to produce perspective distortions, such as in axonometric projections.)
Besides, Ptolemy developed my own calendar, which, in addition to weather predictions, indicated the times of rising and setting of stars in the morning and evening twilight. Other mathematical publications contain a work (in two volumes) entitled "Hypotheseis ton planomenon" ("The Planetary Hypothesis"), and two separate geometric publications, one of which contains a rationale for the existence of no more than three dimensions of space; in another he attempts to prove Euclid's parallel postulate. According to one review Ptolemy wrote three books on mechanics; another manual, however, mentions only one - "Peri rope" ("On balancing").
Ptolemy's work in the field of optical phenomena was recorded in "Optics" ("Optica"), the original edition of which consisted of five volumes. In the last volume, he works with the theory of refraction (the change in the direction of light and other energy waves when they cross the interface between a medium of one density and a medium of another density) and at the same time discusses changes in the location of celestial bodies depending on the height above the horizon. This was the first documented attempt to explain an actually observed phenomenon (atmospheric refraction). Mention should also be made of Ptolemy's three-volume monograph on music, known as Harmonica.
Ptolemy's reputation as a geographer rests chiefly on his "Geographike hyphegesis" ("Handbook of Geography"), which was divided into eight volumes; and which contained information on how to create maps and lists of places in Europe, Africa and Asia and create tables of the location of geographic features by latitude and longitude. We note, however, that there were many errors in the Manual - for example, the equator was set too far to the north, and the circumference of the Earth was almost 30 percent less than what, strictly speaking, had already been determined quite accurately (by Eratosthenes); there were also some contradictions between the text and the maps. Of course, the Guide as a whole cannot be considered "good geography" because Ptolemy makes no mention of the climate, natural conditions, inhabitants, or peculiar characteristics of the countries with which he deals. Also sloppy is his geographical elaboration of features such as rivers and mountainous areas. Those. the work turned out to be of very limited use.
The name “Almagest” does not belong to Ptolemy himself, it is of later origin, moreover, of Arab origin. Ptolemy wrote in Greek and called his work: (“Megale syntax”), which means “Great Construction.” The word "syntax" has several meanings. It can be translated both as “treatise” and “essay.” All these translation options are found in various sources.
Ptolemy himself, in references to his book, often calls it, which means “Mathematical Construction.” Did the Arab translators of Ptolemy's work turn it out of respect for its author or simply out of negligence?????? (“big”) in ??????? (“the greatest”), so the Arabs began to call Ptolemy’s book for short Al Magisti, which is where the name “Almagest” came from.
What is “Almagest”? This is a very extensive work, English translation it covers more than 600 large format pages. The Almagest was divided by Ptolemy himself into 13 books (the text sometimes contains references to one or another book). Subsequently, scribes, translators or commentators divided each book into further chapters (from 5 to 19 chapters in each book, for a total of 146 chapters). The fact that the division into chapters does not belong to Ptolemy is convinced by the absence in the text of his work of any references to chapter numbers or titles.
The Almagest books do not have titles; their content can be judged (if you do not read the entire text) by the chapter headings.
Book I is introductory. It states that the vault of heaven moves as a single sphere, that the Earth is spherical, is located in the center of the celestial sphere, has negligible (point-like) dimensions in comparison with it, and is motionless. The second half of Book I provides the basics of Ptolemaic spherical trigonometry and a number of useful tables, as well as a description of some simple goniometer instruments.
Book II provides a solution to a number of general problems of spherical astronomy, Book III examines the movement of the Sun along the ecliptic and the solar anomaly (arising, as we now know, from the uneven movement of the Earth around the Sun in an elliptical orbit), Book IV discusses the apparent movement of the Moon and its anomalies. In Book V, Ptolemy builds his theory of the movement of the Moon, based on a combination of several circular movements, and introduces the concepts of eccentric and epicycle.
Book VI is devoted to the theory of solar and lunar eclipses, the basis for which are calculations of the moments of syzygies (new moons and full moons), as well as the movement of the Moon in latitude, due to the fact that its orbit is inclined to the ecliptic plane at a small angle (500"). Here Tables of eclipses are given.
Books VII and VIII are devoted to the fixed stars. They contain descriptions of the constellations accessible to observation in Greece and Alexandria, and the famous catalog of stars compiled by Ptolemy based on the observations of Hipparchus and his own. This catalog shows the positions of 1025 stars.
In books IX - XI, the theory of planetary motion is built, that famous “Ptolemaic world system”, which is described (not always correctly) in all astronomy textbooks and in many popular books.
In Book XII, Ptolemy examines the retrograde movements of the planets on the celestial sphere and finds that the arcs they cover are in agreement with his theory. Here is a table of planetary stations (at which the planet changes its direct motion along the ecliptic to a retrograde motion or vice versa). Book XIII is devoted to the movement of planets in latitude.
This brief listing does not cover all the issues presented in Ptolemy's ore. While developing his geometric constructions, he has to “along the way” prove a number of theorems, he gives numerous examples and calculations, describes the instruments and observation methods used, as well as the results of observations of a wide range of celestial phenomena, both his own and his predecessors: Greek and Babylonian astronomers. These phenomena include solar and lunar eclipses, lunar occultation of stars, positions of planets relative to stars, solstices, equinoxes, lunar phases, etc.
