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Ptolemy's Almagest
"Whatever we now understand of Ptolemy ... is in this book."--Noel Swerdlow, University of Chicago
693 pages, Hardcover
First published January 1, 150
About the author
Ptolemy
286 books118 followersGeocentric model of Greek astronomer and geographer Ptolemy, who flourished in 2nd century at Alexandria, for the universe dominated cosmological theory until the Renaissance.
Ptolemy compiled Almagest , a comprehensive treatise on astronomy, geography, and mathematics, about 150.
The Ptolemaic system dominated medieval cosmology until Nicolaus Copernicus contradicted it.
Claudius Ptolemy (circa 90 – circa 168), a Roman citizen of Egypt, wrote. As a poet, he composed a single epigram in the Anthology. He lived in Egypt under Roman rule. Theodore Meliteniotes proposed possibly correct but late and unsupported birthplace in the town of Ptolemais Hermiou in the Thebaid circa 1360. No reason exists to suppose that he ever lived anywhere else.
Ptolemy authored at least three works of continuing importance to later Islamic and European science. People first knew originally Μαθηματικὴ Σύνταξις, "Mathematical Treatise"). The second Geography thoroughly discusses the knowledge of the Roman world. In the third, known sometimes as the Apotelesmatika (Ἀποτελεσματικά), more commonly as the Tetrabiblos (Τετράβιβλος, and in Latin as the Quadripartitum or four books, he attempted to adapt horoscopes to the Aristotelian natural philosophy of his day.
Ptolemy compiled Almagest , a comprehensive treatise on astronomy, geography, and mathematics, about 150.
The Ptolemaic system dominated medieval cosmology until Nicolaus Copernicus contradicted it.
Claudius Ptolemy (circa 90 – circa 168), a Roman citizen of Egypt, wrote. As a poet, he composed a single epigram in the Anthology. He lived in Egypt under Roman rule. Theodore Meliteniotes proposed possibly correct but late and unsupported birthplace in the town of Ptolemais Hermiou in the Thebaid circa 1360. No reason exists to suppose that he ever lived anywhere else.
Ptolemy authored at least three works of continuing importance to later Islamic and European science. People first knew originally Μαθηματικὴ Σύνταξις, "Mathematical Treatise"). The second Geography thoroughly discusses the knowledge of the Roman world. In the third, known sometimes as the Apotelesmatika (Ἀποτελεσματικά), more commonly as the Tetrabiblos (Τετράβιβλος, and in Latin as the Quadripartitum or four books, he attempted to adapt horoscopes to the Aristotelian natural philosophy of his day.
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November 13, 2019
… it is not fitting even to judge what is simple in itself in heavenly things on the basis of things that seem to be simple among us.
In my abysmal ignorance, I had for years assumed that tracking the orbits of the sun and planets would be straightforward. All you needed was a starting location, a direction, and the daily speed—and, with some simple arithmetic and a bit of graph paper, it would be clear as day. Attempting to read Ptolemy has revealed the magnitude of my error. Charting the heavenly bodies is a deviously complicated affair; and Ptolemy’s solution must rank as one of the greatest intellectual accomplishments of antiquity—fully comparable with the great scientific achievements of European Enlightenment. Indeed, Otto Neugebauer, the preeminent scholar of ancient astronomy, went so far as to say:
One can perfectly well understand the ‘Principia’ without much knowledge of earlier astronomy but one cannot read a single chapter in Copernicus or Kepler without a thorough knowledge of Ptolemy’s “Almagest”. Up to Newton all astronomy consists in modifications, however ingenious, of Hellenistic astronomy.
With more hope than sense, I cracked open my copy of The Great Books of the Western World, which has a full translation of the Almagest in the 16th volume. Immediately repulsed by the text, I then acquired a students’ edition of the book published by the Green Lion Press. This proved to be an excellent choice. Through introductions, preliminaries, footnotes, and appendices—not to mention generous omissions—this edition attempts to make Ptolemy accessible to a diligent college student. Even so, for someone with my background to attain a thorough knowledge of this text, he would still require months of dedicated study with a teacher as a guide. For the text is difficult in numerous ways.
Most obviously, this book is full of mathematical proofs and calculations, which are not exactly my strong suit. Ptolemy’s mathematical language—relying on the Greek geometrical method—will be unfamiliar to students who have not read some Euclid; and even if it is familiar, it proves cumbrous for the sorts of calculations demanded by the subject. To make matters worse, Ptolemy employs the sexagesimal system (based on multiples of 60) for fractions; so his numbers all must be converted into our decimals for calculation. What is more, even the names of the months Ptolemy uses are different, bearing their Egyptian names (Thoth, Phaöphi, Athur, etc.), since Ptolemy was an Alexandrian Greek. Yet even if we put these technical obstacles to the side, we are left with Ptolemy’s oddly infelicitous prose, which the translator describes thus:
In general, there is a sort of opacity, even awkwardness, to Ptolemy’s writing, especially when he is providing a larger frame for a topic or presenting a philosophical discussion.
Thus, even in the non-technical parts of the book, Ptolemy’s writing tends to be headache-inducing. All this combines to form an unremitting slog. So since my interest in this book was amateurish, I skimmed and skipped liberally. Yet this text is so rich that, even proceeding in such a dilettantish fashion, I managed to learn a great deal.
Ptolemy’s Almagest, like Euclid’s Elements, proved so comprehensive and conclusive when it was published that it rendered nearly all previous astronomical work obsolete or superfluous. For this reason, we know little about Ptolemy’s predecessors, since there was little point in preserving their work after Ptolemy summed it up in such magnificent fashion. As a result it is unclear how much of this book is original and how much is simply adapted. As Ptolemy himself admits, he owes a substantial debt to the astronomer Hipparchus, who lived around 200 years earlier. Yet it seems that Ptolemy originated the novel way of accounting for the planets’ position and speed, which he puts forth in later books.
Ptolemy begins by explaining the method by which he will measure chords; this leads him to construct one of the most precise trigonometric tables from antiquity. Later, Ptolemy goes on to produce several proofs of spherical trigonometry, which allows him to measure distances on the inside of a sphere, making this book an important source for Greek trigonometry as well as astronomy. Ptolemy also employs Menelaus’ Theorem, which uses the fixed proportions of a triangle to establish ratios. (From this I see that triangles are marvelously useful shapes, since they are the only shape which is rigid—that is, the angles cannot be altered without also changing the ratio of the sides, and vice versa. This is also, by the way, what makes triangles such strong structural components.)
Ptolemy gets down to business in analyzing the sun’s motion. This is tricky for several reasons. For one, the sun does not travel parallel to the “fixed stars” (so called because the stars do not position change relative to one another), but rather at an angle, which Ptolemy calculates to be around 23 degrees. We now know this is due to earth’s axial tilt, but for Ptolemy it was called the obliquity of the ecliptic (the angle of the sun's path). Also, the angle that the sun travels through the sky (straight overhead or nearer the horizon) is determined by one’s latitude; this also determines the seasonal shifts in day-length; and during these shifts, the sun rises on different points on the horizon. To add to these already daunting variables, the sun also shifts in speed during the course of the year. And finally, Ptolemy had to factor in that the procession of the equinoxes—the ecliptic’s gradual westward motion from year to year.
The planets turn out to be even more complex. For they all exhibit anomalies in their orbits which entail further complications. Venus, for example, not only speeds up and slows down, but also seems to go forwards and backwards along its orbit. This leads Ptolemy to the adoption of epicylces—little circles which travel along the greater circle, called the “deferent,” of the planet’s orbit. But to preserve the circular motion of the deferent, Ptolemy must place the center (called the "eccentric") away from earth, in empty space. Then, Ptolemy introduces another imaginary circle, around which the planet travels with constant velocity: and the center of this is called the “equant,” which is also in empty space. Thus the planet’s motion was circular around one point (the eccentric) and constant around another circle (the equant), neither of which coincide with earth (so much for geocentric astronomy). In addition to all this, the orbit of Venus is not exactly parallel with the sun’s orbit, but tilted, and its tilt wobbles throughout the year. For Ptolemy to account for all this using only the most primitive observational instruments and without the use of calculus or analytic geometry is an extraordinary feat of patience, vision, and drudgery.
Even after writing all this, I am not giving a fair picture of the scope of Ptolemy’s achievement. This book also includes an extensive star catalogue, with the location and brightness of over one thousand stars. He argues strongly for earth’s sphericity and even offers a calculation of earth’s diameter (which was 28% too small). Ptolemy also calculates the distance from the earth to the moon, using the lunar parallax (the difference in the moon’s appearance when seen from different positions on earth), which comes out the quite accurate figure of 59 earth radii. And all of this is set forth in dry, sometimes baffling prose, accompanied by pages of proofs and tables. One can see why later generations of astronomers thought there was little to add to Ptolemy’s achievement, and why Arabic translators dubbed it “the greatest” (from which we get the English name).
A direct acquaintance with Ptolemy belies his popular image as a metaphysical pseudo-scientist, foolishly clinging to a geocentric model, using ad-hoc epicycles to account for deviations in his theories. To the contrary, Ptolemy scarcely ever touches on metaphysical or philosophical arguments, preferring to stay in the precise world of figures and proofs. And if science consists in predicting phenomena, then Ptolemy’s system was clearly the best scientific theory around for its range and accuracy. Indeed, a waggish philosopher might dismiss the whole question of whether the sun or the earth was at the “center” as entirely metaphysical (is it falsifiable?). Certainly it was not mere prejudice that kept Ptolemy’s system alive for so long.
Admittedly, Ptolemy does occasionally include airy metaphysical statements:
We propose to demonstrate that, just as for the sun and moon, all the apparent anomalistic motions of the five planets are produced through uniform, circular motions; these are proper to the nature of what is divine, but foreign to disorder and variability.
Yet notions of perfection seem hard to justify, even within Ptolemy’s own theory. The combined motions of the deferent and the epicycle do not make a circle, but a wavy shape called an epitrochoid. And the complex world of interlocking, overlapping, slanted circles—centered on imaginary points, riddled with deviations and anomalies—hardly fits the stereotypical image of an orderly Ptolemaic world.
It must be said that Ptolemy’s system, however comprehensive, does leave some questions tantalizingly unanswered. For example, why do Mercury and Venus stay within a definite distance from the sun, and travel along at the same average speed as the sun? And why are the anomalies of the “outer planets” (Mars, Jupiter, Saturn) sometimes related to the sun’s motion, and sometimes not? All this is very easy to explain in a heliocentric model, but rather baffling in a geocentric one; and Ptolemy does not even attempt an explanation. Even so, I think any reader of this volume must come to the conclusion that this is a massive achievement—and a lasting testament to the heights of brilliance and obscurity that a single mind can reach.
July 16, 2021
Today, most use the date of birth of Jesus Christ as a reference point from which we measure time along with the Gregorian calendar to track time and a geographical reference line or longitude 0° that passes through Greenwich, London.
Claudius Ptolemy (c.100-c.170CE) in the Almagest (150CE) uses the original ancient Egyptian solar calendar (12-month, 365-day calendar) although his meridian for all time determination passes through Alexandria, Egypt where he worked and his reference point of time, the epoch, is the Era of Nabonassar in which year 1 is the commencement of the reign of this Babylonian King. Ptolemy selected this era as this was the beginning from which ancient astronomical observations are preserved.
This book is written in Ancient Greek with the title Mathematike Syntaxis or the English equivalent Mathematical Systematic Treatise but the book only became famous under its Arabic name the Almagest meaning "The Greatest".
Ptolemy applies Euclid's and Apollonius' geometry with Hipparchus' trigonometry to present the structure of the heavens and behavior of the celestial bodies; Earth, Moon, Sun, the five planets, and the "fixed" stars. He employs the language of mathematics to describe heavenly phenomena and arithmetic calculations that can predict the movements and positions of the celestial objects and their relation to one another in his intricate geometrical design of the (Ptolemaic) geocentric system.
Even though Ptolemy did not possess a telescope for his observations, as the telescope was only invented by the Dutch spectacle maker at the beginning of the 17th century, he uses other instruments such as the armillary sphere (similar to the astrolabe that Ptolemy referred to as the horoscopic instrument) to map the position of the stars around the Earth and the parallactic instrument (triquetrum) to determine the altitudes of the heavenly bodies.
It took Ptolemy (not to be confused with the members of the Ptolemaic dynasty) a quarter of a century to gather the data and write the Almagest but it was all worthwhile as his geocentric model reigned for 1,500 years until it was officially replaced by Copernicus' heliocentric system.
In all likelihood, Ptolemy's reference books came from the Great Library of Alexandria but unfortunately, he makes no mention of it which would have been a nice historical account of the library before it was destroyed. Also, there was not one birds-eye view illustration of his entire geocentric model with the Earth at the center and the 365-day path of the planets revolving in epicycles (small circles) that orbit along the deferent (large circle); a somewhat complex drawing of numerous orbiting loops.
This 700-page book was a rather dry read. Nevertheless, Ptolemy wrote the book without the constraints of his European successors, particularly the natural philosophers of the Early modern period, that were obligated to dedicate their work to a King or an Empress for allowing them to think (pun intended) and wherein every chapter they had to praise God to avoid persecution. Ptolemy virtually thanks no nobility other than Hipparchus whom he refers to as the "a great lover of truth" as he compares his observations and results with those of Hipparchus. So, there are no references to the ancient Gods or emperors. This book is in a way proof that in this period, place, and time the academia was unburdened by unnecessary praise to physical and metaphysical superiors; perhaps the golden age of Alexandria.
Claudius Ptolemy (c.100-c.170CE) in the Almagest (150CE) uses the original ancient Egyptian solar calendar (12-month, 365-day calendar) although his meridian for all time determination passes through Alexandria, Egypt where he worked and his reference point of time, the epoch, is the Era of Nabonassar in which year 1 is the commencement of the reign of this Babylonian King. Ptolemy selected this era as this was the beginning from which ancient astronomical observations are preserved.
This book is written in Ancient Greek with the title Mathematike Syntaxis or the English equivalent Mathematical Systematic Treatise but the book only became famous under its Arabic name the Almagest meaning "The Greatest".
Ptolemy applies Euclid's and Apollonius' geometry with Hipparchus' trigonometry to present the structure of the heavens and behavior of the celestial bodies; Earth, Moon, Sun, the five planets, and the "fixed" stars. He employs the language of mathematics to describe heavenly phenomena and arithmetic calculations that can predict the movements and positions of the celestial objects and their relation to one another in his intricate geometrical design of the (Ptolemaic) geocentric system.
Even though Ptolemy did not possess a telescope for his observations, as the telescope was only invented by the Dutch spectacle maker at the beginning of the 17th century, he uses other instruments such as the armillary sphere (similar to the astrolabe that Ptolemy referred to as the horoscopic instrument) to map the position of the stars around the Earth and the parallactic instrument (triquetrum) to determine the altitudes of the heavenly bodies.
It took Ptolemy (not to be confused with the members of the Ptolemaic dynasty) a quarter of a century to gather the data and write the Almagest but it was all worthwhile as his geocentric model reigned for 1,500 years until it was officially replaced by Copernicus' heliocentric system.
In all likelihood, Ptolemy's reference books came from the Great Library of Alexandria but unfortunately, he makes no mention of it which would have been a nice historical account of the library before it was destroyed. Also, there was not one birds-eye view illustration of his entire geocentric model with the Earth at the center and the 365-day path of the planets revolving in epicycles (small circles) that orbit along the deferent (large circle); a somewhat complex drawing of numerous orbiting loops.
This 700-page book was a rather dry read. Nevertheless, Ptolemy wrote the book without the constraints of his European successors, particularly the natural philosophers of the Early modern period, that were obligated to dedicate their work to a King or an Empress for allowing them to think (pun intended) and wherein every chapter they had to praise God to avoid persecution. Ptolemy virtually thanks no nobility other than Hipparchus whom he refers to as the "a great lover of truth" as he compares his observations and results with those of Hipparchus. So, there are no references to the ancient Gods or emperors. This book is in a way proof that in this period, place, and time the academia was unburdened by unnecessary praise to physical and metaphysical superiors; perhaps the golden age of Alexandria.
April 9, 2020
Claudius Ptolemy was active during the 2nd century and the Almagest is his most influential work. Ptolemy was an astronomer and he accepted the geocentric view of the cosmos, which was fairly common in his day. Indeed, it was the most commonly accepted cosmology up until the Renaissance. The Almagest assumes this cosmology. Even with that, the trigonometry and geometry that Ptolemy utilized was to a fair extent correct. The use of the former made his work one of the first of its kind. It wound up being translated into Latin and Arabic and was seen as being the most authoritative work on the subject of astronomy for quite some time. Copernicus later proved the geocentric view wrong.
This edition is really a heavily abridged version made up of large extracts of various books that make up the original work. It does have helpful introductions, footnotes and an appendix provided by the editor and contributors. One of the more notable features of Ptolemy's work is the use of tables mapping the movement of the planets and stars. Ptolemy was dependent on earlier astronomers for some of the observations done before his time. Though these early astronomers may not have known of the cause behind precession, they were able to observe its ultimate effect in the movement of the zodiacal stars.
This work is very influential in the history of science in general and in astronomy in particular. It is an essential work because of the former. I don't slight authors on obsolete knowledge, so I still give the work (or at least what is presented here) around four stars. It's not a particularly enthralling read and I didn't bother checking the reliability of the figures. I am actually glad this edition was an abridgement. I think if it had been any longer it would have been a trial getting through it.
This edition is really a heavily abridged version made up of large extracts of various books that make up the original work. It does have helpful introductions, footnotes and an appendix provided by the editor and contributors. One of the more notable features of Ptolemy's work is the use of tables mapping the movement of the planets and stars. Ptolemy was dependent on earlier astronomers for some of the observations done before his time. Though these early astronomers may not have known of the cause behind precession, they were able to observe its ultimate effect in the movement of the zodiacal stars.
This work is very influential in the history of science in general and in astronomy in particular. It is an essential work because of the former. I don't slight authors on obsolete knowledge, so I still give the work (or at least what is presented here) around four stars. It's not a particularly enthralling read and I didn't bother checking the reliability of the figures. I am actually glad this edition was an abridgement. I think if it had been any longer it would have been a trial getting through it.
August 16, 2014
Ok, geocentricism is wrong. But, the way that most people call it "pseudo- science" is intolerable. It's easy in retrospect to look back at theories such as these and ridicule them for their inaccuracy. But, look up in the sky: doesn't the sun rise and set? Of coarse. Just because our horizons have been extended, doesn't mean everything under it has vanished from our sight. Take for instance the atom, which by defintion is uncuttable or the universe which holds all that exists.
In other words, paradigms shift, but the illusions stay. Reading a book such as this- "riddled with inaccuracies"- is a lesson in science that is imperrative to learn. His intellect was powerful and his calculations and explanations were influencial to astronomy up to the renaissance. I confess my lack of training in mathematics but, the diagrams filled in these picture tell me enough of the inquisitive nature of his mind. He builds off of and improves upon Aristotle's cosmology- another paradigm shifter- and quotes earlier authorities of astronomy for calculations.
He is famous for categorizing the 48 constellations with their mythological origins and it's here that Ptolemy is still relaven also. Greek and Roman religion may be dead, but the patterns in the sky are still there. Through every paradigm shift and religious evolution, it's descent into history and mythology preserves it's emblem.
In other words, paradigms shift, but the illusions stay. Reading a book such as this- "riddled with inaccuracies"- is a lesson in science that is imperrative to learn. His intellect was powerful and his calculations and explanations were influencial to astronomy up to the renaissance. I confess my lack of training in mathematics but, the diagrams filled in these picture tell me enough of the inquisitive nature of his mind. He builds off of and improves upon Aristotle's cosmology- another paradigm shifter- and quotes earlier authorities of astronomy for calculations.
He is famous for categorizing the 48 constellations with their mythological origins and it's here that Ptolemy is still relaven also. Greek and Roman religion may be dead, but the patterns in the sky are still there. Through every paradigm shift and religious evolution, it's descent into history and mythology preserves it's emblem.
June 29, 2019
Well I am finished with the Almagest. While I did give the book a 5/5 star rating because of its complexity and depth I was profoundly impacted with the scientific process of the findings, the methodology and the sheer complexity of the system involved.
For the layman, the first two books will do. The first two books are also the most clearly defined books, everything after the Astrolabe gets a little fuzzy (that is to say, some of the data in the tables are not clearly defined as to how they are actually gotten). But anyone should be able to follow the first two books of the Almagest without any additional help. A fair warning: it will involve a sufficient amount of page-flipping to satisfy nearly any reader.
Because of life, it had taken me a little over a year to complete this. I recommend perhaps not stretching it out -so- long, but you definitely can with a book like this, moreso than other books. I am still left with many different facts and figures memorized from the star tables and relations of the planets in particular. You learn quite a lot about stars and planetary visibilities at night. This is a book for someone who does want to learn more, not just about how they calculated astronomical data back at the beginning of the first millennium, but about stars and planetary movements in general.
For the lover of the philosophy of science itself, this book does not have too much to work with. It does have -some- important statements here and there, but nothing major. It is more of an analytical book. And if you enjoy mathematics or astronomy or just want to know where and how the categorization of the stars and systems in the sky came from in astrophysics, look no further than this highly influential book. Quite a complex read at times and also contains the foundation for trigonometry. The theorems of Menelaus are used here and by Fibonacci as well in some of his numerically proportional relations, so if you liked the findings of book I, look there for their other early adaptation as well.
A great read. Wouldn't do it again, though.
For the layman, the first two books will do. The first two books are also the most clearly defined books, everything after the Astrolabe gets a little fuzzy (that is to say, some of the data in the tables are not clearly defined as to how they are actually gotten). But anyone should be able to follow the first two books of the Almagest without any additional help. A fair warning: it will involve a sufficient amount of page-flipping to satisfy nearly any reader.
Because of life, it had taken me a little over a year to complete this. I recommend perhaps not stretching it out -so- long, but you definitely can with a book like this, moreso than other books. I am still left with many different facts and figures memorized from the star tables and relations of the planets in particular. You learn quite a lot about stars and planetary visibilities at night. This is a book for someone who does want to learn more, not just about how they calculated astronomical data back at the beginning of the first millennium, but about stars and planetary movements in general.
For the lover of the philosophy of science itself, this book does not have too much to work with. It does have -some- important statements here and there, but nothing major. It is more of an analytical book. And if you enjoy mathematics or astronomy or just want to know where and how the categorization of the stars and systems in the sky came from in astrophysics, look no further than this highly influential book. Quite a complex read at times and also contains the foundation for trigonometry. The theorems of Menelaus are used here and by Fibonacci as well in some of his numerically proportional relations, so if you liked the findings of book I, look there for their other early adaptation as well.
A great read. Wouldn't do it again, though.
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February 27, 2011I can’t rate this book. Quite frankly, I didn’t understand most of it. The Almagest, a transliteration of the Arabic title meaning “The Greatest”, was the standard for astronomical calculations for over 1000 years. Written in Hellenistic Egypt around 150 AD by Claudius Ptolemaeus (not to be confused with the Ptolemic line of pharaohs from Alexander’s general Ptolemy to Cleopatra), the Almagest provides the astronomical data, geometry and trigonometry to explain a geocentric universe. Though initially lost to the West, the manuscript survived through Arabic translations for several hundred years.
The mathematics could be beautiful. I have heard others describe it as so. I simply just don’t have a strong enough background to appreciate it. Even the layman knows his model is wrong, but the impressive catalogue and proofs demonstrate a level of rigorous thinking that still escapes most of us today.
The mathematics could be beautiful. I have heard others describe it as so. I simply just don’t have a strong enough background to appreciate it. Even the layman knows his model is wrong, but the impressive catalogue and proofs demonstrate a level of rigorous thinking that still escapes most of us today.
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February 12, 2024Ancient science, like modern science, was something that was mathematized. This is not unique to modernity. What’s striking is that the mathematical basis for ancient science is geometry, whereas for us it is algebra. The effects of this are astonishing: Ptolemy right out the gate says that astronomy can instill nobility and beauty in the soul of the stargazer. Moderns would blanch at the notion that science serves a moral or aesthetic function. But in no way is this difference a mark that ancient science is primitive or naive; indeed I would wager that algebraization has made our science, enslaved to a notion of truth as something to be instrumentalized rather than contemplated, far less human, indeed more barbaric and evil, than the science of antiquity. Much to consider.
February 11, 2012
I had to read this and discuss it extensively in college. They just don't make mathematicians like they used to.
October 5, 2017
Ptolemy has grown on me the more I have read it. The approach is a little unclear at times, especially for those who have read Euclid. But his goal seems to be noble, and his model of the cosmos is surprisingly appealing. Also, this opens up the discussion of whether science merely "saves the phenomena" or not...
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September 30, 2016Just finished Ptolemy today *sighs a sigh that's a mixture of relief and disappointment* in math, now on to Copernicus. Should be weird. I feel like I'm pretty well convinced of the legitimacy of the Ptolemaic system wherein Earth is at the center of the universe, so I hope that Copernicus knows what he's doing!
March 25, 2022
It served as the basic guide for Islamic and European astronomers until about the beginning of the 17th century. Its original name was Mathematike Syntaxis (“The Mathematical Arrangement”); Almagest arose as an Arabic corruption of the Greek word for “greatest” (megiste). It was translated into Arabic in the late 8th and early 9th centuries and then from Arabic to Latin by Gerard of Cremona in the last half of the 12th century. Beginning in the 15th century, the Greek text circulated widely in Europe, although the Latin translations from Arabic continued to be more influential.
The Almagest is divided into 13 books. Book 1 gives arguments for a geocentric spherical cosmos and introduces the necessary trigonometry, along with a trigonometry table, that allowed Ptolemy in subsequent books to explain and predict the motions of the Sun, Moon, planets, and stars. Book 2 uses spherical trigonometry to explain cartography and astronomical phenomena (such as the length of the longest day) characteristic of various localities. Book 3 deals with the motion of the Sun and how to predict its position in the zodiac at any given time, and Books 4 and 5 treat the more difficult problem of the Moon’s motion. Book 5 also describes the construction of instruments to aid in these investigations. The theory developed to this point is applied to solar and lunar eclipses in Book 6.
Books 7 and 8 mainly concern the fixed stars, giving ecliptic coordinates and magnitudes for 1,022 stars. This star catalog relies heavily on that of Hipparchus (129 bce), and in the majority of cases Ptolemy simply converted Hipparchus’s description of the location of each star to ecliptic coordinates and then shifted these values by a constant to account for precession over the intervening centuries. These two books also discuss the construction of a star globe that adjusts for precession. The remaining five books, the most original, set forth in detail geometric models for the motion of the five planets visible to the naked eye, together with tables for predicting their positions at any given time.
Earth, he argued, is a stationary sphere at the centre of a vastly larger celestial sphere that revolves at a perfectly uniform rate around Earth, carrying with it the stars, planets, Sun, and Moon—thereby causing their daily risings and settings. Through the course of a year the Sun slowly traces out a great circle, known as the ecliptic, against the rotation of the celestial sphere. (The Moon and planets similarly travel backward—hence, the planets were also known as “wandering stars”—against the “fixed stars” found in the ecliptic.) The fundamental assumption of the Almagest is that the apparently irregular movements of the heavenly bodies are in reality combinations of regular, uniform, circular motions.
The Almagest is divided into 13 books. Book 1 gives arguments for a geocentric spherical cosmos and introduces the necessary trigonometry, along with a trigonometry table, that allowed Ptolemy in subsequent books to explain and predict the motions of the Sun, Moon, planets, and stars. Book 2 uses spherical trigonometry to explain cartography and astronomical phenomena (such as the length of the longest day) characteristic of various localities. Book 3 deals with the motion of the Sun and how to predict its position in the zodiac at any given time, and Books 4 and 5 treat the more difficult problem of the Moon’s motion. Book 5 also describes the construction of instruments to aid in these investigations. The theory developed to this point is applied to solar and lunar eclipses in Book 6.
Books 7 and 8 mainly concern the fixed stars, giving ecliptic coordinates and magnitudes for 1,022 stars. This star catalog relies heavily on that of Hipparchus (129 bce), and in the majority of cases Ptolemy simply converted Hipparchus’s description of the location of each star to ecliptic coordinates and then shifted these values by a constant to account for precession over the intervening centuries. These two books also discuss the construction of a star globe that adjusts for precession. The remaining five books, the most original, set forth in detail geometric models for the motion of the five planets visible to the naked eye, together with tables for predicting their positions at any given time.
Earth, he argued, is a stationary sphere at the centre of a vastly larger celestial sphere that revolves at a perfectly uniform rate around Earth, carrying with it the stars, planets, Sun, and Moon—thereby causing their daily risings and settings. Through the course of a year the Sun slowly traces out a great circle, known as the ecliptic, against the rotation of the celestial sphere. (The Moon and planets similarly travel backward—hence, the planets were also known as “wandering stars”—against the “fixed stars” found in the ecliptic.) The fundamental assumption of the Almagest is that the apparently irregular movements of the heavenly bodies are in reality combinations of regular, uniform, circular motions.
February 10, 2016
I definitely cheated on this one (only skimming over the intro. & first book), as I suspect most of the reviewers here did, too. I skimmed the intro. and the first half of Book I, although I read summaries on the other twelve books of this formidable astronomical treatise. A proper appreciation of this work would take months of careful study and thorough familiarity with the ancient Greek and Egyptian astronomical and mathematical traditions preceding him. This isn't for those, in other words, with a merely dilettantish interest in the subject, like myself. Ptolemy was writing around the 150s in what was then the Greco-Roman city of Alexandria, drawing on the period's best resources, stored in the ancient library at Alexandria. He had at his disposal troves of astronomical charts, containing detailed information--stellar, solar, lunar, planetary movements, for instance--that ancient Greek and Babylonian astronomers had been accumulating for hundreds of years before Ptolemy (not to be confused with the royal Ptolemys) came on the scene. In 230 b.c., Aristarchus of Samos (the "ancient Copernicus") had argued for a heliocentric model of the universe, though his words were largely unheeded. Writing in the second century b.c., Hipparchus was crucial in synthesizing Greek astronomy (largely geometrical until then) with the advanced numerical mathematics of the Babylonians. This synthesis breathed new life into Hellenistic astronomic inquiry, the pinnacle of which we find in Ptolemy's Almagest ("the greatest," in Arabic and Greek).
The Almagest is the single most comprehensive work of astronomical theory to come down to us from antiquity. So wide-ranging was its appeal and subject matter that it eclipsed virtually all other Greek astronomical sources written before the Almagest. These works were no longer copied, and the Almagest was regarded as the most authoritative and comprehensive astronomy text until the scientific revolution in the sixteenth century. Ptolemy's universe is based on Aristotle's vision of the cosmos as a series of concentric spheres with the earth at the very center. Ptolemy helped to develop the advanced mathematics that allowed him to predict (with varying levels of accuracy) the motions of the sun, moon, and planets, and his calculations had unprecedented predictive powers, even though they were based on an the erroneous premise of geocentricism that Aristotle and Plato had posited.
A beneficiary of Hipparchus and Babylonian mathematics, Ptolemy believed that the divine would be reached through the numerical and geometrical study of the planetary bodies. Theology was too far-removed from discernible reality, he reasoned, and physics was too variable, as it dealt with the countless irregularities of the terrestrial sphere. The superlunary realm of aether or quintessence, however, was perfect, and studying it through mathematics, he thought, could lead one to knowledge of the divine Prime mover.
The Ptolemeic model worked remarkably well, though based on central false assumptions. It was a way for him to have his cake and eat it, too--preserving the deeply ingrained ideological beliefs about the place of the earth in the universe (reinforced by common sense, centuries of astronomical thinking, Plato, & Aristotle) and gaining a sophisticated mathematical tool to predict the future of planetary movements.
The Almagest is the single most comprehensive work of astronomical theory to come down to us from antiquity. So wide-ranging was its appeal and subject matter that it eclipsed virtually all other Greek astronomical sources written before the Almagest. These works were no longer copied, and the Almagest was regarded as the most authoritative and comprehensive astronomy text until the scientific revolution in the sixteenth century. Ptolemy's universe is based on Aristotle's vision of the cosmos as a series of concentric spheres with the earth at the very center. Ptolemy helped to develop the advanced mathematics that allowed him to predict (with varying levels of accuracy) the motions of the sun, moon, and planets, and his calculations had unprecedented predictive powers, even though they were based on an the erroneous premise of geocentricism that Aristotle and Plato had posited.
A beneficiary of Hipparchus and Babylonian mathematics, Ptolemy believed that the divine would be reached through the numerical and geometrical study of the planetary bodies. Theology was too far-removed from discernible reality, he reasoned, and physics was too variable, as it dealt with the countless irregularities of the terrestrial sphere. The superlunary realm of aether or quintessence, however, was perfect, and studying it through mathematics, he thought, could lead one to knowledge of the divine Prime mover.
The Ptolemeic model worked remarkably well, though based on central false assumptions. It was a way for him to have his cake and eat it, too--preserving the deeply ingrained ideological beliefs about the place of the earth in the universe (reinforced by common sense, centuries of astronomical thinking, Plato, & Aristotle) and gaining a sophisticated mathematical tool to predict the future of planetary movements.
December 9, 2008
Beautiful mathematical proofs and lots of empirical evidence. A must read to those thinking that serious empirical investigations were not part of science before Galileo.
August 19, 2024
5 stars: loved it. This gave me a lot to think about!
According to Ptolemy in around AD 150, astronomy is the most important mathematical science. The Almagest conveys how the ancient astronomers viewed the relation of the earth to the universe: the earth is round; it does not move; the stars, planets, sun, and moon move around the earth in uniform circular motion; the heavenly bodies are perfect beings that do not change and are not subject to external forces.
Strong Aristotle vibes here. The importance of uniform, circular motion came from him and was in contrast to the rectilinear (up and down) motion of earth's four elements (earth, water, air, fire). For Aristotle--and for Ptolemy--it was important that the heavens be made of a different, 5th element, which meant it needed to move in a different motion: circular because it has no contrary and therefore is unchanging.
Given Ptolemy's fundamental axiom that the motions of the heaven are uniform and circular, there must be an explanation for why the motion of the stars, planets, sun, and moon do not appear to move in a uniform and circular motion. He explains it by combinations of circles, using geometry to demonstrate why it works.
Ptolemy was an incredible thinker. His proofs are thorough and seem to explain the movement of the heavens... but we know that his hypotheses, although accepted for 1500 years, do not hold up to our current observations. What does this say about scientific reasoning? Can we ever know if it is correct? Did Ptolemy consider that the "uniform, circular motion" premise might be incorrect? Still thinking about this. Good reminder that even what seem to be the most settled scientific theories are just that: theories.
So no, we don't read Ptolemy for a science lesson. Instead, we ponder that it is evident that humans have a relentless desire to explain the apparently inexplicable.
According to Ptolemy in around AD 150, astronomy is the most important mathematical science. The Almagest conveys how the ancient astronomers viewed the relation of the earth to the universe: the earth is round; it does not move; the stars, planets, sun, and moon move around the earth in uniform circular motion; the heavenly bodies are perfect beings that do not change and are not subject to external forces.
Strong Aristotle vibes here. The importance of uniform, circular motion came from him and was in contrast to the rectilinear (up and down) motion of earth's four elements (earth, water, air, fire). For Aristotle--and for Ptolemy--it was important that the heavens be made of a different, 5th element, which meant it needed to move in a different motion: circular because it has no contrary and therefore is unchanging.
Given Ptolemy's fundamental axiom that the motions of the heaven are uniform and circular, there must be an explanation for why the motion of the stars, planets, sun, and moon do not appear to move in a uniform and circular motion. He explains it by combinations of circles, using geometry to demonstrate why it works.
Ptolemy was an incredible thinker. His proofs are thorough and seem to explain the movement of the heavens... but we know that his hypotheses, although accepted for 1500 years, do not hold up to our current observations. What does this say about scientific reasoning? Can we ever know if it is correct? Did Ptolemy consider that the "uniform, circular motion" premise might be incorrect? Still thinking about this. Good reminder that even what seem to be the most settled scientific theories are just that: theories.
So no, we don't read Ptolemy for a science lesson. Instead, we ponder that it is evident that humans have a relentless desire to explain the apparently inexplicable.
May 9, 2024
"What has been affirmed without proof, can also be denied without proof" said Euclid. The actual truth is that he was a very good writer, as it is perhaps easier to understand what he writes, even Aristotle understood, but conceptually it was hard for me personally to reason on how he jumped to the conclusion of Geocentrism, other than the fact that he was obviously exaggeratedly into politics and that might have "eclipsed" his vision. In reality the geocentric theory is preceded by the attempt of understanding the moon as ether/ethics, therefore mixing the science with the politics (as back then philosophy, the sciences and politics were not yet separate) and forcing conventions may have obfuscated the views of those ancient philosophers, although they were lovers of the Earth, and that's a very positive thing about it. The same mistake is committed later by Nietzsche after all as he classifies science as a system of faith, which however, it is not, as correctly asserted by the positivists. It's still really nice the fact that the philosophers and the politicians of the time, loved planet earth more than the surroundings, however, to answer certain questions, one must step out of the comfort zone, as Plato stated too (stepping out of a cave), and liking the earth won't mean one can't love the surroundings space.
December 19, 2022
5 stars for impact on human thought. 1 star for readability of the casual browser curious to see what is going on. Leaving aside the Euclid-requiring geometric proofs in spheres, the prose, even with the best translation, is heavy and nearly indecipherable. One wonders if this were intentional or just awkward writing. Nevertheless the achievement is wondrous. Working out longitudes and meridians. Makes me wonder about astrolabes and ship navigation devices and techniques. Working out the ‘fixed sphere of stars’ and their 23 degree tilt from the poles. Learning about epicycles and elongation, station and retrograde to describe the puzzling motion of the planets on the backdrop of the constellations, why thy loop back and forth across the sky. Learning about how Ptolemy concluded the earth was like a point in this stellar geometry, implying the massive size of the celestial sphere. Cool, even for a browser like me.
April 24, 2025
*4.37 Stars
Notes: I read this novel primarily for research purposes. The types of nonfiction content in the book were readable enough for me to understand.
I would advise for this book only to entirely be read through with varying years of past research. There is advanced science and math content (along with other advanced content), that could maybe be difficult to understand otherwise.
I had researched other nonfiction books before earlier last year, so I could easily read through this novel.
There were easy enough to understand written explanations of content, that I had no issue with reading through the book.
However - this novel can only truly be read and understood with past research for years.
This is not light research material at all, and I would not put in any spoilers in this review, simply because I was glad enough to find a copy.
Notes: I read this novel primarily for research purposes. The types of nonfiction content in the book were readable enough for me to understand.
I would advise for this book only to entirely be read through with varying years of past research. There is advanced science and math content (along with other advanced content), that could maybe be difficult to understand otherwise.
I had researched other nonfiction books before earlier last year, so I could easily read through this novel.
There were easy enough to understand written explanations of content, that I had no issue with reading through the book.
However - this novel can only truly be read and understood with past research for years.
This is not light research material at all, and I would not put in any spoilers in this review, simply because I was glad enough to find a copy.
May 24, 2021
The Green Lion edition of the Almagest is quite good. It selects the most important parts of the original work, the preliminaries (for the most part) serve as a helpful foundation for the concepts that Ptolemy goes over, and the translation is quite readable. The formating of the propositions could have been better though; it is not as pleasant to look at as that of Toomer's edition.
This edition of the Almagest makes a decent starting point for those who want to learn ancient Greek astronomy.
This edition of the Almagest makes a decent starting point for those who want to learn ancient Greek astronomy.
December 15, 2023
I first discovered this book when it was referenced on Khan Academy, in the article 'READ: Greco-Roman', in Unit 3, in the course 'World History Project - Origins to the Present'. The article states that this book was written in the Library of Alexandria by the author, who was a scientist, who unfortunately ignored the ideas of Aristarchus who also studied at the library, and theorised almost 2,000 years before Copernicus that the Earth circled the Sun.
September 3, 2021
It's pretty... great. Also long. It's very long.
September 29, 2023
What is he even DOING
January 20, 2024
Very complex and ultimately wrong.
July 13, 2025
had to discuss this for hours on end in a seminar where we couldn’t disagree w the author (hello, convoluted logic ensuring that a geocentric universe is correct!)
December 19, 2025
Erg handig voor profiel werkstuk!
March 8, 2025
Fantastic. The Earth is a point but at the centre of heaven's spheres — the humility and grandiosity of that side by side.
Ptolemy is concise and persuasive. In fact he starts by telling us how a great research paper sets out. I don't blame him for his faults, it would be devilishly hard to understand the Earth is rotating without knowing how far the stars are away. Yes he goes off on epicycles, but the level of numinous mystery at the time, it is miraculous the progress he made.
Ptolemy is concise and persuasive. In fact he starts by telling us how a great research paper sets out. I don't blame him for his faults, it would be devilishly hard to understand the Earth is rotating without knowing how far the stars are away. Yes he goes off on epicycles, but the level of numinous mystery at the time, it is miraculous the progress he made.
December 5, 2016
Both a great milestone in astronomy, as well as a visually beautiful tome, the Almagest seems to exude its own celestial aura. Even in its arcane and often tedious passages, it offers the profound effect of being immersed in the higher inquiries of man's place in the universe. At the very least, The Almagest is worth flipping through, and catching a glimpse into the mind of one of the most influential figures in science.
June 12, 2007
It was good enough for the moon-shot engineers, it's good enough for me.
January 3, 2008
That I shouldn't be an astronomer.
August 13, 2008
The book that proves it doesn't matter if you're right, it matters that you went about it with style.
August 11, 2011
The Manuel of the ancient astronomers.
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