Cláudio Ptolomeu ¾ Nome oriundo da forma latinizada Claudius ainda, denominada pelos árabes de ” Almagesto ” os conhecimentos astronômicos de seus. Almagesto de Claudio 1, × 1,; MB. Almagesto Libro I . × ; 73 KB. Marinus e × ; 89 KB. The following 28 files are in this category, out of 28 total. Satz des Ptolemäus. svg × ; 68 KB. Almagesto Libro I FIG png ×

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Na Astronomia, Ptolomeu sintetiza no ano de d. Dentre eles podemos citar: Ademais, ele fazia uma analogia entre o Sol e a Lua e afirmava que: Ele era usado para determinar a altura dos astros acima do horizonte, sobretudo a do Sol.

Feito em ferro, a rodela graduada era suspensa por um anel e apontado para o objeto celeste de modo a poder-se tomar a altura deste. Os temas abordados foram de maior leveza e simplicidade. However, of all the ancient Greek mathematicians, it is fair to say that his work has generated more discussion and argument than any other. We shall discuss the arguments below for, depending on which are correct, they portray Ptolemy in very different lights.

The ce of some historians show that Ptolemy was a mathematician of the very top rank, arguments of others show that he was no more than a superb expositor, but far worse, some even claim that almsgesto committed a crime against his fellow scientists by betraying the pfolomeu and integrity of his profession. We know very little of Ptolemy’s life.

He made astronomical observations from Alexandria in Egypt during the years AD In fact the first observation which we can date exactly was made by Ptolemy on 26 March while the last was made on 2 Ptoolmeu It was claimed by Theodore Meliteniotes in around that Ptolemy was born in Hermiou which is in Upper Egypt rather than Lower Egypt where Alexandria is situated but since this claim first appears more than one thousand years after Ptolemy lived, it must be treated as relatively unlikely to be true.

In fact there is no evidence that Ptolemy was ever anywhere other than Alexandria. This would indicate that he almahesto descended dr a Greek family living in Egypt and that he was a citizen of Rome, which would be as a result of a Roman emperor giving that ‘reward’ to one of Ptolemy’s ancestors. We do know that Ptolemy used observations made by ‘Theon the mathematician’, and this was almost certainly Theon of Smyrna who almost certainly was his teacher.

Certainly this would make sense since Theon of Smyrna was both an observer and a mathematician who had written on astronomical topics such as conjunctionseclipses, occultations and transits.

Most of Ptolemy’s early works are dedicated to Syrus who may have also been one of his teachers in Alexandria, but nothing is known of Syrus.

If these facts about Ptolemy’s slmagesto are correct then certainly in Theon of Smyrna he did not have a great scholar, for Theon of Smyrna seems not to have understood in any depth the astronomical work he describes. On the other hand Alexandria had a tradition for scholarship which would mean that even if Ptolemy did not have access to the best teachers, he would have access to the libraries where he would have found the valuable reference otolomeu of which he made good use.

Ptolemy’s major works have survived and we shall discuss them in this article. The most important, however, is the Almagest which is a treatise in thirteen books. We should say straight away that, although the work is now almost always known as the Almagest that was not its original name. Its original Greek title translates as The Mathematical Compilation but this title was soon replaced by another Greek title which means The Greatest Compilation. This was translated into Arabic as “al-majisti” and from this the title Almagest was given to the work when it was translated from Arabic to Latin.

The Almagest is the earliest of Ptolemy’s works and gives in detail the almagezto theory of the motions of the Sun, Moon, and planets. Ptolemy made his most original contribution by presenting details for the motions of each of the planets. The Almagest was not superseded until a century after Copernicus presented his heliocentric theory in the De revolutionibus of Grasshoff writes in [8]: From its conception in the second century up to the late Renaissance, this work determined astronomy as a science.

During this time the “Almagest” was not only almagesro work on astronomy; the subject was defined as what is described in the “Almagest”. Ptolemy describes himself very clearly what he is attempting to do in writing the work see for example [15]: For the sake of completeness in our treatment we shall set out everything useful for the theory of the heavens in the proper order, but to avoid undue length we shall merely recount what has been adequately established by the ancients.

However, those topics which have not been dealt with by our predecessors at all, or not as usefully as they might have been, will be discussed at length to the best of our ability. Ptolemy first of all justifies his description of the universe based on the earth-centred system described by Aristotle.


It is a view of the world based on a fixed earth around which the sphere of the fixed stars rotates every day, almagesgo carrying with it the spheres of the sun, moon, and planets. Ptolemy used geometric models to predict the positions of the sun, moon, and planets, using combinations of circular motion known as epicycles.

Having set up this model, Ptolemy then goes on to akmagesto the mathematics which he needs in the rest of the work. Ptolemy devised new geometrical proofs and theorems. This occupies the first two of the 13 books of the Almagest and then, quoting again from the introduction, we almmagesto Ptolemy’s own description of how he intended to develop the rest of the mathematical astronomy in the work see for example [15]: Our final task in this way of approach is the theory of the stars.

Here too it would be appropriate to deal first with the sphere of the so-called ptolomey stars’, and follow that by treating the five ‘planets’, as they are ptolomej. In examining the theory of the sun, Ptolemy compares his own observations of equinoxes with those of Hipparchus and the earlier observations Meton in BC. We shall discuss below in more detail the accusations which have been made against Ptolemy, but this illustrates almagssto the grounds for these accusations since Ptolemy had to have an error of 28 dee in his observation of the equinox to produce this error, and even given the accuracy that could be expected with ancient instruments and methods, it is essentially unbelievable that he could have made an error of this magnitude.

A good almagesyo of this strange error is contained in the excellent article [19]. Based pgolomeu his observations of solstices and equinoxes, Ptolemy found the lengths of the seasons and, based on these, he proposed a simple model for the sun which was a circular motion of uniform angular velocity, but the earth was not at the centre of the circle but almagdsto a distance called the eccentricity from this centre.

This theory of the sun forms the subject of Book 3 of the Almagest. In Books 4 and 5 Ptolemy gives his theory of the moon. Here he follows Hipparchus who had studied three different periods which one could associate with the motion of the moon.

There is the time taken for the moon to return to the same longitude, the time taken for it to return to the same velocity the anomaly and the time taken for it to return ptolomeuu the same latitude. Ptolemy also discusses, as Hipparchus had done, the synodic month almagfsto, that is the time between successive oppositions of the sun and moon. In Book 4 Ptolemy gives Hipparchus ‘s epicycle model for the motion of the moon but he notes, as in fact Hipparchus had done himself, that there are small discrepancies between the model and the observed parameters.

Although noting the discrepancies, Hipparchus seems not to al,agesto worked out a better model, but Ptolemy does this in Book 5 where the model he almagseto improves markedly on the one proposed by Hipparchus. An interesting discussion almaagesto Ptolemy’s theory of the moon is given in [24].

Having given a theory for the motion of the sun and of the moon, Ptolemy was in a position to apply these to obtain a theory of eclipses which he does in Almagfsto 6. The two books deal with the fixed stars and in Book 7 Ptolemy uses his own observations together with those of Hipparchus to justify his belief that the fixed stars always maintain the same positions relative to each other.

He wrote see for example [15]: In these two book Ptolemy also discusses precession, the discovery of which he attributes to Hipparchusbut his figure is somewhat in lamagesto mainly because of the error in the aljagesto of the tropical year which he used. Much of Books 7 and 8 are taken up with Ptolemy’s star catalogue containing over one thousand stars. The final five books of the Almagest discuss planetary theory. This must be Ptolemy’s greatest achievement in terms of an original contribution, since there does not appear to have been any satisfactory theoretical model to explain the rather complicated motions of the five planets before the Almagest.

Ptolemy combined the epicycle and eccentric methods to give his model for the motions of the planets. The path of a planet P therefore consisted of circular motion on an epicycle, the centre C of the epicycle moving round ptolome circle whose centre was offset from the earth.

Category:Ptolemy’s theorem – Wikimedia Commons

Ptolemy’s really clever ptollomeu here was to make the motion of C uniform not about the centre of the circle around which it moves, but around a point called the equant which is symmetrically placed on the opposite side of the centre from the earth.


The planetary theory which Ptolemy developed here is a masterpiece.

He created a sophisticated mathematical model to fit observational data which before Ptolemy’s time was scarce, and the model he produced, although complicated, represents the motions of ee planets fairly well. Toomer sums up the Almagest in [1] as follows: Ptolkmeu it is much more than that. Far from being a mere ‘systemisation’ of polomeu Greek astronomy, as it is sometimes described, it is in many respects an original work.

We will return to discuss some of the accusations made against Ptolemy after commenting briefly on his other works. He published the tables which are scattered throughout the Almagest separately under the title Handy Tables. These were not merely lifted from the Almagest however but Ptolemy made numerous improvements in their presentation, ease of use and he even made improvements in the basic parameters to give greater accuracy.

We only know details of the Handy Tables through the commentary by Theon of Alexandria but in [77] the author shows that care is required since Theon was not fully aware of Ptolemy’s procedures. Ptolemy also did what many writers of deep scientific works have done, and still do, in writing a popular account of his results under the title Planetary Hypothesis. This prolomeu, in two books, again follows the familiar route of reducing the ptoomeu skills needed by a reader.

Ptolemy does this rather cleverly by replacing the abstract geometrical theories by mechanical ones. Ptolemy also wrote a work on astrology.

It may seem strange to the modern reader that someone who wrote such excellent scientific books should write on astrology. However, Ptolemy sees it rather differently for he claims that the Almagest allows one to find the positions of the heavenly bodies, while his astrology book he sees as a companion work describing the effects of the heavenly bodies on people’s ptloomeu.

In a book entitled Analemma he discussed methods of finding the angles need to construct a sundial which involves the projection of points on the celestial sphere.

In Planisphaerium he is concerned with stereographic projection of the celestial sphere onto a plane. This is discussed in [49] where it is stated: Ptolemy does not prove the important property that circles on the sphere become circles on the plane.

Ptolemy’s major work Geography, in eight books, attempts to map the known world giving coordinates of the major places in terms of latitude and longitude. It is not surprising that the maps given by Ptolemy were quite inaccurate in many places for he could not be expected to do more than use the available data and this was of very poor quality for anything outside the Roman Empire, and even parts of the Roman Empire are severely distorted.

In [19] Ptolemy is described as: Another work on Optics is in five books and in it Ptolemy studies colour, reflection, refractionand mirrors of various shapes.

Toomer comments in [1]: Whether the subject matter is largely derived or original, “The Optics” is an impressive example of the development of a mathematical science with due regard to physical data, and is worthy of the author of the “Almagest”.

An English translation, attempting to xlmagesto the inaccuracies introduced in the poor Arabic translation which is our only source of the Optics is given in [14]. The first to make accusations against Ptolemy was Tycho Brahe. He discovered that there was a systematic error of one degree in the longitudes of the stars in the allmagesto catalogue, and he claimed that, despite Ptolemy saying that it represented his own observations, it was merely a conversion of a catalogue due to Hipparchus ptollmeu for precession to Ptolemy’s date.

There is of course definite problems comparing two star catalogues, one of which we have a copy of while the other is lost. After comments by Laplace and Lalande, the to attack Ptolemy vigorously was Delambre. He suggested that perhaps the errors came from Hipparchus and that Ptolemy might have done nothing more serious than to have failed to almagesho Hipparchus ‘s data for the time between the equinoxes and solstices.

However Delambre then goes on to say see [8]: However, Ptolemy was not without his supporters by any means and further analysis led to a belief that the accusations made against Ptolemy by Delambre were false.

Boll writing in says [4]: Vogt showed clearly in his important paper [78] that by considering Hipparchus ‘s Commentary on Aratus and Eudoxus and making the reasonable assumption that the data given there agreed with Hipparchus ‘s star catalogue, then Ptolemy’s star catalogue cannot have been produced from the positions of the stars as given by Hipparchusexcept for a small number of stars where Ptolemy does appear to have taken the data from Hipparchus.