Claudius Ptolemy free essay sample

Born: approximately 85 in Egypt Died: approximately 165 in Alexandria, Egypt One of the most influential Grecian uranologists and geographers of his clip, Ptolemy propounded the geocentric theory in a signifier that prevailed for 1400 old ages. However, of all the ancient Grecian mathematicians, it is just to state that his work has generated more treatment and statement than any other. We shall discourse the statements below for, depending on which are right, they portray Ptolemy in really different visible radiations. The statements of some historiographers show that Ptolemy was a mathematician of the really top rank, statements of others show that he was no more than a brilliant expounder, but far worse, some even claim that he committed a offense against his fellow scientists by bewraying the moralss and unity of his profession. We know really small of Ptolemy s life. He made astronomical observations from Alexandria in Egypt during the old ages AD 127-41. In fact the first observation which we can day of the month precisely was made by Ptolemy on 26 March 127 while the last was made on 2 February 141. It was claimed by Theodore Meliteniotes in around 1360 that Ptolemy was born in Hermiou ( which is in Upper Egypt instead than Lower Egypt where Alexandria is situated ) but since this claim foremost appears more than one thousand old ages after Ptolemy lived, it must be treated as comparatively improbable to be true. In fact there is no grounds that Ptolemy was of all time anyplace other than Alexandria. His name, Claudius Ptolemy, is of class a mixture of the Grecian Egyptian Ptolemy and the Roman Claudius . This would bespeak that he was descended from a Grecian household life in Egypt and that he was a citizen of Rome, which would be as a consequence of a Roman emperor giving that reward to one of Ptolemy s ascendants. We do cognize that Ptolemy used observations made by Theon the mathematician , and this was about surely Theon of Smyrna who about surely was his instructor. Surely this would do sense since Theon of Smyrna was both an perceiver and a mathematician who had written on astronomical subjects such as concurrences, occultations, eclipses and theodolites. Most of Ptolemy s early plants are dedicated to Syrus who may hold besides been one of his instructors in Alexandria, but nil is known of Syrus. If these facts about Ptolemy s instructors are right so surely in Theon of Smyrna he did non hold a great bookman, for Theon of Smyrna seems non to hold understood in any deepness the astronomical work he describes. On the other manus Alexandria had a tradition for scholarship which would intend that even if Ptolemy did non hold entree to the best instructors, he would hold entree to the libraries where he would hold found the valuable mention stuff of which he made good usage. Ptolemy s major plants have survived and we shall discourse them in this article. The most of import, nevertheless, is the Almagest which is a treatise in 13 books. We should state straight off that, although the work is now about ever known as the Almagest that was non its original name. Its original Grecian rubric translates as The Mathematical Compilation but this rubric was shortly replaced by another Greek rubric which means The Greatest Compilation. This was translated into Arabic as al-majisti and from this the rubric Almagest was given to the work when it was translated from Arabic to Latin. The Almagest is the earliest of Ptolemy s plants and gives in item the mathematical theory of the gestures of the Sun, Moon, and planets. Ptolemy made his most original part by showing inside informations for the gestures of each of the planets. The Almagest was non superseded until a century after Copernicus presented his heliocentric theory in the De revolutionibus of 1543. Grasshoff writes in: Ptolemy s Almagest portions with Euclid s Elementss the glorification of being the scientific text longest in usage. From its construct in the 2nd century up to the late Renaissance, this work determined astronomy as a scientific discipline. During this clip the Almagest was non merely a work on uranology ; the topic was defined as what is described in the Almagest . Ptolemy describes himself really clearly what he is trying to make in composing the work ( see for illustration ) : We shall seek to observe down everything which we think we have discovered up to the present clip ; we shall make this every bit briefly as possible and in a mode which can be followed by those who have already made some advancement in the field. For the interest of completeness in our intervention we shall put out everything utile for the theory of the celestial spheres in the proper order, but to avoid undue length we shall simply tell what has been adequately established by the ancients. However, those subjects which have non been dealt with by our predecessors at all, or non every bit usefully as they might hold been, will be discussed at length to the best of our ability. Ptolemy foremost of all justifies his description of the existence based on the earth-centred system described by Aristotle. It is a position of the universe based on a fixed Earth around which the domain of the fixed stars rotates every twenty-four hours, this transporting with it the domains of the Sun, Moon, and planets. Ptolemy used geometric theoretical accounts to foretell the places of the Sun, Moon, and planets, utilizing combinations of round gesture known as epicycles. Having set up this theoretical account, Ptolemy so goes on to depict the mathematics which he needs in the remainder of the work. In peculiar he introduces trigonometrical methods based on the chord map Crd ( which is related to the sine map by wickedness a = ( Crd 2a ) /120 ) . Ptolemy devised new geometrical cogent evidence and theorems. He obtained, utilizing chords of a circle and an inscribed 360-gon, the estimate # 61552 ; = 3 17/120= 3.14166 and, utilizing 3 = chord 60, 3 = 1.73205. He used expression for the Crd map which are correspondent to our expressions for wickedness ( a + B ) , wickedness ( a B ) and sin a/2 to make a tabular array of the Crd map at intervals of 1/2 a grade. This occupies the first two of the 13 books of the Almagest and so, citing once more from the debut, we give Ptolemy s ain description of how he intended to develop the remainder of the mathematical uranology in the work ( see for illustration ) : [ After presenting the mathematical constructs ] we have to travel through the gestures of the Sun and of the Moon, and the phenomena attach toing these gestures ; for it would be impossible to analyze the theory of the stars exhaustively without first holding a appreciation of these affairs. Our concluding undertaking in this manner of attack is the theory of the stars. Here excessively it would be appropriate to cover foremost with the domain of the alleged fixed stars , and follow that by handling the five planets , as they are called. In analyzing the theory of the Sun, Ptolemy compares his ain observations of equinoxes with those of Hipparchus and the earlier observations Meton in 432 BC. He confirmed the length of the tropical twelvemonth as 1/300 of a twenty-four hours less than 365 1/4yearss, the precise value obtained by Hipparchus. Since, as Ptolemy himself knew, the truth of the remainder of his informations depended to a great extent on this value, the fact that the true value is 1/128of a twenty-four hours less than 365 1/4yearss did produce mistakes in the remainder of the work. We shall discourse below in more item the accusals which have been made against Ptolemy, but this illustrates clearly the evidences for these accusals since Ptolemy had to hold an mistake of 28 hours in his observation of the equinox to bring forth this mistake, and even given the truth that could be expected with ancient instruments and methods, it is basically incredible that he could hold made an mistake of this magnitude. A g ood treatment of this unusual mistake is contained in the first-class article. Based on his observations of solstices and equinoxes, Ptolemy found the lengths of the seasons and, based on these, he proposed a simple theoretical account for the Sun which was a round gesture of unvarying angular speed, but the Earth was non at the Centre of the circle but at a distance called the eccentricity from this Centre. This theory of the Sun forms the topic 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 tie in with the gesture of the Moon. There is the clip taken for the Moon to return to the same longitude, the clip taken for it to return to the same speed ( the anomalousness ) and the clip taken for it to return to the same latitude. Ptolemy besides discusses, as Hipparchus had done, the synodic month, that is the clip between consecutive resistances of the Sun and Moon. In Book 4 Ptolemy gives Hipparchus s epicycle theoretical account for the gesture of the Moon but he notes, as in fact Hipparchus had done himself, that there are little disagreements between the theoretical account and the ascertained parametric quantities. Although observing the disagreements, Hipparchus seems non to hold worked out a better theoretical account, but Ptolemy does this in Book 5 where the theoretical account he gives improves markedly on the one proposed by Hipp archus. An interesting treatment of Ptolemy s theory of the Moon is given in. Having given a theory for the gesture of the Sun and of the Moon, Ptolemy was in a place to use these to obtain a theory of occultations which he does in Book 6. The following two books cover with the fixed stars and in Book 7 Ptolemy uses his ain observations together with those of Hipparchus to warrant his belief that the fixed stars ever maintain the same places relative to each other. He wrote ( see for illustration ) : If one were to fit the above alliances against the diagrams organizing the configurations on Hipparchus s heavenly Earth, he would happen that the places of the relevant stars on the Earth ensuing from the observations made at the clip of Hipparchus, harmonizing to what he recorded, are really about the same as at nowadays. In these two book Ptolemy besides discusses precession, the find of which he attributes to Hipparchus, but his figure is slightly in mistake chiefly because of the mistake in the length of the tropical twelvemonth which he used. Much of Books 7 and 8 are taken up with Ptolemy s star catalogue incorporating over one thousand stars. The concluding five books of the Almagest discuss planetal theory. This must be Ptolemy s greatest accomplishment in footings of an original part, since at that place does non look to hold been any satisfactory theoretical theoretical account to explicate the instead complicated gestures of the five planets before the Almagest. Ptolemy combined the epicycle and bizarre methods to give his theoretical account for the gestures of the planets. The way of a planet P hence consisted of round gesture on an epicycle, the centre C of the epicycle traveling round a circle whose Centre was offset from the Earth. Ptolemy s truly cagey invention here was to do the gesture of C unvarying non 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 chef-doeuvre. He created a sophisticated mathematical theoretical account to suit experimental informations which before Ptolemy s clip was scarce, and the theoretical account he produced, although complicated, represents the gestures of the planets reasonably good. Toomer amounts up the Almagest in every bit follows: As a didactic work the Almagest is a chef-doeuvre of lucidity and method, superior to any ancient scientific text edition and with few equals from any period. But it is much more than that. Army for the liberation of rwanda from being a mere systemisation of earlier Grecian uranology, as it is sometimes described, it is in many respects an original work. We will return to discourse some of the accusals made against Ptolemy after noticing briefly on his other plants. He published the tabular arraies which are scattered throughout the Almagest individually under the rubric Handy Tables. These were non simply lifted from the Almagest nevertheless but Ptolemy made legion betterments in their presentation, easiness of usage and he even made betterments in the basic parametric quantities to give greater truth. We merely know inside informations of the Handy Tables through the commentary by Theon of Alexandria but in the writer shows that attention is required since Theon was non to the full cognizant of Ptolemy s processs. Ptolemy besides did what many authors of deep scientific plants have done, and still make, in composing a popular history of his consequences under the rubric Planetary Hypothesis. This work, in two books, once more follows the familiar path of cut downing the mathematical accomplishments needed by a reader. Claudius ptolemaeus does this instead cleverly by replacing the abstract geometrical theories by mechanical 1s. Ptolemy besides wrote a work on star divination. It may look strange to the modern reader that person who wrote such first-class scientific books should compose on star divination. However, Ptolemy sees it instead otherwise for he claims that the Almagest allows one to happen the places of the celestial organic structures, while his star divination book he sees as a comrade work depicting the effects of the celestial organic structures on people s lives. In a book entitled Analemma he discussed methods of happening the angles need to build a sundial which involves the projection of points on the celestial domain. In Planisphaerium he is concerned with stereographic projection of the celestial sphere onto a plane. This is discussed in where it is stated: In the stereographic projection treated by Ptolemy in the Planisphaerium the celestial domain is mapped onto the plane of the equator by projection from the south pole. Ptolemy does non turn out the of import belongings that circles on the sphere become circles on the plane. Ptolemy s major work Geography, in eight books, efforts to map the known universe giving co-ordinates of the major topographic points in footings of latitude and longitude. It is non surprising that the maps given by Ptolemy were rather inaccurate in many topographic points for he could non be expected to make more than utilize the available informations and this was of really hapless quality for anything outside the Roman Empire, and even parts of the Roman Empire are badly distorted. In Ptolemy is described as: a adult male working [ on map-construct without the support of a developed theory but within a mathematical tradition and guided by his sense of what is appropriate to the job. Another work on Optics is in five books and in it Ptolemy surveies colour, contemplation, refraction, and mirrors of assorted forms. Toomer remarks in: The constitution of theory by experiment, often by building particular setup, is the most dramatic characteristic of Ptolemy s Optics . Whether the capable affair is mostly derived or original, The Optics is an impressive illustration of the development of a mathematical scientific discipline with due respect to physical informations, and is worthy of the writer of the Almagest . An English interlingual rendition, trying to take the inaccuracies introduced in the hapless Arabic interlingual rendition which is our lone beginning of the Optics is given in. The first to do accusals against Ptolemy was Tycho Brahe. He discovered that there was a systematic mistake of one grade in the longitudes of the stars in the star catalogue, and he claimed that, despite Ptolemy stating that it represented his ain observations, it was simply a transition of a catalogue due to Hipparchus corrected for precession to Ptolemy s day of the month. There is of class definite jobs comparing two star catalogues, one of which we have a transcript of while the other is lost. After remarks by Laplace and Lalande, the following to assail Ptolemy smartly was Delambre. He suggested that possibly the mistakes came from Hipparchus and that Ptolemy might hold done nil more serious than to hold failed to rectify Hipparchus s information for the clip between the equinoxes and solstices. However Delambre so goes on to state ( see ) : One could explicate everything in a less favorable but all the simpler mode by denying Ptolemy the observation of the stars and equinoxes, and by claiming that he assimilated everything from Hipparchus, utilizing the minimum value of the latter for the precession gesture. However, Ptolemy was non without his protagonists by any agencies and farther analysis led to a belief that the accusals made against Ptolemy by Delambre were false. Boll composing in 1894 says: To all visual aspects, one will hold to recognition Ptolemy with giving an basically richer image of the Greek celestial sphere after his high predecessors. Vogt showed clearly in his of import paper that by sing Hipparchus s Commentary on Aratus and Eudoxus and doing the sensible premise that the informations given there agreed with Hipparchus s star catalogue, so Ptolemy s star catalogue can non hold been produced from the places of the stars as given by Hipparchus, except for a little figure of stars where Ptolemy does look to hold taken the information from Hipparchus. Vogt writes: This allows us to see the fixed star catalogue as of his ain devising, merely as Ptolemy himself smartly provinces. The most recent accusals of counterfeit made against Ptolemy came from Newton in. He begins this book by saying clearly his positions: This is the narrative of a scientific offense. I mean a offense committed by a scientist against fellow scientists and bookmans, a treachery of the moralss and unity of his profession that has everlastingly deprived world of cardinal information about an of import country of uranology and history. Towards the terminal Newton, holding claimed to turn out every observation claimed by Ptolemy in the Almagest was fabricated, writes: [ Ptolemy ] developed certain astronomical theories and discovered that they were non consistent with observation. Alternatively of abandoning the theories, he intentionally fabricated observations from the theories so that he could claim that the observations prove the cogency of his theories. In every scientific or scholarly scene known, this pattern is called fraud, and it is a offense against scientific discipline and scholarship. Although the grounds produced by Brahe, Delambre, Newton and others surely do demo that Ptolemy s mistakes are non random, this last quotation mark from is, I [ EFR ] believe, a offense against Ptolemy ( to utilize Newton s ain words ) . The book [ 8 ] is written to analyze cogency of these accusals and it is a work which I strongly believe gives the right reading. Grasshoff writes: 1 has to presume that a significant proportion of the Ptolemaic star catalogue is grounded on those Hipparchan observations which Hipparchus already used for the digest of the 2nd portion of his Commentary on Aratus . Although it can non be ruled out that co-ordinates ensuing from echt Ptolemaic observations are included in the catalogue, they could non amount to more than half the catalogue. the assimilation of Hipparchan observations can no longer be discussed under the facet of plagiarism. Ptolemy, whose purpose was to develop a comprehensive theory of heavenly phenomena, had no entree to the methods of informations rating utilizing arithmetical agencies with which modern uranologists can deduce from a set of changing measurement consequences, the one representative value needed to prove a hypothesis. For methodological ground, so, Ptolemy was forced to take from a set of measurings the one value matching best to what he had to see as the most dependable informations. When an intuitive choice among the information was no longer possible Ptolemy had to see those values as observed which could be confirmed by theoretical anticipations. As a concluding remark we quote the quip which is accepted by many bookmans to hold been written by Ptolemy himself, and it appears in Book 1 of the Almagest, following the list of contents ( see for illustration [ 11 ] ) : Well do I know that I am mortal, a animal of one twenty-four hours. But if my head follows the weaving waies of the stars Then my pess no longer rest on Earth, but standing by Zeus himself I take my fill of beebread, the godly dish. J J OConnor and E F Robertson