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Ptolemy's and model
Ptolemy's Handy Tables provided the model for later astronomical tables or zījes.
* The Ptolemaic model of planetary motion: Based on the geometrical model of Eudoxus of Cnidus, Ptolemy's Almagest, demonstrated that calculations could compute the exact positions of the Sun, Moon, stars, and planets in the future and in the past, and showed how these computational models were derived from astronomical observations.
Using data he collected from his own observations Gersonides ' refuted Ptolemy's model in what the notable physicist Yuval Ne ' eman has considered as " one of the most important insights in the history of science, generally missed in telling the story of the transition from epicyclic corrections to the geocentric model to Copernicus ' heliocentric model ".
Ne ' eman argued that after Gersonides reviewed Ptolemy's model with its epicycles he realized that it could be checked, by measuring the changes in the apparent brightnesses of Mars and looking for cyclical changes along the conjectured epicycles.
The results of his observations did not fit Ptolemy's model at all.
Levi also showed that Ptolemy's model for the Lunar orbit, though reproducing correctly the evolution of the Moon's position, fails completely in predicting the apparent sizes of the Moon in its motion.
Copernicus later used this observation to disprove Ptolemy's model of lunar distance.
The astronomical predictions of Ptolemy's geocentric model were used to prepare astrological charts for over 1500 years.
Ptolemy's model, in part, sought to explain this behavior.
To accommodate this, Ptolemy's model fixed the motion of Mercury and Venus so that the line from the equant point to the center of the epicycle was always parallel to the earth-sun line.
Some Greek astronomers ( e. g., Aristarchus of Samos ) speculated that the planets ( Earth included ) orbited the Sun, but the optics ( and the specific mathematics – Newton's Law of Gravitation for example ) necessary to provide data that would convincingly support the heliocentric model did not exist in Ptolemy's time and would not come around for over fifteen hundred years after his death.
Ptolemy's model is probably optimal in this regard.
16th-century representation of the Ptolemy's geocentric model
In the 16th century, the terms were modified by Copernicus, who rejected Ptolemy's geocentric model, to distinguish a planet's orbit's size in relation to the Earth's.
Alhazen wrote a scathing critique of Ptolemy's model in his Doubts on Ptolemy ( c. 1028 ), which some have interpreted to imply he was criticizing Ptolemy's geocentrism, but most agree that he was actually criticizing the details of Ptolemy's model rather than his geocentrism.
In the 16th century, Nicolaus Copernicus De revolutionibus presented a full discussion of a heliocentric model of the universe in much the same way as Ptolemy's Almagest had presented his geocentric model in the 2nd century.

Ptolemy's and like
The Suevi Angeli would have been in Lower Saxony or near it and, like Ptolemy's Suevi Semnones, were among the Suebi at the time.
Ptolemy's astrological outlook was quite practical: he thought that astrology was like medicine, that is conjectural, because of the many variable factors to be taken into account: the race, country, and upbringing of a person affects an individual's personality as much if not more than the positions of the Sun, Moon, and planets at the precise moment of their birth, so Ptolemy saw astrology as something to be used in life but in no way relied on entirely.
Jordanes referred to Ptolemy's description of Scandia " as a great island shaped like a juniper leaf " ( i. e. long and not round ) " having bulging sides and which tapered down in the south at a long end ".
The Dacian town Amutria is mentioned in ancient sources like Ptolemy's Geographia ( c. 150 AD ) and Tabula Peutingeriana ( 2nd century AD ), and potentially placed here.
Ptolemy's enemies include typical fantasy beings like orcs, mages, ogres, and dragons.
The forms Argidava and Arcidava found in other ancient sources like Ptolemy's Geographia ( c. 150 AD ) and Tabula Peutingeriana ( 2nd century AD ), clearly place a Dacian town with those names at this geographical location.

Ptolemy's and those
The location of those Vandals is not stated, but there is a match with his contemporary Ptolemy's east German tribes.
In the case of Ptolemy's Dacia, most of the tribal names are similar to those on the list of civitates, with few exceptions. Georgiev counts the Triballi, the Moesians and the Dardanians as Daco-Moesians.
Ptolemy's elephants were of the now extinct, smaller North African breed of Elephants ; those of Antiochus were mainly of the large Syrian Elephants, brought from India.
Al-Biruni's work, The Keys of Astronomy, lists a number of those works, which can be classified into studies as part of commentaries on Ptolemy's Almagest as in the works of al-Nayrizi and al-Khazin where each demonstrated particular cases of Menelaus ' theorem that led to the sine rule, or works composed as independent treatises such as:
Ptolemy's two maps of Germany portrayed Germania Inferior on the left bank of the Rhine, which was populated by Germanics, including those who had occupied the region before the Romans, and Magna Germania on the other side of the river, which acted as the Roman frontier.

Ptolemy's and was
This was not simpler but much more difficult than exercises within Ptolemy's astronomy.
That such deficiencies existed within Ptolemy's theory was not discovered de novo by Copernicus.
Ptolemy's view of Germans in the region indicates that the tribal structure had lost its grip in the Black Forest region and was replaced by a canton structure.
α CVn was Ptolemy's " 28th of Ursa Major ", and β CVn was his " 29th of Ursa Major ".
When the Greek astronomer Ptolemy's Almagest was translated from Greek to Arabic, the translator Johannitius ( following Alberuni ) did not know the Greek word and rendered it as the nearest-looking Arabic word, writing العصى ذات الكلاب in ordinary unvowelled Arabic text " al -` aşā dhāt al-kullāb ", which means " the spearshaft having a hook ".
The first historic name for the city was, according to Claudius Ptolemy's reports, Treva.
It was shown on Ptolemy's map as the " Golden Khersonese ".
This was so that when the plaster with Ptolemy's name fell off, Sostratus's name would be visible in the stone.
No particular animal was associated with it until the Latin translation of Ptolemy's work identified it with the wolf.
Indeed, prior to the reintroduction of Ptolemy's Geography to Europe around 1400, there was no single convention in the West.
The writer was attempting to square information gleaned from Portuguese trade along the coast with Ptolemy's world map.
It would have suited custom if the first of Ptolemy's family to become a citizen ( whether he or an ancestor ) took the nomen from a Roman called Claudius who was responsible for granting citizenship.
The maps in surviving manuscripts of Ptolemy's Geographia, however, date only from about 1300, after the text was rediscovered by Maximus Planudes.
In the 15th century Ptolemy's Geographia began to be printed with engraved maps ; the earliest printed edition with engraved maps was produced in Bologna in 1477, followed quickly by a Roman edition in 1478 ( Campbell, 1987 ).
( Ptolemy's own latitude was in error by 14 '.
Much of the content of the Tetrabiblos was collected from earlier sources ; Ptolemy's achievement was to order his material in a systematic way, showing how the subject could, in his view, be rationalized.
George of Trebizond who was Bessarion's philosophical rival had recently produced a new Latin translation of Ptolemy's Almagest from the Greek, which Bessarion, correctly, regarded as inaccurate and badly translated, so he asked Peuerbach to produce a new one.
The year is stated as the ninth year of Ptolemy V's reign ( equated with 197 / 196 BC ), and it is confirmed by naming four priests who officiated in that same year: Aëtus son of Aëtus was priest of the divine cults of Alexander the Great and the five Ptolemies down to Ptolemy V himself ; his three colleagues, named in turn in the inscription, led the worship of Berenice Euergetis ( wife of Ptolemy III ), Arsinoe Philadelpha ( wife and sister of Ptolemy II ) and Arsinoe Philopator, mother of Ptolemy V. However, a second date is also given in the Greek and hieroglyphic texts, corresponding to, the official anniversary of Ptolemy's coronation.
The star catalog of Hipparchus ( 2nd century BC ) included 1020 stars and was used to assemble Ptolemy's star catalogue.

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