Copernicus did not question it, Ptolemy could not.

Ptolemy presented his astronomical models in convenient tables, which could be used to compute the future or past position of the planets.

Ptolemy wrote about how musical notes could be translated into mathematical equations and vice versa in Harmonics.

There are two possible occasions when this could have happened: the first was in 145 BC, when Ptolemy VIII purged Alexandria of the intellectuals who supported his rivals for the throne ; and in 132 BC after Ptolemy, who had been driven from his kingdom by a rebellion in Alexandria, returned and exacted reprisals on that city.

Geographer Ptolemy in the 2nd century made a map of Hibernia full of data on rivers, mountains and people demonstrating a knowledge of the island that could have been originated even from the presence in Hibernia of Roman explorers / traders living in small trading places of the Ireland's south and eastern coast.

At the moment of Ptolemy XII's restoration, Roman creditors demanded the return on their investments but the Alexandrian treasury could not repay the king's debt.

This presumed second wife of the Egyptian king could have been the mother of Cleopatra VII and this daughter's younger siblings, while Berenice IV was the daughter of Cleopatra V because Strabo only calls the oldest daughter of Ptolemy XII a legitimate child.

As noted above Ptolemy often dropped the initial letters of names and a shift from " Ebhlana " to " Delvin " could be seen as a phonic shift possibility.

Ptolemy lists the Brigantes also as a tribe in Ireland, where they could be found around Wexford, Kilkenny and Waterford while another probably Celtic tribe named Brigantii is mentioned by Strabo as a sub-tribe of the Vindelici in the region of the Alps.

Eventually, Ptolemy IV ( r. 221 – 204 BC ) built a " forty " ( tessarakonteres ) that was 128 m long, required 4, 000 rowers and 400 other crew, and could support a force of 3, 000 marines on its decks.

Evidence within the Almagest reveals that the astronomical work could not have been completed before about 145 AD, which demonstrates that Ptolemy wrote the Tetrabiblos towards the end of his life, sometime between completing the Almagest and his death, generally reported to be around 168 A. D.

Cleopatra IV may be the mother of Ptolemy XII Auletes and Ptolemy of Cyprus, although an unnamed concubine could be the mother of these two men as well.

Eventually, Cleopatra acceded to a proposal from Ptolemy, but before her design could be realized, she was captured.

The only ruler to whom the narrative can properly refer is Ptolemy V Epiphanes ( 205-182 ), who in 193 BCE married Cleopatra, the daughter of Antiochus III In that case, however, Joseph could not have farmed the Egyptian taxes, since Cœle-Syria was then under Syrian, and not under Egyptian, suzerainty, while the assertion that the two powers had divided the revenues of the country is merely an attempt on the part of Josephus to evade the difficulty.

Nor was the period between Ptolemy V's marriage ( 193 ) and his death ( 182 ) sufficiently long to agree with the statement concerning the length of time during which Joseph farmed the taxes ( twenty-two years ), and still less could Hyrcanus have reached manhood in so short a space.

This form could potentially be link to Zargidaua mentioned by Ptolemy at a different geographical location.

While the young king gave himself up to luxury and debauchery, the whole administration of the kingdom appears to have been left to Sosibius, who allowed both the finances and military defences to fall into a state of the greatest decay, so that when Antiochus the Great declared war against Ptolemy, and invaded Coele-Syria, it was some time before the Egyptian monarch or his ministers could muster an army to oppose him.

But that one should superimpose all these charts, run a pin through the common point, and then scale each planetary deferent larger and smaller ( to keep the epicycles from ' bumping ' ), this is contrary to any intention Ptolemy ever expresses.

But no single planetary problem ever required of Ptolemy more than six epicycles at one time.

This is more ambitious than Ptolemy is ever required to be when he faces his isolated problems.

Along with the surviving table of Ptolemy ( c. AD 90 – c. 168 ), they were all tables of chords and not of half-chords, i. e. the sine function. The table produced by the Indian mathematician Āryabhaṭa is considered the first sine table ever constructed.

Ptolemy ( c. AD 90 – c. AD 168 ) stated " We consider it a good principle to explain the phenomena by the simplest hypothesis possible ",.

Astronomers such as Eudoxus ( contemporary with Plato ) observed planetary motions and cycles, and created a geocentric cosmological model that would be accepted by Aristotle – this model generally lasted until Ptolemy, who added epicycles to explain the retrograde motion of Mars.

Ptolemy attempted to explain the Moon illusion through atmospheric refraction in the Almagest, and later ( in the Optics ) as an optical illusion due to apparent distance, although interpretations of the account in the Optics are disputed.

Furthermore, Nasir al-Din al-Tusi ( 1201 – 1274 ), an astronomer and mathematician from Baghdad, authored the Treasury of Astronomy, a remarkably accurate table of planetary movements that reformed the existing planetary model of Roman astronomer Ptolemy by describing a uniform circular motion of all planets in their orbits.

A notable example is the now defunct belief in the Ptolemy planetary model that held sway until changes in scientific and religious thinking were brought about by Galileo and proponents of his views.

* c. 1350 – Ibn al-Shatir anticipates Copernicus by abandoning the equant of Ptolemy in his calculations of planetary motion, and he provides the first empirical model of lunar motion which accurately matches observations

140 — Ptolemy completes his Almagest, which contains a catalog of stars, observations of planetary motions, and treatises on geometry and cosmology

Johannes Kepler ( 27 December 1571 – 15 November 1630 ) was the first to closely integrate the predictive geometrical astronomy, which had been dominant from Ptolemy to Copernicus, with physical concepts to produce a New Astronomy, Based upon Causes, or Celestial Physics .... His work led to the modern laws of planetary orbits, which he developed using his physical principles and the planetary observations made by Tycho Brahe.

Ptolemy did not predict the relative sizes of the planetary deferents in the Almagest.

Ptolemy assigned the following order to the planetary spheres, beginning with the innermost:

Campion has pointed out that these planetary associations with psychological qualities are not original to Ptolemy, being present in the Corpus Hermeticum which was in circulation in Alexandria at the time Ptolemy compiled his text.

Here Ptolemy shows employment of the astrological technique known as synastry, in which the planetary positions of two separate horoscopes are compared with each other for indications of relationship harmony or enmity.

Edmond Halley published the first measurements of the proper motion of a pair of nearby " fixed " stars, demonstrating that they had changed positions from the time of the ancient Greek astronomers Ptolemy and Hipparchus.

It is widely accepted that Copernicus's De revolutionibus followed the outline and method set by Ptolemy in his Almagest and employed geometrical constructions that had been developed previously by the Maragheh school in his heliocentric model, and that Galileo's mathematical treatment of acceleration and his concept of impetus rejected earlier medieval analyses of motion, rejecting by name ; Averroes, Avempace, Jean Buridan, and John Philoponus ( see Theory of impetus ).

It is reasonable to assume that Hipparchus, like Ptolemy, thought of precession in geocentric terms as a motion of the heavens.

Ptolemy discusses the correction needed to convert the meridian crossing of the Sun to mean solar time and takes into consideration the nonuniform motion of the Sun along the ecliptic and the meridian correction for the Sun's ecliptic longitude.

Equant ( or punctum aequans ) is a mathematical concept developed by Claudius Ptolemy in the 2nd century AD to account for the observed motion of heavenly bodies.

He is said ( e. g. by Roman astronomer / astrologer Vettius Valens ) to have published tables to compute the motion of the Moon ; said to have been used by the Greeks, until superseded by the work of Hipparchus and later by Ptolemy ( Claudius Ptolemaios ).

According to Aristotle, Ptolemy, and other philosophers among the Greeks, the stars have no motion of their own, being firmly attached to spheres whose center is the earth.

No attempt is made by Ptolemy to weld into a single scheme ( a-la-Aristotle ), these independent predicting-machines.

If in any one calculation Ptolemy had had to invoke 83 epicycles all at once, while Copernicus never required more than one third this number, then ( in the sense obvious to Margenau ) Ptolemaic astronomy would be simpler than Copernican.

Copernicus, to an extent unachieved by Ptolemy, approximated to Euclid's vision.

During that time he gave lessons not only to Alexander, but also to two other future kings: Ptolemy and Cassander.

It was one of the 48 constellations listed by the 2nd century AD astronomer Ptolemy, and it remains one of the 88 modern constellations.

Another possibility, raised in an essay by the Swedish fantasy writer and editor Rickard Berghorn, is that the name Alhazred was influenced by references to two historical authors whose names were Latinized as Alhazen: Alhazen ben Josef, who translated Ptolemy into Arabic ; and Abu ' Ali al-Hasan ibn al-Haytham, who wrote about optics, mathematics and physics.

Hipparchus's successor, Ptolemy, included a catalogue of 1, 022 stars in his work the Almagest, giving their location, coordinates, and brightness.

Like the earlier catalogs of Hipparchus and Ptolemy, Ulugh Beg's catalogue is estimated to have been precise to within approximately 20 minutes of arc.

Tacitus stated that they traded with Rhaetia, which in Ptolemy is located across the Danube from Germania Superior.

However, no Hermunduri appear in Ptolemy, though after the time of Ptolemy the Hermunduri joined with the Marcomanni in the wars of 166 – 180 against the empire.

Before the mention of Alemanni in the time of Caracalla, you would search in vain for Alemanni in the moderately detailed geography of southern Germany in Claudius Ptolemy, written in Greek in the mid-2nd century ; it is likely that at that time, the people who later used that name were known by other designations.

Nevertheless some conclusions can be drawn from Ptolemy.

However, if we look for the peoples in the region from the upper Main in the north, south to the Danube and east to the Czech Republic where the Quadi and Marcomanni were located, Ptolemy does not give any tribes.

Alexander's claims were recognized by the Roman Senate, Ptolemy Philometor of Egypt and others.

Whatever the truth behind this, the young king was forced to depend heavily on his Ptolemaic support and even struck portraits with the characteristic features of king Ptolemy I.

Ptolemy Philometor, who was Alexander's father-in-law, went over to his side, and Alexander was defeated in the battle of Antioch ( 145 BC ) in Syria, sometimes known as the battle of the Oenoparus.

He fled for refuge to a Nabataean prince, who murdered him and sent his head to Ptolemy Philometor, who had been mortally wounded in the engagement.

He married his paternal half-sister Olympias II of Epirus, by whom he had two sons, Pyrrhus II of Epirus, Ptolemy of Epirus and a daughter, Phthia of Macedon.

He flourished about 280 BC, in the reign of Ptolemy II Philadelphus.