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I imagine that Ptolemy's epicycles were performed as real circles - around equants - in two dimensions, e.g that he was able not only to give the angles to planets and the Sun as seen from the Earth, but actually able to point out the location in space in a projection in two dimensions or otherwise, of all then known planets in the system. He would then have had the same type of knowledge as Kepler had, at least in principle, albeit with lower accuracy.
Is that actually the case?
I suppose you mean in three dimensions, but anyhow…
Yes, Ptolemy did know that planets move also in latitude, not only in longitude, and thus the Almagest includes sections for how to predict the latitude of a planet for a given moment. In fact, Book XIII of the Almagest is entirely written about this specific subject of the latitude of the planets.
Ptolemy is one of the ancient astronomers from Egypt during the second century A.C and he was considered to be the most important and influential astronomer of antiquity. Egyptians have always been most curious about the earth, space and time. There are many clues and evidence, which explains that people were aware of the universe and most of the Egyptians were capable of recognizing the stars and the planets. Their knowledge of cosmology was found to be accurate and over a period of time, it is found to be fundamental and many advanced civilizations carried it further.
The cosmological model suggested by Ptolemy is known as the Ptolemaic system or Ptolemaic model and the Ptolemaic system is often also referred to as a geocentric system. The term ‘ge’ in Greek means the earth. In the geocentric system or Ptolemaic system, the earth is statically situated at the centre and the rest of the planets are revolving around it, including the sun, which was also considered a planet. In this article, we will have a deep insight into the Ptolemaic system or Ptolemaic model.
The initial days of astronomy had been extremely painful for the astronomers. It was highly impossible to convince people against their holy thoughts. Around four centuries ago, during the 16th and 17th centuries, the fear of heretics teaching and opinions that contradicted the bible dominated the catholic church. A kind of war between science and religion got into action, but there were a lot of casualties on the side of science. Before we start with the Ptolemaic model or the Ptolemy geocentric model, let us have a brief history of the heliocentric model.
What is the Heliocentric Model?
The word ‘helio’ means the sun and the centric means located at the centre. The heliocentric model or the heliocentric theory suggests that the sun is situated at the centre of the system and the earth is revolving around the sun in a circular orbit. And this was against the catholic church and the holy books.
In his book ‘The Mathematical Collection’, which later renamed and to be called ‘the Almagest’, Ptolemy has described that the structure of the planetary system (Ptolemaic system definition) and the location and position of each star within it which can be referred to even in modern astronomy. In his book, Ptolemy summarizes the activities of centuries of ancient Greek astronomy and also adds a number of new concepts with theoretical and mathematical descriptions.
Ptolemy Geocentric Model:
According to Claudius Ptolemy, the Earth was situated at the centre of the Universe, whose view of the cosmos persisted for more than 1400 years until it was overturned, with controversies by discoveries of Copernicus, Galileo, and Newton.
Ptolemy is a great astronomer in ancient times based in Egypt who lived in Alexandria back in the early 2nd centuries AC. Under the supervision of Greek rulers, Alexandria cultivated and established a famous library that attracted many scholars and scientists from Greece, and its school for astronomers received generous patronage. After the Romans conquered Egypt during 30 BCE (when Cleopatra got defeated by Octavian), Alexandria became the second huge city in the entire Roman Empire and a major source of Rome’s economy and grain, but less funding was provided for the scientific study of the stars and the planets.
Ptolemy was the only great ancient astronomer of Roman Alexandria. Ptolemy was not only an astronomer but also he was a mathematician, geographer, and astrologer. Befitting his diverse and versatile intellectual pursuits, he had a motley cultural makeup. Ptolemy lived in Egypt, wrote theories in Greek, and bore a Roman first name, Claudius, indicating he was a Roman citizen, probably a gift from the Roman emperor to one of Ptolemy’s ancestors.
Ptolemy studied, utilised, and synthesized the Greek knowledge and facts of the known Universe, we can call it the Ptolemy view of the universe or Ptolemaic universe. Ptolemy’s work has enabled many astronomers to make accurate predictions of planetary positions and solar and lunar eclipses, promoting acceptance of his view of the cosmos in the catholic and many other religious worlds and throughout Europe for more than 1400 years, which let us know that he has given us a strong foundation for the cosmology.
Ptolemy accepted Aristotle’s idea of the earth being at a constant position and the Sun and the planets revolving around a spherical Earth, a geocentric view. Later, Ptolemy developed this idea through rigorous observation and gave a mathematical description in detail. During this process of proceeding with the Ptolemy geocentric model, Ptolemy ended up rejecting the hypothesis of Aristarchus of Samos, who visited Alexandria about 350 years before Ptolemy was born. Aristarchus' hypothesis claimed that the Earth revolves around the Sun, but he could not produce any evidence to back it up. Though it was true due to lack of documentation and proofs he could not convince society.
Ptolemy, based on observations that he made with his naked eye, he was able to witness the Universe as a set of nested, transparent spheres, with Earth in the centre. In the Ptolemy solar system, the only planets that were present are the sun, mars, moon and venus apart from the earth. Because Ptolemy was able to locate the Moon, Mercury, Venus, and the Sun all revolving around the Earth. Beyond the Sun, he thought, Mars, Jupiter and Saturn, the only other planets in our universe and only planets known at the time (as they were visible to the naked eye). Beyond Saturn lay a final and one last sphere with all the stars fixed to it that revolved around the other spheres. And this was known as the Ptolemy geocentric theory.
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This idea of the universe did not fit exactly with all of Ptolemy’s observations and the idea of the Ptolemaic universe. Ptolemy was aware that the size, motion, and brightness of the planets varied from one another. Thus, Ptolemy incorporated Hipparchus’s concepts of epicycles, which was put forth a few centuries earlier, to work out his calculations. Epicycles were considerably small circular orbits around imaginary centres on which the planets were assumed to move while making a revolution around the Earth.
By using Ptolemy’s tables, astronomers could accurately predict eclipses and the positions and locations of planets. Due to real visible events in the sky seemed to accept and confirm the truth of Ptolemy’s views. Ptolemy’s ideas were accepted for centuries until the Polish and advanced astronomers, such as Copernicus, proposed in 1543 that the Sun, rather than the Earth, belonged in the centre. That began another controversy between the geocentric model and the heliocentric model.
Did You Know?
Ptolemy's astronomy is almost based on the Physics of Aristotle which separates the activities of the sub-lunar world (i.e., on the earth) and the supra-lunar world. According to Aristotle, the supra-lunar world is made up of special material or matter that differs from the material on earth. This material is known as ether. Ether is very hard and considered to be a massless material, i.e., lighter than anything known on earth. Ether's main and significant feature is its circular motion, and thus all the stars, by their nature, move in circles.
In the Ptolemaic system, all-stars move along spheres. These spheres revolve around the earth, but the earth is not always precisely at its centre. According to the Ptolemaic model, each planet has a system of spheres along which it moves. The merging of the circular motions of the planets results in non-circular motion. Beyond the spheres of the planets, all the stars are positioned within a single sphere. These stars have accurate fixed places in the sphere.
The stars are all positioned within a single sphere and this sphere revolves around the earth and completes an entire revolution every 24 hours (that makes a complete day). Thus, this movement around the earth is also common to the planets, including the sun. The daily revolution around the earth in particular path is added to the various movements of the different planets, each in relation to its own spheres.
The name Claudius is a Roman nomen the fact that Ptolemy bore it indicates he lived under the Roman rule of Egypt with the privileges and political rights of Roman citizenship. 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. If, as was common, this was the emperor, citizenship would have been granted between AD 41 and 68 (when Claudius, and then Nero, were emperors). The astronomer would also have had a praenomen, which remains unknown.
Ptolemaeus (Πτολεμαῖος – Ptolemaios) is a Greek name. It occurs once in Greek mythology, and is of Homeric form.  It was common among the Macedonian upper class at the time of Alexander the Great, and there were several of this name among Alexander's army, one of whom made himself King of Egypt in 323 BC: Ptolemy I Soter. All the kings after him, until Egypt became a Roman province in 30 BC, were also Ptolemies.
Perhaps for no other reason than the association of name, the 9th-century Persian astronomer Abu Ma'shar assumed Ptolemy to be a member of Egypt's royal lineage, stating that the ten kings of Egypt who followed Alexander were wise "and included Ptolemy the Wise, who composed the book of the Almagest". Abu Ma'shar recorded a belief that a different member of this royal line "composed the book on astrology and attributed it to Ptolemy". We can evidence historical confusion on this point from Abu Ma'shar's subsequent remark “It is sometimes said that the very learned man who wrote the book of astrology also wrote the book of the Almagest. The correct answer is not known”.  There is little evidence on the subject of Ptolemy's ancestry, apart from what can be drawn from the details of his name (see above) however, modern scholars refer to Abu Ma’shar’s account as erroneous,  and it is no longer doubted that the astronomer who wrote the Almagest also wrote the Tetrabiblos as its astrological counterpart. 
Ptolemy wrote in Greek and can be shown to have utilized Babylonian astronomical data.   He was a Roman citizen, but most scholars conclude that Ptolemy was ethnically Greek,    although some suggest he was a Hellenized Egyptian.    He was often known in later Arabic sources as "the Upper Egyptian",  suggesting he may have had origins in southern Egypt.  Later Arabic astronomers, geographers and physicists referred to him by his name in Arabic: بطليموس Batlaymus.