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Ptolemy

Ptolemy is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Ptolemy rather than just read about it. In short: Claudius Ptolemy (; Ancient Greek: Πτολεμαῖος, Ptolemaios; Latin: Claudius Ptolemaeus; c. 100 – 160s/170s AD), better known mononymously as Ptolemy, was a Greco-Roman mathematician, astronomer, astrologer, geographer, and music theorist who wrote about a dozen scientific treatises, three of which were important to later Byzantine, Islamic, and Western European science. The first was his astronomical treatise now kno…

Ptolemy — main illustration
Ptolemy — illustration

Key takeaways

  • Ptolemy belongs to mathematics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Ptolemy to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Ptolemy from memory before moving on to harder problems.

Reference excerpt

Claudius Ptolemy (; Ancient Greek: Πτολεμαῖος, Ptolemaios; Latin: Claudius Ptolemaeus; c. 100 – 160s/170s AD), better known mononymously as Ptolemy, was a Greco-Roman mathematician, astronomer, astrologer, geographer, and music theorist who wrote about a dozen scientific treatises, three of which were important to later Byzantine, Islamic, and Western European science. The first was his astronomical treatise now known as the Almagest, originally entitled Mathēmatikḗ Syntaxis (Μαθηματικὴ Σύνταξις, 'Mathematical Treatise'). The second is the Geography, which is a thorough discussion on maps and the geographic knowledge of the Greco-Roman world. The third is the astrological treatise in which he attempted to adapt horoscopic astrology to the Aristotelian natural philosophy of his day. This is sometimes known as the Apotelesmatika (Αποτελεσματικά, 'On the Effects') but more commonly known as the Tetrábiblos (from the Koine Greek meaning 'four books'; Latin: Quadripartitum). The Catholic Church promoted his work, which included the only mathematically sound geocentric model of the Solar System. Unlike that of most Greek mathematicians, Ptolemy's writings (foremost the Almagest) were copied or evaluated in late antiquity and into the Middle Ages. However, it is likely that only a few truly mastered the mathematics necessary to understand his works, as evidenced particularly by the many abridged and watered-down introductions to Ptolemy's astronomy that were popular among the Arabs and Byzantines.

Biography Ptolemy's date of birth and birthplace are both unknown. The 14th-century astronomer Theodore Meliteniotes wrote that Ptolemy's birthplace was Ptolemais Hermiou, a Greek city in the Thebaid region of Egypt (now El Mansha, Sohag Governorate). This attestation is quite late, however, and there is no evidence to support it. It is known that Ptolemy lived in or around the city of Alexandria, in the Roman province of Egypt under Roman rule. He had a Latin name, Claudius, which is generally taken to imply he was a Roman citizen. He was familiar with Greek philosophers and used Babylonian observations and Babylonian lunar theory. In half of his extant works, Ptolemy addresses a certain Syrus, a figure of whom almost nothing is known but who likely shared some of Ptolemy's astronomical interests. Ptolemy died in Alexandria. Ptolemy's year of death is not directly recorded by primary sources, and has to be inferred from the scale of his work. Suggested years of death include c. 165, c. 168, c. 170, and c. 175.

Naming and nationality

Ptolemy is often called Ptolemaeus, which is a Latinised version of his original ancient Greek personal name Πτολεμαῖος (Latin transcript: Ptolemaîos). 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 several people of this name were among Alexander's army, one of whom made himself pharaoh in 323 BC: Ptolemy I Soter, the first pharaoh of the Ptolemaic Kingdom. Almost all subsequent pharaohs of Egypt, with a few exceptions, were named Ptolemy until Egypt became a Roman province in 30 BC, ending the Macedonian family's rule. The name Claudius is a Roman name, belonging to the gens Claudia; the peculiar multipart form of the whole name Claudius Ptolemaeus is a Roman custom, characteristic of Roman citizens. This indicates that Ptolemy would have been a Roman citizen. Gerald Toomer, the translator of Ptolemy's Almagest into English, suggests that citizenship was probably granted to one of Ptolemy's ancestors by either the emperor Claudius or the emperor Nero. The 9th century Persian astronomer Abu Ma'shar al-Balkhi mistakenly presents Ptolemy as a member of Ptolemaic Egypt's royal lineage, stating that the descendants of the Alexandrine general and Pharaoh Ptolemy I Soter 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". Historical confusion on this point can be inferred 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." Not much positive evidence is known on the subject of Ptolemy's ancestry, apart from what can be drawn from the details of his name, although modern scholars have concluded that Abu Ma'shar's account is erroneous. It is no longer doubted that the astronomer who wrote the Almagest also wrote the Tetrabiblos as its astrological counterpart. In later Arabic sources, he was often known as "the Upper Egyptian", suggesting he may have had origins in southern Egypt. Arabic astronomers, geographers, and physicists referred to his name in Arabic as Baṭlumyus (Arabic: بَطْلُمْيوس). Ptolemy wrote in Koine Greek, and can be shown to have used Babylonian astronomical data. He might have been a Roman citizen, but was ethnically either a Greek or at least a Hellenized Egyptian.

Astronomical writings Astronomy was the subject to which Ptolemy devoted the most time and effort; about half of all the works that survived deal with astronomical matters, and even others such as the Geography and the Tetrabiblos have significant references to astronomy.

Mathēmatikē Syntaxis

… excerpt ends here. Continue reading the full article.

Illustrations

Ptolemy illustration
Ptolemy: Engraving of a crowned Ptolemy being guided by Urania, by Gregor Reisch (1508), from Margarita Philosophica showing an early conflation of the mathematician with the royal house of Ptolemaic Egypt, with the same last name.
Engraving of a crowned Ptolemy being guided by Urania, by Gregor Reisch (1508), from Margarita Philosophica showing an early conflation of the mathematician with the royal house of Ptolemaic Egypt, with the same last name.
Ptolemy: Pages from the Almagest in Arabic translation showing astronomical tables.
Pages from the Almagest in Arabic translation showing astronomical tables.
Ptolemy: A depiction of the non-Ptolemaic Universe with no epicycles, possibly from 500 years before Ptolemy, as described in the Planetary Hypotheses by Bartolomeu Velho (1568).
A depiction of the non-Ptolemaic Universe with no epicycles, possibly from 500 years before Ptolemy, as described in the Planetary Hypotheses by Bartolomeu Velho (1568).
Ptolemy: A printed map from the 15th century depicting Ptolemy's description of the Ecumene by Johannes Schnitzer (1482).
A printed map from the 15th century depicting Ptolemy's description of the Ecumene by Johannes Schnitzer (1482).

Worked examples

Example 1 — a first encounter with Ptolemy

Start with the simplest possible case. Write down what Ptolemy claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Ptolemy before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Ptolemy ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Ptolemy

In research
Ptolemy appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Ptolemy in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Ptolemy is common in secondary-school and first-year university syllabi. It links to neighbouring topics 100s births, 1st-century Romans, 2nd-century Greek philosophers, so understanding it makes those chapters shorter.
In everyday life
Look for Ptolemy outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.
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How to study Ptolemy in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Ptolemy means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Ptolemy out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Ptolemy in simple terms?

Claudius Ptolemy (; Ancient Greek: Πτολεμαῖος, Ptolemaios; Latin: Claudius Ptolemaeus; c. 100 – 160s/170s AD), better known mononymously as Ptolemy, was a Greco-Roman mathematician, astronomer, astrologer, geographer, and music theorist who wrote about a dozen scientific treatises, three of which w…

Why does Ptolemy matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Ptolemy?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Ptolemy.

Tags

  • 100s births
  • 1st-century Romans
  • 2nd-century Greek philosophers
  • 2nd-century Romans
  • 2nd-century astronomers
  • 2nd-century deaths
  • 2nd-century geographers
  • 2nd-century mathematicians
  • Ancient Greek astrologers
  • Ancient Greek astronomers
  • Ancient Greek geographers
  • Ancient Greek mathematicians

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