Ptolemy

1) His Biography:

Ptolemy lived in or around Alexandria, in the Roman province of Egypt, under Roman control, had a Latin name (which various historians have taken to infer he was actually a Roman citizen), cited Greek thinkers, and employed Babylonian observations and lunar theory. Ptolemy addresses a certain Syrus in half of his extant writings, a man about whom nothing is known but who likely shared some of Ptolemy’s astronomical concerns.

Theodore Meliteniotes, a 14th-century astronomer, claimed to have been born in the ancient Greek city of Ptolemais Hermiou in the Thebaid. However, this attestation is relatively late, and there is no evidence to back it up. Around the year 168, Ptolemy died in Alexandria. Ptolemy committed the most time and effort to astronomy; over half of all the works that have survived deal with astronomical topics, and even works like the Geography and the Tetrabiblos contain astronomical references.

2) His Main Works:

• Quadripartitum (in Latin). Venezia: Ottaviano Scoto (1.) eredi & C. 1519.

• [Opere] (in Latin). Basel: Heinrich Petri. 1541.

• In Claudii Ptolemaei Quadripartitum (in Latin). Basel: Heinrich Petri. 1559.

• Quadripartitum (in Latin). Frankfurt am Main: Johann Bringer. 1622.

• Quadripartitum (in Latin). Padova: Paolo Frambotto. 1658.

• De iudicandi facultate et animi principatu (in Latin). Paris: Sebastian Cramoisy (1.) &

Sebastian Mabre-Cramoisy. 1663.

• De iudicandi facultate et animi principatu (in Latin). Den Haag: Adriaen Vlacq. 1663.

• Harmonicorum libri (in Latin). Oxford: Theatrum Sheldonianum. 1682.

3) Main themes in his writings:

Mathēmatikē Syntaxis:

The Almagest, often known as Ptolemy’s Mathmatik Syntaxis (Ancient Greek: Μαθηματικὴ Σύvταξις, lit. “Mathematical Systematic Book”), is the sole surviving comprehensive ancient treatise on astronomy. Even though Babylonian astronomers developed arithmetical techniques for determining and forecasting astronomical occurrences, they were not based on any underlying model of the heavens; on the other hand, early Greek astronomers provided qualitative geometrical concepts to “save the appearances” of celestial occurrences without the capacity to make forecasts.

Hipparchus was the first to try to combine these two approaches, creating geometric models that could not only reflect the arrangement of the planets and stars but also be used to compute celestial motions. Following Hipparchus, Ptolemy generated each of his geometrical models for the Sun, Moon, and planets from a selection of astronomical observations made over a period of more than 800 years; yet, many astronomers have speculated for ages that some of his models’ attributes were adopted independent of observations.

Handy Tables:

The Handy Tables consist of a series of astronomical tables as well as canons for their use. Ptolemy collected all the data needed to compute the locations of the Sun, Moon, and planets, the rise and setting of the stars, and eclipses of the Sun and Moon to make astronomical calculations easier, making it a helpful tool for astronomers and astrologers. Theon of Alexandria’s version of the tables is widely recognised. Despite the fact that Ptolemy’s Handy Tables do not exist in Arabic or Latin, they serve as the model for most Arabic and Latin astronomical tables or zījes.

Planetary Hypotheses:

The Planetary Hypotheses (Ancient Greek: Ὑποθέσεις τῶv πλανωμένων, lit. “Planetary Hypotheses”) is a two-volume cosmology treatise by Ptolemy that deals with the structure of the world and the principles that govern celestial movement. Ptolemy goes beyond the Almagest’s mathematical models to give a physical representation of the world as a set of interconnected spheres, in which he computed the universe’s dimensions using the epicycles of his planetary model.

He calculated that the Sun was 1,210 Earth radii away (now known to be around 23,450 radii), and that the radius of the stars was 20,000 times that of the Earth. The work is particularly notable for including instructions on how to construct instruments that represent the planets and their motions from a geocentric perspective, similar to what an orrery would have done for a sun – centered one, probably for educational purposes.

Cartography:

Ptolemy’s Geography, a handbook on how to construct maps using coordinates for sections of the Roman world known, is his second most well-known work. The first section of the Geography is devoted to a review of the data and methodology he employed. Ptolemy emphasises the superiority of astronomical data over ground measurements or travellers’ reports, despite the fact that he only had this data for a few locations.

The significant novelty in Ptolemy’s book comes in the second half, when he presents an inventory of 8,000 places he gathered from Marinus and others, the largest such database from antiquity. Approximately 6,300 of these sites and geological features have been allocated coordinates, allowing them to be put in a grid that spans the globe.

Although latitude was measured from the equator, as it is now, Ptolemy chose to represent it in climata, the duration of the longest day, rather than degrees of arc: as one travels from the equator to the polar circle, the duration of the midsummer day grows from 12 to 24 hours. The now-lost Stone Tower, which marked the midpoint of the ancient Silk Road and which researchers have been attempting to locate ever since, was one of the spots Ptolemy documented specific coordinates for.

Ptolemy gives instructions on how to make maps of the entire inhabited world (oikoumenē) and of the Roman provinces in the third part of the Geography, including topographic lists and descriptions for the maps. Ptolemy was well aware that he only knew about a quarter of the globe, and an erroneous extension of China southward suggests his sources did not reach all the way to the Pacific Ocean. His oikoumenē spanned 180 degrees of longitude from the Blessed Islands in the Atlantic Ocean to the middle of China, and about 80 degrees of latitude from Shetland to the east coast of Afric, anti-Meroe.

The topographical tables in the second section of the book (Books 2–7) are most likely cumulative texts that were updated as new knowledge became available after Ptolemy’s time. As a result, information found in various portions of the Geography is likely to be of varying dates, as well as including numerous scribal inaccuracies. Despite the fact that the regional and world maps in extant copies date from around 1300 AD (after the text was unearthed by Maximus Planudes), some researchers believe they originate from Ptolemy himself.

Astrology:

The astrological impacts of the planets are explained in some detail, based on their cumulative effects of heating, cooling, humidifying, and drying. Other astrological practises that Ptolemy believed to be without sound basis, such as considering the numerological significance of names, are dismissed, and popular topics such as electional astrology which is to interpret astrological charts to determine plans of action, and medical astrology are left out for similar reasons.

The Tetrabiblos’ immense popularity might be due to its role as an exposition of the art of astrology and a storehouse of astrological learning, rather than as a textbook. It speaks in broad terms, eschewing visuals and practical facts. Ptolemy’s Centiloquium, a compilation of one hundred astrological aphorisms, was widely copied and discussed on by Arabic, Latin, and Hebrew authors, and was sometimes bound together in mediaeval copies after the Tetrabiblos as a form of conclusion. It is currently thought to be a pseudepigraphical work from a much later period. The name and date of the work’s true author, now known as Pseudo-Ptolemy, are unknown.

Music:

Ptolemy wrote the Harmonikon, also known as the Harmonics, a three-volume study on music theory and the mathematics underlying musical notes. It starts with a description of harmonic theory, followed by a lengthy discussion of the link between reasoning and perception in terms of supporting theoretical assumptions. After critiquing his predecessors’ methods, Ptolemy proposes (in contrast to Aristoxenus’ followers) that musical intervals be based on mathematical ratios, which he backs up with actual evidence as opposed to the overly theoretical approach of the Pythagoreans.

Ptolemy first introduces the harmonic canon, an experimental equipment that will be employed in the following sections for demonstrations, before moving on to Pythagorean tuning. Pythagoreans felt that musical mathematics should be based on a precise ratio of 3:2, but Ptolemy only thought that it should involve tetrachords and octaves in principle. He offered his own tetrachord and octave divisions, which he obtained with the aid of a monochord. The book comes to a close with a more speculative discussion of the connections between harmony, the soul (emotional state), and the planets (harmony of the spheres).

Optics:

The Optica, often known as the Optics, is a text that only exists in a mediocre Latin translation, which was translated from a lost Arabic original by Eugenius of Palermo (about 1154). Ptolemy discusses the qualities of sight (not light) in it, such as reflection, refraction, and colour. The book is an important element of the early history of optics, and it influenced Ibn al-Haytham’s renowned and superior Book of Optics from the 11th century.

Many phenomena relating to illumination, colour, size, form, movement, and stereoscopic vision were explained by Ptolemy. He also distinguished between illusions brought on by physical or visual elements and those brought on by judgmental considerations. He proposed an enigmatic explanation based on the difficulties of gazing upwards for the sun or moon illusion i.e. the larger visual size on the horizon.

There are three primary portions to the work. The first section (Book II) starts with the fundamentals of direct vision and concludes with a review of stereopsis. Reflection in flat, convex, concave, and compound mirrors is covered in the second half (Books III-IV). The final portion (Book V) is devoted to refraction and contains the earliest surviving table of refraction from air to water, the values of which (excluding the 60Æ angle of incidence) appear to have been derived using an arithmetic progression.

Ptolemy’s table, on the other hand, was partly based on real tests, according to Mark Smith. The rays (or flux) emanating from the eye formed a cone, with the vertex inside the eye and the base constituting the visual field, according to Ptolemy’s theory of vision. The rays were sensitive, and they relayed information about the distance and orientation of surfaces to the observer’s mind.

Overall shape and size were ascertained by the visual angle subtended at the eye combined with perceived distance and orientation. This was one of the first presentations of size-distance invariance as a reason of perceived size and form constancy, which the Stoics supported.

Philosophy:

He authored a short essay called On the Criterion and Hegemonikon, which may have been one of his earliest works. Ptolemy discusses the nature and form of the human psyche or soul, notably its dominating capacity, as well as how humans attain scientific knowledge (i.e., the “criterion” of truth).

Ptolemy claims that in order to reach the truth, one must apply both reason and sense perception in complementary ways. On the Criterion is also notable for being Ptolemy’s only work that is not based on mathematics. Ptolemy asserts the superiority of mathematical knowledge above other forms of knowledge in numerous places. Ptolemy, like Aristotle before him, considers mathematics to be a type of theoretical philosophy; nonetheless, he considers mathematics to be superior to theology or metaphysics because the latter are speculative, whilst the former can guarantee certain knowledge. This viewpoint is in opposition to the Platonic and Aristotelian traditions, which placed theology or metaphysics at the top of the priority list.

4) His influence in the history of ideas:

Ptolemy displayed his astronomical models with useful tables that could be used to calculate the planets’ future or previous positions. The Almagest also includes a star catalogue, which is a recreation of Hipparchus’ list. Its list of forty-eight constellations is similar to the contemporary system, although they did not encompass the entire sky, unlike the modern system (only what could be seen with the naked eye). The Almagest was the canonical treatise on astronomy across Europe, the Middle East, and North Africa for almost a thousand years, and its author, Ptolemy, King of Alexandria, became a near-legendary figure. Ptolemy wrote an astrological treatise in four sections, known as Tetrabiblos (lit. “Four Books”) in Greek or Quadripartitum in Latin. Its original title is unknown, however it could have been Apotelesmatik. (bibla), which approximately translates to “(books) on the Effects” or “Outcomes” or “Prognostics” in Greek manuscripts.

The Tetrabiblos is believed to have “enjoyed almost the authority of a Bible among the astrological writers of a thousand years or more” as a source of reference. Plato of Tivoli (Tiburtinus) was the first to translate it from Arabic into Latin, in 1138, while in Spain.

Ptolemy’s achievement was to order his material in a systematic way, showing how the subject could, in his opinion, be rationalised. Much of the content of the Tetrabiblos was gathered from earlier sources. It is, in fact, presented as the second part of an astronomical study, the Almagest being the first, dealing with the effects of celestial bodies on the sublunary sphere.

Despite the fact that Ptolemy’s Harmonics did not have the same influence as his Almagest or Geography, it is a well-structured treatise with more methodological comments than any other of his works. During the Renaissance and the seventeenth century, it had a great influence; Kepler, for example, studied and was influenced by this work in his own meditations about world harmony.

Ptolemy engaged in epistemological and psychological debates throughout his corpus, despite being best known for his contributions to astronomy and other scientific subjects. Ptolemy’s views were echoed by other mathematicians such as Hero of Alexandria, despite being a minority viewpoint among ancient thinkers.