Claudius Ptolemaeus

Claudius Ptolemy, the astronomer of Alexandria, lived from about AD 100 to about 170.¹ Almost everything we know about him has to be worked out from his own books.^1,2 The best evidence for his dates is the observations of the sky that he reports in his great work on astronomy: the earliest is dated 26 March 127 and the latest 2 February 141.¹ The only place named in any of his observations is Alexandria, and there is no reason to think he lived anywhere else.¹ His name tells us a little more: Ptolemaeus suggests an inhabitant of Egypt of Greek or Greek-speaking family, and Claudius that he was a Roman citizen, probably because the emperor Claudius or Nero had made an ancestor one.¹

The only formal notice of his life, in the tenth-century Byzantine encyclopedia called the Suda, is a few lines long.¹ It calls him «Πτολεμαῖοϲ, ὁ Κλαύδιοϲ χρηματίϲαϲ, Ἀλεξανδρεύϲ, φιλόϲοφοϲ», “Ptolemy, called Claudius, of Alexandria, philosopher” (our translation), and places him in the time of the emperor Marcus, that is Marcus Aurelius, who reigned from 161 to 180.^1,3

Ancient tradition / legend Later writers filled the gaps. A sixth-century commentator, Olympiodorus, says Ptolemy practised astronomy for forty years at Canopus, near the mouth of the Nile; Gerald Toomer thinks this probably a fiction spun from an inscription said to be his.¹ A description of his looks, handed down in Arabic, turns out to be the stock portrait of a philosopher from Greek handbooks on reading character in the face.²

Debated among scholars A fourteenth-century astronomer, Theodore Meliteniotes, says that he was born at Ptolemais in Upper Egypt.⁴ Frank Robbins, his translator, thought we can probably rely on that, and on an eleventh-century Arabic report that he lived to 78; Toomer allows that the first could be correct but calls it late and unsupported, and sets the Arabic sources aside as adding nothing credible.^1,2

What he wrote

Astronomy was the subject he gave the most time and effort to: about half of his surviving works deal with it.⁴ His great work, in thirteen books, was called the Mathematical Syntaxis, «μαθηματικῆς συντάξεως» in the reader's heading, that is, the Mathematical Compilation.^1,5 In later antiquity it came to be called the Great, or Greatest, compilation; Arabic translators turned the Greek word for “greatest”, megistē, into al-majisṭī, and medieval Latin made that almagesti or almagestum: our Almagest.^1,6 Starting from first principles, it leads the reader to tables that give the places of the sun, the moon, the five planets then known and the stars for any date.¹ Around a round, motionless earth the heavens turn.¹ To make the planets' uneven motions come out right he combined small circles riding on larger ones (epicycles), circles whose centre is not the earth (eccentrics), and a new device: a point off the centre about which the motion looks even, later called the equant.^1,6 Books 7 and 8 hold a catalogue of 1,022 stars in forty-eight constellations.¹

The Almagest is the earliest of his major works, and several of the later ones mention it.¹ The Handy Tables gathered its tables into a more practical form, and the Planetary Hypotheses turned its geometry into a physical model of the universe and worked out its size.¹ The Tetrabiblos (“Four Books”) is a handbook of astrology, which Ptolemy saw as the natural partner of the Almagest: one tells where the heavenly bodies will be, the other what they do to things on earth.¹ The Geography, in eight books, teaches how to draw a map of the known world, and most of it is a list of some eight thousand places with their longitudes and latitudes, so that the map can be rebuilt from the text alone.^1,7 The Harmonics, in three books, works out the mathematics of musical intervals, steering between the followers of Pythagoras, who trusted theory over the ear, and the followers of Aristoxenus, who did the reverse.¹

Some works survive only in translation: the Optics in a twelfth-century Latin version made from a lost Arabic one, and the Planisphaerium, on mapping the sky onto a flat plane (the mathematics behind the astrolabe), in Arabic and Latin.¹ Others are lost, among them a Mechanics in three books, which the Suda lists.^1,3

The reader has the Almagest in J. L. Heiberg's Greek, the Tetrabiblos in two Greek editions, and a short On Music, which is not the Harmonics but twenty-seven brief notes headed «ΠΤΟΛΕΜΑΙΟΥ ΜΟΥΣΙΚΑ», printed by Karl von Jan in 1895; his own notes show that some repeat passages of Cleonides and Nicomachus.^1,8,9 It has no English translation of Ptolemy, so the English here is our own unless a translator is named.⁸

Reading Ptolemy

The Almagest opens with a short essay on knowledge, addressed «ὦ Σύρε», “O Syrus”, to a man of whom nothing else is known.^1,10 Following Aristotle, Ptolemy divides theoretical philosophy into theology, physics and mathematics, and then ranks them: the first two are guesswork rather than knowledge, but «μόνον δὲ τὸ μαθηματικόν, εἴ τις ἐξεταστικῶς αὐτῷ προσέρχοιτο, βεβαίαν καὶ ἀμετάπιστον τοῖς μεταχειριζομένοις τὴν εἴδησιν παράσχοι», “only the mathematical kind, if one comes to it in a spirit of inquiry, would give those who practise it sure and unshakeable knowledge” (our translation).¹⁰ Astronomy, he adds, improves character too, «ἐραστὰς μὲν ποιοῦσα τοὺς παρακολουθοῦντας τοῦ θείου τούτου κάλλους», “making those who follow it lovers of this divine beauty” (our translation).¹⁰

The headings of book 1 announce its picture of the world one claim at a time: «ὅτι μέση τοῦ οὐρανοῦ ἐστιν ἡ γῆ», “that the earth is in the middle of the heavens”, and «ὅτι οὐδὲ κίνησίν τινα μεταβατικὴν ποιεῖται ἡ γῆ», “that the earth does not move from place to place either” (our translations).⁵ He sets himself a rule: «ὅλως δὲ ἡγούμεθα προσήκειν διʼ ἁπλουστέρων ὡς ἔνι μάλιστα ὑποθέσεων τὰ φαινόμενα ἀποδεικνύειν», “in general we think it right to account for the phenomena by hypotheses as simple as possible” (our translation), so long as nothing of weight in the observations tells against it.¹¹ The planets would not be simple, and in the last book he defends his elaborate models: «καὶ μηδεὶς τὰς τοιαύτας τῶν ὑποθέσεων ἐργώδεις νομισάτω σκοπῶν τὸ τῶν παῤ ἡμῖν ἐπιτεχνημάτων κατασκελές· οὐ γὰρ προσήκει παραβάλλειν τὰ ἀνθρώπινα τοῖς θείοις», “and let no one think such hypotheses troublesome, looking at the inadequacy of our own devices; for it is not right to compare human things with divine” (our translation).¹² The great Greek dictionary, LSJ, cites this very sentence for the rare word κατασκελής: “the meagreness or inadequacy of human contrivances”.¹³

The Tetrabiblos begins by looking back at the Almagest.^14,15 The study of the heavens' motions, Ptolemy tells Syrus, «κατʼ ἰδίαν σύνταξιν ὡς μάλιστα ἐνῆν ἀποδεικτικῶς σοι περιώδευται», in Robbins' translation “has been expounded to you as best we could in its own treatise by the method of demonstration”.^14,15 Readers do not agree about his style. Toomer calls the Almagest “a masterpiece of clarity and method”;¹ Robbins found Ptolemy “a difficult author even for the ancients”, fond of “long, involved sentences”.²

Debated among scholars The most famous lines under his name are a short poem, kept in the Greek Anthology and copied on the first page of manuscripts of the Almagest: “I know that I am a mortal, a creature of a day; but when I search into the multitudinous revolving spirals of the stars my feet no longer rest on the earth, but, standing by Zeus himself, I take my fill of ambrosia, the food of the gods” (W. R. Paton's translation, slightly modified by Cristian Tolsa).¹⁶ Whether Ptolemy wrote it is uncertain.¹⁶ Synesius of Cyrene engraved it on an astrolabe shortly before 400 and called it old, without naming an author; Tolsa argues that it was added to the Almagest as a note on its preface, and that this is what led the anthologies to call it Ptolemy's.¹⁶

Why he matters

The Almagest became the standard textbook almost at once and ruled theoretical astronomy until the end of the sixteenth century.¹ It was translated into Arabic about 800, and Western Europe knew it mainly through Gerard of Cremona's Latin translation from the Arabic, of 1175.¹ Even Copernicus' De revolutionibus (1543), which put the sun at the centre, is, in Toomer's words, “cast in a firm Ptolemaic mold”; only Kepler's work, built on Tycho Brahe's observations, made the Almagest obsolete.¹ The Geography, in Latin from about 1406, lay behind most maps printed in the fifteenth and sixteenth centuries.¹ The Tetrabiblos, Robbins says, “enjoyed almost the authority of a Bible” among astrological writers for a thousand years or more.²

Debated among scholars His honesty has been questioned. His own observations of the equinoxes are each about a day out, in a way that agrees with his predecessor Hipparchus; Jean-Baptiste Delambre, in the early nineteenth century, held that he copied Hipparchus, and in 1977 Robert R. Newton called him “the most successful fraud in the history of science”.^1,4,6 Toomer finds wholesale copying implausible, though he thinks Ptolemy probably picked the observations that best agreed with Hipparchus; Owen Gingerich, admitting “some remarkably fishy numbers”, also rejected the charge of fraud.^1,6 Toomer's verdict on the system that bears his name: “The Ptolemaic system is indeed named after the right man.”¹