Abstract
In 2012 the Union of German Academies of Sciences and Humanities announced the funding of a 25-year Academy Project of research into the reception and study of medieval Arabic and Latin versions of Ptolemaic works. Known as Ptolemaeus Arabus et Latinus (PAL), its primary aim is “to make the Ptolemaic corpus on the science of the stars available to researchers” (p. 3). To achieve this simply stated goal the organizers have created what is probably the largest collaborative, current project in the history of astronomy. Interested scholars may follow the activities of PAL on its website: https://ptolemaeusbadwe.de. This volume represents results of the first triennial PAL conference, offering a deliberately broad coverage of Ptolemaic astronomy and astrology in Latin, Arabic and Greek.
After a useful overview of each of its fourteen contributions, the book begins with four papers on the Greek and Near Eastern Traditions. In his lead-in paper, “The Ancient Ptolemy,” Alexander Jones seeks to present Ptolemy “in the round” and begins by asking which “Ptolemaic” works Ptolemy wrote. Reviewing the evidence on the doubtful works, he exploits the searchability of the digital Thesaurus Linguae Graecae (TLG) to identify traits of Ptolemy’s writing that allow a secure test of his authorship. One result of this is a strong argument for accepting the previously doubtful philosophical work, Criterion, as a work of Ptolemy. After considering the relative order in which Ptolemy composed his works, Jones presents two views of the Ptolemaic canon: a view by discipline and another by prevailing themes. For example, both the Almagest and the Harmonics, although in different disciplines, are “deeply concerned with applying sense perception . . .and reason” to create models underlying observed phenomena (p. 28). Jones concludes by emphasizing Ptolemy’s concern with “mathematically defined modes of representation of the cosmos” (p. 29).
To Jones’s examples one might add the Analemma, the subject of Nathan Sidoli’s “Mathematical Methods in Ptolemy’s Analemma.” The analemma was an ancient method of geometrically representing a sphere on a plane, a problem Ptolemy faced in his Planispherium and Geography. Sidoli carefully explains the method, based on the division of the celestial sphere into eight octants by three mutually perpendicular great circles all passing through the observer’s position at the center of that sphere. These three circles, taken in pairs, provide pairs of arcs, each pair sufficient to locate the Sun with respect to the local horizon. One can then use the analemma to show, with geometric constructions, how an artisan can construct and then measure spherical arcs and angles in true size. Aware that such constructions can never give the precision of trigonometric calculations, Ptolemy points out that they are sufficient for practical purposes. Again, one thinks of the Geography, which provides two methods of making a world map, one rough-and-ready, the other more exact (but also more exacting!).
Of course, it is well-enough to represent the cosmos, whether in two dimensions or three, but which spheres were being represented in the geocentric model of ancient astronomy? Paul Hullmeine addresses this question with his “Was There a Ninth Sphere in Ptolemy?,” which begins with a brief overview of Greek cosmology, from Aristotle’s 55 or 49 homocentric spheres to Alexander of Aphrodesias’s eight spheres. There is no reference to a ninth sphere in the Almagest but a number of Arabic and Jewish scholars believed that Ptolemy thought there were nine spheres. Hullmeine’s careful analysis of technical terms in the Arabic translation of the relevant passages from Book II of Planetary Hypotheses (whose Greek text is lost) makes it clear that Ptolemy did not write about a ninth sphere, although the detailed argument is, admittedly, quite complex. The confusion arose, Hullmeine suggests, in the Greek commentary tradition, specifically that of Philoponus, who was motivated by theological concerns and whose commentary was cited by al-Bīrūnī.
The section on Greek and Near Eastern Traditions closes with Boyadar Dimitrov’s “‘Fort.recte’: Witnesses to the Text of Ptolemy’s Tetrabiblos in Its Near Eastern Transmission,” which considers a “fragmentarily preserved, possibly pre-Islamic Syriac translation” of Ptolemy’s classic work on astrology (p. 97). The background to this paper is G. Vuillemin-Diem’s and C. Steel’s 2015 publication of William of Moerbeke’s Latin translation of the Greek text of Ptolemy’s Tetrabiblos. They made a careful comparison of that translation with W. Hubner’s Greek text and called attention to a number of places where William’s readings were “probably right” (fort. recte). Dimitrov’s task is to see what the Syriac translation can tell us about these readings. As often happens in these matters, the Latin and both Arabic translators had access to Greek texts older than that used by Hübner in preparing his edition of the Greek text. But new texts raise new problems and this paper asks what can be learned from a comparison of the syntax, grammar and vocabulary of readings from ten passages in each of the above-mentioned five works. In eight of the ten cases, the Syriac text supports Moerbeke’s readings, and Dimitrov shows good reason to accept the Syriac as an important translation.
The second section of the book, devoted to the Arabic Tradition, opens with Johannes Thomann’s “The Oldest Translation of the Almagest made for al-Ma’mūn . . .” In 1974 Paul Kunitzsch called attention to a passage in Ibn al-Ṣalāḥ’s (died 1154 CE) critique of the Almagest’s star catalog where he named, as one of four translations of that work available to him, one by “al-Ḥasan b. Quraysh,” done for the Calif al-Ma’mūn’ prior to that of Ḥajjāj. Citing Ibn al-Ṣalāḥ’s reputation for careful scholarship, Thomann argues that his statement “has to be taken seriously” (p. 127). Not wanting to prejudge the name of the translator, Thomann simply refers to him as “Anonymous.” Thomann makes a strong case for attributing quotations from the Almagest V,19 1 in Ibn al-Ṣalaḥ’s Critique of al-Fārābī’s Commentary on the Almagest to the Anonymous translation. Specifically, Thomann’s tables displaying differences in vocabulary between the translations of Anonymous, al-Ḥajjāj, and Isḥāq/Thābit show that the Almagest quotations found in Ibn al-Ṣalāḥ are from a very early translation, close to the time of al-Khwārizmī. Having established that Ibn al-Ṣalāḥ’s source for his quotations of the Almagest was an unknown early translation, Thomann supports Kunitzsch’s opinion that al-Ḥasan was the translator and he offers a number of reasons why Ibn al-Nadīm’s account of the various translations should be treated “with great caution” (p. 130).
Thomann’s arguments for a Ma’mūnic translation prior to those listed by Ibn al-Nadīm are followed by those of Dirk Grupe, in “Thābit ibn Qurra’s Version of the Almagest and Its Reception in Arabic Astronomical Commentaries,” for accepting another translation later than those listed by Ibn al-Nadīm. Grupe reviews the four translations of the Almagest and then presents evidence that there was a fifth Arabic translation that “historic witnesses from the tenth to the fifteenth centuries” refer to as a version by Thābit alone” (p. 141). Thābit’s translation, Grupe argues, is characterized by a “Euclidization” of the theorems and consistent replacement of chords by sines (However Thābit, in his On the Sector Figure, consistently uses chords and, as Grupe points out, so does the Dresden Latin Translation of Books I–IV, which Grupe feels is a translation of Thābit’s version.) Grupe also links to Thābit’s version a copy of al-Shīrāzī’s Epitome of the Almagest, Ibn Sinā’s K. al-Shifā’ in Tehran and a very much abridged version of the Almagest which shows similarities with the Dresden MS. On the basis of these manuscripts and his belief that the Dresden MS reflects Thābit’s version of the Almagest, Grupe concludes that a Tehran MS of Books VI and IX–XIII and a controversial manuscript in Jaipur containing Books I–VI provide further insight into Thābit’s translation.
Although Hullmeine addressed the question of the number of heavenly spheres, Tzvi Langermann addresses Arabic discussion of whether the heavens are spherical in his “Revamping Ptolemy’s Proof of the Sphericity of the Heavens.” Specifically, Langermann considers treatments of sphericity by Ibn al-Haytham, Jābir b. Aflaḥ, and al-Bīrūnī in three different literary contexts. Since Ptolemy believed that the cosmos represented perfection and the sphere, of all solids, has the largest volume for a given surface area, the cosmos must be spherical. However, although Ptolemy alludes to the maximality principle he gives no proof. Ibn al-Haytham wrote his Commentary on the Almagest to facilitate the beginner’s study. His mathematical proof of Ptolemy’s postulate is limited to showing that, for a given surface area, the sphere has greater volume than all polyhedral solids, the cone and the cylinder. Langermann also takes the reader through the various features of Ibn al-Haytham’s non-mathematical arguments, including experience with sundials and philosophical arguments. Jābir b. Aflaḥ’s Correction (Islāḥ), “a thorough reworking of the Almagest, both in terms of content and organization, which contains some criticisms as well” (p. 167), shows marked differences from Ibn al-Haytham’s work. In his geometric proof of the maximality principle, Jābir explicitly states that the surface of a regular polyhedron circumscribed about a sphere is greater than the surface of the sphere. The analogous fact for plane figures is a crucial step in Ibn al-Haytham’s argument but he never mentions it; Jābir’s argument would be easier for a beginner to follow. Coming finally to al-Bīrūnī, Langermann points out that his Questions to Ibn Sīnā mention possibilities other than the sphere and explain why Aristotle was wrong to dismiss them; al-Bīrūnī confesses that he is unable to refute them. Thirty years later, in his Qānūn al-Mas’ūdī I, al-Bīrūnī accepts the sphericity of the cosmos but argues that to settle the question definitively we must first ascertain the shape of the earth.
Jose Bellver’s “Arabic Versions of Jābir b. Aflaḥ’s al-Kitāb fī l-Hay’a” deals with the work of one of Langermann’s subjects, discussing the authorship and order of composition of four extant versions of Jābir’s al-Kitāb fī l-Hay’a, whose alternate title, Iṣlāḥ al-majisṭī, is a later accretion. Jābir wrote his treatise to create a version of the Almagest focused on theoretical astronomy, and, for the most part, he avoided such practical matters as instruments. Bellver’s study is focused on two versions preserved in the Escorial (Ea and Eb); a third, B, is in Berlin; the fourth, T, in Tehran (Books I–VI only). Bellver comes to a tentative ordering of the composition of the four Arabic versions of al-Kitāb fī l-Hay’a and its Latin translation by Gerard of Cremona: Eb Book I is the only remaining witness to the first edition; Ea is the revised first edition; Eb, containing Books II–IX, is the second edition; Gerard’s Latin translation, which generally follows Eb, is an augmented second edition; B, a revised second edition; and T, a third edition. These various versions represent Jābir’s modifications over an extended period of time.
Josep Casulleras’s “The Astrological Computations Attributed to Ptolemy and Hermes in Medieval Sources” brings us back to astrology as Casulleras asks why, in the absence of any solid evidence, certain practices of natal astrology are attributed to Ptolemy and the mythical Hermes. These practices deal with the astrological notions of ecliptic arcs or chords known as houses, rays and projections, making use of the spherical geometry found in Euclid, Autolycus and Theodosius. Casulleras explains clearly the meaning of the technical terms and then surveys the associated practices, beginning with methods for determining the ecliptic arcs called “houses.” One, called “the standard method,” used the local meridians to project twelve equal equatorial arcs onto ecliptic arcs called houses. The other method defines the houses by intersections of the ecliptic with the curves defining the even-numbered seasonal hours. Andalusian sources attribute both methods to Ptolemy and both use the astrolabe. However Ptolemy’s one astrological work, the Tetrabiblos, contains no procedure for projection of rays or the division of houses and Casulleras notes that, with one possible exception, no attributions of a method to Hermes are corroborated by the extant works attributed to him. This reviewer found much of interest in this study, including the account of Ibn Mu’ādh’s discourse on astrology and the treatment of medieval texts found in the extract from Rabiçag.
The section on the Latin Tradition opens with Henry Zepeda’s “Glosses on the Almagest by Campanus of Novarra and Others in Paris . . .,” a study of marginalia in the 45 available manuscripts of the Latin translation of the Almagest by Gerard of Cremona. Zepeda is particularly, but not exclusively, interested in the 13th-century glosses by Campanus of Novarra and how glosses ‘migrate’ from one MS to another. Among the glosses discussed here are outlines of topics in a given section of the Almagest; a striking example is an outline of the section on chords in a circle, which goes from section to subsection down to the twelfth level! Zepeda suggests that such glosses probably reflect teaching practice. Another type represents the “Euclidization” of the Almagest, that is, numbering the theorems and supplying more complete proofs. (This is the same phenomenon that Grupe saw in Thābit’s Almagest.) Given that the Elements was the model of a mathematical science and that Campanus had provided the editio princeps of the Elements, it is hardly surprising to see this approach in his commentary on the Almagest. This work is rich in detail and provides new insight into medieval teaching and learning of astronomy.
The next two contributions take us again to astrology: Carlos Steel on “A Discussion on Ptolemy’s Authority: Henry Bate’s Prologue to His Translation of Ibn Ezra’s Book of the World” and Jean-Patrice Boudet a work regarded (at the time) as Ptolemaic, the Centiloquium.
In the latter part of the 13th century, the English scholar and church official Henry Bate began a project of translating astrological works by the 12th-century Jewish scholar Abraham ibn Ezra. The focus of this paper is Bate’s preface to Ibn Ezra’s Book of the World, concerned with historical and meteorological astrology. Bate considers particularly a passage in which Ibn Ezra takes strong exception to the value of the Tetrabiblos and doubts its ascription to Ptolemy. Ibn Ezra claims that Ptolemy said, without saying where, that it was not possible to determine the time of the vernal equinox. Bate feels the reference must be to Book II, 11 of the Tetrabiblos which deals with the beginning of the year. 2
Two issues emerge. The first is the spirit in which Ibn Ezra reads the texts of Ptolemy and Albumasar, which Bate feels violated a well-established principle of reading an ancient text in a way that puts the author in as favorable a light as possible. (An issue also raised in Langermann’s treatise.) Bate feels that what Ptolemy intends is that since the equinoxes are difficult to time exactly one should use conjunctions/oppositions of the Sun and Moon nearest the equinoctial points. After all, the issue is about the general weather to be expected as the Sun moves through the signs and absolute exactitude is of no great importance. Having shown that Ptolemy cannot be cited in support of a claim that one can ignore the entrance of the Sun into Aries, Bate addresses the more general question of the role of exactitude in astronomy and astrology and asserts that since we cannot know if the revolutions of the heavenly spheres have rational or irrational ratios to one another we can never know if we have reached the true ratio. We must be content with the best approximation possible.
One hears that sometimes a work was claimed to be by Ptolemy in order to gain the readership that a famous name attracts. However, as Jean-Patrice Boudet points out in “The Medieval Latin Versions of Pseudo-Ptolemy’s Centiloquium: A Survey,” the medieval popularity of the Centiloquium was probably due (in part at least) to the fact that one-fifth of its hundred sayings concern the practice of medicine. The Centiloquium was originally an anonymous, Greek astrological treatise titled Karpos (Fruit). Most of the numerous Latin manuscripts of the work are 12th-century translations of a 10th-century Arabic translation (al-Thamara) and commentary by Abū Ja’far Aḥmad b. Yūsuf. 3 Indeed, the Arabic version was translated six times into Latin, the version most often encountered being that of Plato of Tivoli in 1136. And there are at least five Latin versions of Abū Ja’far’s commentary. Boudet points out how the Centiloquium, in addition to its inclusion in the medical curriculum, was relevant to the debate on the doctrinal validity of astrology from the mid-13th century onward. Active interest in the text peaked during the 15th century, with three different editions of Plato of Tivoli’s translation, new commentaries and a new translation from the Greek by George of Trebizond. This carefully-researched paper is both interesting and informative. But this reader wished that the writer had translated the sections from the Latin texts quoted in extenso (e.g. pp. 295–298).
George of Trebizond published his translation of the Centiloquium in 1456, 5 years after he had published his translation of the Almagest that gave rise to the controversy that is the subject of Michael H. Shank’s “Regiomontanus versus George of Trebizond on Planetary Order, Distances and Orbs (Almagest 9.1).” This paper concerns a quarrel centering on three works: George of Trebizond’s 1451 publication of his translation of the Almagest based on a Greek manuscript lent to him by Cardinal Bessarion; his 300-page Commentary on the Almagest attacking Theon of Alexandria, whose work Bessarion had recommended as a guide to the Almagest; and Regiomontanus’s composition in 1462 of his Defence of Theon against George of Trebizond. Shank’s paper focuses on the controversy between George and Regiomontanus in which the real issue was the sort of evidence, authority and arguments required for astronomy. For example, in the 15th century it was a “commonplace” that the order of cosmic bodies was Earth—Moon—Mercury—Venus and then the three outer planets. The issue was the degree of certainty attached to this ordering, particularly for Mercury and Venus. Since they exhibit no parallax, Ptolemy had said they had to be further than the Moon but one could not be absolutely sure which was closer to the Earth. However, George thought he could be sure, based on natural philosophy, noting Simplicius’s undocumented report that Mercury had been observed to pass in front of Venus and that it had the shorter period (so lower being faster). George went on to calculate the sizes of the spheres for the celestial bodies, where—following Campanus of Navarra (13th c.) in his Theorica Planetarum—he added the planetary radii to the size of their spheres. As Shanks points out, “Almost all of George’s results and procedures are identical with those of Campanus” (p. 336). Regiomontanus’s response to all of this, which breaks away from the requirement of uniform circular motion, occupies a good part of this highly interesting paper.
The next paper returns to the subject of astrology, a topic that occupies three of the six papers in the Latin section. Unlike the other two, which record support for astrology, H. Darrel Rutkin’s “Optimus Malorum: Giovanni Pico della Mirandola’s Complex and Highly Interested Use of Ptolemy in the Disputationes adversus astrologiam divinatricem (1496). A Preliminary Survey” deals with a man who was a passionate foe. The “Optimus Malorum” (“the best of the bad”) in the title of this work is Giovanni Pico’s put-down of Ptolemy’s astrological work. Although Pico agreed that celestial objects and events can influence earthly events, his goal was, as Rutkin puts it, “to wrench off the by-his-time entrenched astrological superstructure from its still-solid Aristotelian foundations” (p. 390). The paper centers on Pico’s use of Ptolemy’s writings in support of this goal. He “directly and sometimes abusively” attacks Ptolemy the astrologer. But when Ptolemy criticizes some astrological theories Pico uses Ptolemy the astronomer to add weight to the criticisms. He is also quick to cite conflicting views of astrologers—including Ptolemy—as evidence that astrologers cannot agree among themselves. Rutkin’s closing assertion that Pico’s Disputationes “played a significant role” in astrology’s disappearance from the university curriculum (see Boudet’s paper) certainly invites further exploration (p. 403).
It is perhaps fitting that a volume of studies of the influence of Ptolemy’s writings in the ancient and medieval worlds should conclude with Richard L. Kremer’s “Longomontanus on Mars: The Last Ptolemaic Mathematical Astronomer Creates a Theory.” Kremer gives a detailed account of the work and results of the Danish astronomer Christian Longomontanus as presented in his Astronomica Danica (1622); in particular, Kremer studies Longomontanus’s discussion of how Ptolemy, Copernicus, Tycho Brahe, and Kepler treated the motions of the three outer planets, Mars in particular. Added interest to the comparisons stems from the fact that both Longomontanus and Kepler had worked with Tycho Brahe. Kremer takes Kepler’s vicarious hypothesis as a reference point in his discussions of Longomontanus’s two attacks on the problem of Mars and shows how he used material from Copernicus, Tycho and Kepler—and faith in perfect numbers—to reduce the errors in the Copernican/Ptolemaic theory of Mars by a factor of ten. (He must have been the last serious astronomer to use numerology as a guide to his discipline!) For an account of Longomontanus’s first attempt, working with Tycho, on a theory of the motion of Mars, we must rely on Kepler. Although Longomontanus claimed that the theory matched ten observations within 2 arcminutes, Kepler relates that Tycho and Longomontanus “got stuck” on the latitudes and on the planet’s position relative to the Sun.
In the introduction to his second theory for Mars, which he expounded 20 years later, Longomontanus refered to Kepler’s use of ellipses and wrote proudly that “we almost alone uphold that Copernican axiom [uniform circular motion] . . . which in astronomy we value to the highest degree” (p. 439). But he was the last important astronomer to do so. Kremer’s careful account of the steps needed to complete Longomontanus’s theory of Mars makes the reader realize just how much work he had to do to create what might be called the culmination of Ptolemaic astronomy.
The studies in this volume, their extensive bibliographies and the three indices provide modern scholars with the current state-of-the-art in a number of fields as well as with tools to explore a number of directions for future studies. This reviewer found remarkably few typos and can only wish that the publishers had allowed contributors to use colors to distinguish various curves in some of the diagrams. They really are necessary.