Some variants in the materials related to the planetary latitudes, including computational procedures, underlying parameters, numerical tables, and so on, may be addressed in the corpus of the astronomical tables preserved from the medieval Islamic period, which have already been classified comprehensively by Van Dalen. Of these, the new values obtained for the planetary inclinations and the longitude of their ascending nodes might have something to do with actual observations in the period in question, which are the main concern of (...) this paper. The paper is in the following sections. In the first section, Ptolemy’s latitude models and their reception in Islamic astronomy are briefly reviewed. In the next section, the medieval non-Ptolemaic values for the inclinations and the longitudes of the nodal lines are introduced. The paper ends with the discussion and some concluding remarks. The derivation of the underlying inclination values from the medieval planetary latitude tables and determining the accuracy of the tables are postponed to “Appendix” in the end of the paper. (shrink)

A characteristic hallmark of medieval astronomy is the replacement of Ptolemy’s linear precession with so-called models of trepidation, which were deemed necessary to account for divergences between parameters and data transmitted by Ptolemy and those found by later astronomers. Trepidation is commonly thought to have dominated European astronomy from the twelfth century to the Copernican Revolution, meeting its demise only in the last quarter of the sixteenth century thanks to the observational work of Tycho Brahe. The present article seeks to (...) challenge this picture by surveying the extent to which Latin astronomers of the late Middle Ages expressed criticisms of trepidation models or rejected their validity in favour of linear precession. It argues that a readiness to abandon trepidation was more widespread prior to Brahe than hitherto realized and that it frequently came as the result of empirical considerations. This critical attitude towards trepidation reached an early culmination point with the work of Agostino Ricci, who demonstrated the theory’s redundancy with a penetrating analysis of the role of observational error in Ptolemy’s Almagest. (shrink)

ArgumentIn theAlmagest, Ptolemy finds that the apogee of Mercury moves progressively at a speed equal to his value for the rate of precession, namely one degree per century, in the tropical reference system of the ecliptic coordinates. He generalizes this to the other planets, so that the motions of the apogees of all five planets are assumed to be equal, while the solar apsidal line is taken to be fixed. In medieval Islamic astronomy, one change in this general proposition took (...) place because of the discovery of the motion of the solar apogee in the ninth century, which gave rise to lengthy discussions on the speed of its motion. Initially Bīrūnī and later Ibn al-Zarqālluh assigned a proper motion to it, although at different rates. Nevertheless, appealing to the Ptolemaic generalization and interpreting it as a methodological axiom, the dominant idea became to extend it in order to include the motion of the solar apogee as well. Another change occurred after correctly making a distinction between the motion of the apogees and the rate of precession. Some Western Islamic astronomers generalized Ibn al-Zarqālluh's proper motion of the solar apogee to the apogees of the planets. Analogously, Ibn al-Shāṭir maintained that the motion of the apogees is faster than precession. Nevertheless, the Ptolemaic generalization in the case of the equality of the motions of the apogees remained untouchable, despite the notable development of planetary astronomy, in both theoretical and observational aspects, in the late Islamic period. (shrink)

ArgumentThe present paper is an attempt to understand how medieval astronomers working within the Ptolemaic astronomical context in which the annular eclipse is an unjustified and impossible phenomenon, could know, define, justify, and later make attempts that led to success in predicting annular solar eclipses. As a context-based study, it reviews the situation of annular eclipses with regard to the medieval hypotheses applied to the calculation of the angular diameters of the sun and the moon, which was basic for contemplating (...) the possibility of annular eclipses. This gives the premises and the preliminary insights that were necessary to clarify the complex situation of the annular eclipse in the late medieval Islamic period and to explain the historical mechanisms leading to justifying the phenomenon during that period. This was, first due to a convincing and efficient observational evidence which, of course, was available only to a number of medieval astronomers and significantly for only a limited time period, and, second, the result of an amazing interaction amongst various astronomical traditions available to them. At a more general level, the research aims to inspect or, at least, to give some impressions of the essential conditions, i.e., identification of phenomenon, empirical evidence, and the justifying underlying tradition, under which it became possible in the tradition-based science of the `medieval period to permit a not-already-defined and tradition-opposed phenomenon to be posed and justified. (shrink)

The book is an introductory exposition of the development of the physical and astronomical notions of the universe. It covers the period from Greek antiquity to the Copernican revolution and the Renaissance, half of the text being devoted to medieval science within both the Aristotelian and the Archimedean traditions. The book is intended for a general audience interested in intellectual and scientific developments, but should also be useful as a guide to further studies. Thus it has an extensive bibliography classifying (...) much of the secondary literature on the subject, and also a sixty page 'dictionary' of all the scientists and philosophers mentioned in the text. This contains references to printed editions of the sources and to a selection of books and periodicals. (shrink)

Critical edition of the earliest known astrological autobiography. The present book reveals the riches of the earliest known astrological autobiography, authored by Henry Bate of Mechelen (1246-after 1310). Exploiting all resources of contemporary astrological science, Bate conducts in his Nativitas a profound self-analysis, revealing the peculiarities of his character and personality at a crucial moment of his life (1280). The result is an extraordinarily detailed and penetrating attempt to decode the fate of one's own life and its idiosyncrasies. The Astrological (...) Autobiography of a Medieval Philosopher offers the first critical edition of Bate's Nativitas. An extensive introduction presents Bate's life and work and sheds new light on the reception and use of Greek, Latin, Arabic, and Hebrew texts among scholars in Paris at the end of the 13th century. The book thus provides a major new resource for scholars working on medieval science, autobiography, and notions of personhood and individuality. (shrink)

Discusses songs by the troubadours, trouvères, and Guillaume de Machaut, performed live and on the page, in the context of antique, late antique, and medieval thought and poetic practice and in the light of later opera. Topics include cosmology, education, astronomy, breath, beasts, monsters, hybridity, imagination, life, and death.

Levi ben Gerson was a medieval astronomer who responded in an unusual way to the Ptolemaic tradition. He significantly modified Ptolemy’s lunar and planetary theories, in part by appealing to physical reasoning. Moreover, he depended on his own observations, with instruments he invented, rather than on observations he found in literary sources. As a result of his close attention to the variation in apparent planetary sizes, a subject entirely absent from the Almagest, he discovered a new phenomenon of Mars and (...) noticed a serious flaw in Ptolemy’s treatment of the Moon. (shrink)

Alchemical images take many forms, from descriptive illustrations of apparatus to complex allegorical schemes that link practical operations to larger cosmological structures. I argue that George Ripley’s famous Compound of Alchemy (1471) was intended to be read in light of a circular figure appended to the work: the Wheel. In the concentric circles of his “lower Astronomy,” Ripley provided a terrestrial analogue for the planetary spheres: encoding his alchemical ingredients as planets that orbited the earthly elements at the core of (...) the work. The figure alludes to a variety of late medieval alchemical doctrines. Yet the complexity of Ripley’s scheme sometimes frustrated later readers, whose struggles to decode and transcribe the figure left their mark in print and manuscript. (shrink)

This article examines an unstudied set of astronomical tables for the meridian of Cambridge, also known as the Opus secundum, which the English theologian and astronomer John Holbroke, Master of Peterhouse, composed in 1433. These tables stand out from other late medieval adaptations of the Alfonsine Tables in using a different set of parameters for planetary mean motions, which Holbroke can be shown to have derived from a tropical year of $$365\frac{1}{4} - \frac{1}{132}$$ 36514-1132 or $$365.\overline{24}$$ 365.24¯ days. Implicit in (...) this year length was a 33-year cycle of repeating solar longitudes and equinox times, which has left traces in other astronomical tables from fifteenth-century England. An analysis of the manuscript evidence suggests that Holbroke owed his value for the “true length of the year” to a certain Richard Monke, capellanus de Anglia, who employed this parameter and the corresponding 33-year cycle in an attempt to construct a perfect and perpetual solar calendar, leading to his Kalendarium verum anni mundi of 1434. (shrink)

This article explores the changing relationships between geometric and arithmetic ideas in medieval Europe mathematics, as reflected via the propositions of Book II of Euclid’s Elements. Of particular interest is the way in which some medieval treatises organically incorporated into the body of arithmetic results that were formulated in Book II and originally conceived in a purely geometric context. Eventually, in the Campanus version of the Elements these results were reincorporated into the arithmetic books of the Euclidean treatise. Thus, while (...) most of the Latin versions of the Elements had duly preserved the purely geometric spirit of Euclid’s original, the specific text that played the most prominent role in the initial passage of the Elements from manuscript to print—i.e., Campanus’ version—followed a different approach. On the one hand, Book II itself continued to appear there as a purely geometric text. On the other hand, the first ten results of Book II could now be seen also as possiblytranslatable into arithmetic, and in many cases even as inseparably associated with their arithmetic representation. (shrink)

This book explores the changing perspective of astrology from the Middle Ages to the Early Modern Era. It introduces a framework for understanding both its former centrality and its later removal from legitimate knowledge and practice. The discussion reconstructs the changing roles of astrology in Western science, theology, and culture from 1250 to 1500. The author considers both the how and the why. He analyzes and integrates a broad range of sources. This analysis shows that the history of astrology—in particular, (...) the story of the protracted criticism and ultimate removal of astrology from the realm of legitimate knowledge and practice—is crucial for fully understanding the transition from premodern Aristotelian-Ptolemaic natural philosophy to modern Newtonian science. This removal, the author argues, was neither obvious nor unproblematic. Astrology was not some sort of magical nebulous hodge-podge of beliefs. Rather, astrology emerged in the 13th century as a richly mathematical system that served to integrate astronomy and natural philosophy, precisely the aim of the “New Science” of the 17th century. As such, it becomes a fundamentally important historical question to determine why this promising astrological synthesis was rejected in favor of a rather different mathematical natural philosophy—and one with a very different causal structure than Aristotle's. (shrink)

This book focuses on issues in astronomy, cosmology, physics, matter theory, philosophy, and theology vital to the “Copernican Revolution.” It describes efforts among individuals advocating different world views to fit new ideas compatibly into broad perspectives reflecting four traditional patterns of interpretation: teleological, mechanical, occultist, and mathematico-descriptive.

This essay focuses on a neglected and important text, the Nāgarasarvasva of Padmaśrī, as an index to the changing contours of kāmaśāstra in the early second millennium (1000-1500) CE. Focusing on a number of themes which linked Padmaśrī’s work with contemporary treatises, the essay argues that kāmaśāstra incorporated several new conceptions of the body and related para-technologies as well as elements of material and aesthetic culture which had become prominent in the cosmopolitan, courtly milieu. Rather than seeing this development as (...) an attenuation of the earlier science as constituted by Vātsyāyana’s Kāmasūtra, it is possible to see that kāmaśāstra actually developed closer relations with fields of knowledge that had long developed alongside it. (shrink)

ABSTRACT This article is devoted to a thirteenth-century Latin text on how to construct, set up, and use a version of the so-called armillary instrument (instrumentum armillarum), which was first described in Ptolemy’s Almagest as a tool for measuring ecliptic coordinates. Written in 1264 by Guillaume des Moustiers, bishop of Laon, this hitherto unstudied Tractatus super armillas survives in a single manuscript, where it is accompanied by a copious set of glosses. The text and its glosses jointly offer an unusually (...) detailed account of the instrument’s material aspects and methods of assembly. In addition, they reflect a keen awareness of the potential sources of error that may arise in the context of astronomical observation, while making suggestions on how these errors may be minimized or avoided. The Tractatus super armillas accordingly is a valuable source on the observational side of medieval European astronomy, which has often been minimized in modern historical accounts. (shrink)

La presente versión del tratado De Bono Habitu Liber o El libro sobre la buena condición, de Galeno de Pérgamo, se presenta al lector de habla hispana como un acercamiento a la prolífca obra flosófca de quien fuera reconocido en su época como un notable médico anatomista y físico. Los argumentos expuestos por el autor acerca de la ‘buena condición’ dan cuenta de la infuencia retórica de Platón y Aristóteles, al mismo tiempo, de las enseñanzas médicas de Hipócrates. Junto al (...) texto original y la traducción al español, se ofrece una versión en latín empleada en el proceso de traducción como un apoyo para resolver las difcultades textuales y léxicas que presentaba el texto griego, al permitir confrontar una recepción medieval del tratado. (shrink)

The Epistles of the Brethren of Purity' is an encyclopedic compendium, probably composed in tenth-century Iraq by a society of adepts with Platonic, Pythagorean, and Shi'i tendencies. Its 52 sections ('epistles') are divided into four parts (Mathematics, Natural Philosophy, Sciences of the Soul and Intellect, and Theology). The current volume provides an edition, translation, and notes to Epistle 3 ('On Astronomia'), which forms one of the 14 sections on Mathematics. The content is a mixture of elementary astronomy and astrology, but (...) it is not a beginner's textbook. Rather, the purpose is to use examples from those disciplines to provide spiritual, moral, and soteriological guidance. Thus the Epistle uses the argument from design to show the necessity for a Creator who made the harmonious universe; this wondrous design is then employed by the authors as a model, providing humans with a paradigm for proper ethical, political, and even economic conduct; and the study of Astronomia helps the soul achieve ultimate happiness as it seeks to throw off the shackles of this mundane world and oppressive body in favour of the purity of the celestial realm.0Although by no means typical of Islamic astronomical literature, Epistle 3 of the Brethren of Purity gives a window into a fascinating and intriguing group operating during the early period of Islam who sought to continue and adopt one of the esoteric strands of Hellenistic philosophy within an Islamic context, meshing astronomy, astrology, Platonic-Pythagorean philosophy, Quranic and Biblical quotations, and anecdotes from the lives of the Abrahamic prophets. (shrink)

In astronomy Abraham Zacut is best known for the Latin version of his tables, the Almanach Perpetuum, first published in 1496, based on the original Hebrew version that he composed in 1478. These tables for Salamanca, Spain, were analyzed by the authors of this paper in 2000. We now present Zacut’s tables preserved in Latin and Hebrew manuscripts that have not been studied previously, with a concordance of his tables in different sources. Based on a hitherto unnoticed text in a (...) Latin manuscript, we argue that Zacut is the author of the Tabule verificate which, in our publication of 2000, we took to be anonymous. We also discuss in detail Zacut’s tables for epoch 1513 for Jerusalem that are arranged for the Hebrew calendar, rather than the Julian calendar that he used elsewhere. We then consider a number of fragmentary texts that were found in the Cairo Geniza, now scattered in various European and American libraries. The new evidence is consistent with our earlier finding that Zacut depended both on the medieval Hebrew tradition in astronomy and on the Parisian Alfonsine Tables. (shrink)

For forty years, beginning with the publication of the first modern English translation of the Dialogue Concerning the Two Chief World Systems, Stillman Drake was the most original and productive scholar of Galileo's scientific work of our age. During that time, he published sixteen books on Galileo, including translations of almost all the major writings, and Galileo at Work, the most comprehensive study of Galileo's life and works ever written. His collection Discoveries and Opinions on Galileohas remained in print since (...) its appearance in 1957 and has become the most widely read of all books on Galileo. In addition to his books, Drake published about 130 papers, of which nearly 100 are on Galileo and the rest on related aspects of the history and philosophy of science. This three-volume collection includes eighty of those papers. Drake's papers are an essential supplement to his translations and other books because it was in his papers that he wrote his most detailed technical studies of Galileo's scientific work. There is hardly a subject in Galileo's science that is not considered. Perhaps the most important is the series on mechanics and motion, in which Drake analysed Galileo's manuscript notes recording the experiments by which he discovered and confirmed the law of the acceleration of falling bodies. There are also papers on the notes in which Galileo recorded his discovery of Jupiter's satellites and on other aspects of Galileo's astronomy, including his defence of the Copernican theory. Other papers consider Galileo's life and scientific work in general, exploring what Drake calls the 'scientific personality' of Galileo along with his scientific method and philosophy of science. In addition to the papers on Galileo, there are a number of papers on medieval and early modern science, principally on mechanics, and on the philosophers A.B. Johnson and J.B. Stallo, both of whom influenced Drake's own philosophy of science. (shrink)

The medieval computus was intended primarily for literate and numerate ecclesiastical users; reading the Latin computus required a good knowledge of technical Latin, while understanding its calculations presupposed some formal education in arithmetic and astronomy. By the mid-thirteenth century, users would have included a small group of literate and numerate laymen; by the mid-fifteenth century, users would have included the less educated and even semiliterate, as a consequence of a more extensive range of computus material made available for the purpose (...) in the vernacular. (shrink)

Drawing on a half century of scholarship, of Polish studies of Copernicus and Cracow University, and of Copernicus's sources, this book offers a comprehensive re-evaluation of Copernicus's achievement, and explains his commitment to the ...

In this book, 11 leading scholars contribute to the understanding of the scientific and philosophical works of Moses Maimonides (1135-1204), the most luminous Jewish intellectual since Talmudic times. Deeply learned in mathematics, astronomy, astrology (which he strongly rejected), logic, philosophy, psychology, linguistics, and jurisprudence, and himself a practising physician, Maimonides flourished within the high Arabic culture of the 12th century, where he had momentous influence upon subsequent Jewish beliefs and behavior, upon ethical demands, and upon ritual traditions. For him, mastery (...) of the sciences was indispensable in the process of religious fulfilment. (shrink)

Le 'Timée' est incontestablement le dialogue de Platon le plus cité dans l'Antiquité, le plu lu et le plus commenté. Tenu pour la "bible" des médio-platoniciens, il a joui d'une faveur extraordinaire, comme en témoignent les multiples commentaires qui ont vu le jour dans la pensée grecque, de Crantor à Proclus. Cette abondance d'études s'explique par deux raisons principales, intimement liées. D'un côté, le 'Timée', récit qui traite de la "création" du monde et de celle de l'homme, est un texte (...) difficile, exemple paradigmatique de l'obscurité que les auteurs anciens attribuaient à Platon, de l'autre, en proposant un modèle d'univers physique, il se présente comme un traité de cosmologie, le premier en fait à nous être parvenu, et offre une véritable somme des connaissances humaines où interviennent également la psychologie et la métaphysique, une encyclopédie scientifique dont la brièveté même exigeait d'emblée des éclaircissements et des explications préliminaires pour qui ne possédait pas une solide culture scientifique. Ce qui ressortit à la cosmogonie et à la psychogonie est en effet associé aux quatre sciences "mathématiques" (arithmétique, géométrie, musique, astronomie), et pour ce qui se rapporte à l'homme et à l'anthropologie le texte platonicien fait intervenir en outre des sciences comme l'optique ou la médecine. On peut donc comprendre que le caractère "mythique" de l'énoncé et sa dimension scientifique aient constitué autant d'éléments de nature à désarçonner un lecteur non averti. L'importance de cet écrit explique par ailleurs qu'on en trouve de très nombreuses traces dans le monde latin, notamment médiéval, où les traductions fragmentaires et les commentaires sur le 'Timée' servent, entre autres, à l'exégèse biblique. De surcroît, à la Renaissance l'Occident retrouve l'héritage hellène, et les humanistes ont à leur disposition les traditions grecque et latine du "dialogue. (shrink)

Ibn al-Zarqālluh (al-Andalus, d. 1100) introduced a new inequality in the longitudinal motion of the Moon into Ptolemy’s lunar model with the amplitude of 24′, which periodically changes in terms of a sine function with the distance in longitude between the mean Moon and the solar apogee as the variable. It can be shown that the discovery had its roots in his examination of the discrepancies between the times of the lunar eclipses he obtained from the data of his eclipse (...) observations over a 37-year period in the latter part of the eleventh century and the predictions made on the basis of the lunar theories in the Mumta $$\textit{\d{h}}$$ an zīj (Baghdad, ca. 830) and al-Battānī’s zīj (Raqqa, d. 929), which were available to him at the time. What Ibn al-Zarqālluh found is, in fact, a special case of the annual equation of the Moon, which is applicable in the oppositions and, thus, in the lunar eclipses. The inequality was discovered independently by Tycho Brahe (d. 1601) and Johannes Kepler (d. 1630). As Ibn Yūnus (d. 1009) reports in his $$\textit{\d{H}}$$ ākimī zīj, Ibn al-Zarqālluh’s medieval Middle Eastern predecessors, the Persian astronomers Māhānī (d. ca. 880) and Nayrīzī (d. 922) as well as ‘Alī b. Amājūr (fl. ca. 920), were already acquainted with the problem of the eclipse timing errors, but it had remained unresolved until Ibn Yūnus provided a provisional, and incorrect, solution by reducing the size of the lunar epicycle. As we argue, the diverse ways to tackle the same problem stem from two different methodologies in astronomical reasoning in the traditions developed separately in the Eastern and Western regions of the medieval Islamic domain. (shrink)

Une part substantielle de la réflexion philosophique est née et s'est développée aux confins de la science. Depuis l'aube de la philosophie, on ne peut faire l'économie des mathématiques, de l'astronomie, de l'optique... si l'on veut comprendre les voies empruntées par les philosophes et les modèles qu'ils ont élaborés. Cette étude examine quelques-uns de ces liens jusqu'à l'âge moderne.

A discussion of European understanding of the physical world from the 9th century to the 15th, ranging from astronomy to zoology and refuting the more recent ...

Duhem's 1908 essay questions the relation between physical theory and metaphysics and, more specifically, between astronomy and physics–an issue still of importance today. He critiques the answers given by Greek thought, Arabic science, medieval Christian scholasticism, and, finally, the astronomers of the Renaissance.

In this article, we report the discovery of a new type of astronomical almanac by Joseph Ibn Waqār (Córdoba, fourteenth century) that begins at second station for each of the planets and may have been intended to serve as a template for planetary positions beginning at any dated second station. For background, we discuss the Ptolemaic tradition of treating stations and retrograde motions as well as two tables in Arabic zijes for the anomalistic cycles of the planets in which the (...) planets stay at first and second stations for a period of time (in contrast to the Ptolemaic tradition). Finally, we consider some medieval astrological texts where stations or retrograde motions are invoked. (shrink)

This is the first investigation of one of the main interests of astronomy in Islamic civilization, namely, timekeeping by the sun and stars and the regulation of the astronomically-defined times of Muslim prayer. The study is based on over 500 medieval astronomical manuscripts first identified by the author, now preserved in libraries all over the world and originally from the entire Islamic world from the Maghrib to Central Asia and the Yemen.