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)

L'Abrégé de l'Almagested'Averroès, conservé uniquement en traduction hébraïque, reste inédit et peu étudié. Cet article a pour but de le faire connaître. Après avoir retracé l'histoire de l'Abrégé: date de rédaction, traduction, transmission de cette traduction, diffusion et audience, nous procédons à une première étude du texte: aperçu commenté du contenu, identification des sources et examen de leur exploitation critique par Averroès. Nous donnons également une traduction d'extraits significatifs du Prologue de l'Abrégé, avec une brève analyse. Avec l'Abrégé, nous disposons (...) d'un témoignage direct et relativement précoce, dû à l'un des plus importants artisans du mouvement de contestation et de réforme de l'astronomie ptoléméenne, animé au XIIe siécle par des penseurs andalous, philosophes aristotéliciens pour la plupart. (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)

In what way does the construction of three-dimensional spherical models in the early modern period reflect the search for an appropriate representation of subtle, slow changes perceived in the firmament of the fixed stars? The present paper analyses some of the preserved models and assesses the potential they held to stimulate contemporary thinking on this question, termed the “motion of the eighth sphere.” The spheres discussed here reveal different ways of conceiving and visualizing stellar precession, which was more commonly expressed (...) in tabular form, such as the Alfonsine tables, or by means of theoretical texts, such as Peurbach’s Theoricae novae planetarum. One of the spheres unexpectedly turns out to be the only known material representation of Johannes Werner’s alternative theory of trepidation. Although our knowledge of the context in which these spheres were produced is limited, their material characteristics point to their distinct origins. A focus on the rare and understudied species of “trepidation spheres” leads to questions not addressed in studies drawing only on written sources. It brings additional actors into the spotlight, in particular instrument-makers. Moreover, the variety of constructions found in the group of surviving spheres indicates that the available traditional sources allowed for variant interpretations. Besides texts and diagrams, the trepidation spheres are historical tools of thought that can literally be touched. While further investigation is needed, this paper looks at the spheres’ potential role for practitioners in exploring the geometric implications of trepidation in Alfonsine astronomy from the second half of the 15th century onwards. (shrink)

In this paper, we analyze the astronomical tables in al-Zīj al-Muqtabis by Ibn al-Kammād (early twelfth century, Córdoba), based on the Latin and Hebrew versions of the lost Arabic original, each of which is extant in a unique manuscript. We present excerpts of many tables and pay careful attention to their structure and underlying parameters. The main focus, however, is on the impact al-Muqtabis had on the astronomy that developed in the Iberian Peninsula and the Maghrib and, more generally, on (...) the transmission and diffusion of Indian astronomy in the West after the arrival of al-Khwārizmī’s astronomical tables in al-Andalus (Muslim Spain) in the tenth century. This tradition of Indian origin competed with the Greek tradition represented by al-Battānī’s astronomical tables and was much more alive in the Iberian Peninsula and the Maghrib than previously thought. From Spain, the Indian tradition entered mainstream European astronomy, where we find echoes of it in all versions of the Alfonsine Tables, both in manuscript and in the printed editions (beginning in 1483), as well as in Copernicus’s De Revolutionibus, published in 1543. (shrink)