Criticism of trepidation models and advocacy of uniform precession in medieval Latin astronomy

Abstract

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 (1513), who demonstrated the theory's redundancy with a penetrating analysis of the role of observational error in Ptolemy's Almagest.

Trepidation spheres: Variant representations of the eighth sphere and the debate about the movement of the apogees and the fixed stars in Alfonsine astronomy

“…23 It has been pointed out by Chabás & Goldstein (2012, p. 44) that several medieval astronomers were critical of trepidation and continued to use uniform precession, for example, al-Batt anī and Levi ben Gerson. See also Dobrzycki (1965Dobrzycki ( /2010; Nothaft (2017); Wegener (1905, pp. 181-185).…”

Oronce Fine and Sacrobosco: From the Edition of the Tractatus de sphaera (1516) to the Cosmographia (1532)

“…216 As indicated above, the two chapters in which Fine deviated the most from the cosmological model transmitted by Sacrobosco and by later geocentric cosmological accounts are chapters 3 and 5 of Book I, where he respectively dealt with the number of celestial spheres 217 and with the mode of transmission of the diurnal motion (and of motion in general) from the primum mobile (or the first moved sphere) to the inferior spheres. 218 In these two chapters, Fine rejected the systems that admit the existence of one or several mobile spheres deprived of stars above the sphere of the fixed stars on account of their incompatibility with the principles of natural philosophy established by Aristotle (Johnson 1946;Heninger 1977b, 38-39;Pantin 1995, 442;Cosgrove 2007;Nothaft 2017). Such cosmological models, which were by far the most popular in the Middle Ages and in the Renaissance, included therefore not only the representation of the cosmos adopted by Sacrobosco, which postulated the existence of nine concentric contiguous orbs or spheres (with one starless sphere above the Firmament as the primum mobile), but also the models that admitted ten spheres, as illustrated, for example, by the representation of the universe provided in Apian's Liber cosmographicus (Chap.…”

“…Indeed, while the fixed stars were already seen to revolve (along with the planets) from east to west in twenty-four hours, and from west to east uniformly by one degree every century according to the precession of the equinoxes, the equinoxes (the first degrees of Aries and of Libra) were also observed to move back and forth in small circles over a period of seven thousand years, resulting in a complete revolution of the eighth sphere in forty-nine thousand years. This motion of oscillation of the equinoxes, which is described in a work entitled De motu octavae sphaerae and regarded as a Latin translation of a treatise by the Arab mathematician Thâbit ibn Qurra (Thâbit ibn Qurra 1960; Neugebauer and Thâbit ibn Qurra 1962), was commonly called by the Latin astronomers trepidation (trepidatio), or motion of access and recess (accessus et recessus) (Neugebauer 1975, 298, 598, 631-34;Nothaft 2017). While trepidation was initially admitted as a correction of the motion of precession of the equinoxes, it came to be considered in the Latin world as a motion independent of the latter, requiring it to be accounted for by a separate sphere, distinct from the ninth, to which the precession of the equinoxes had been previously attributed (Dobrzycki 2010(Dobrzycki [1965Neugebauer 1975, 633;Grant 1994, 315-16;Nothaft 2017).…”

“…This motion of oscillation of the equinoxes, which is described in a work entitled De motu octavae sphaerae and regarded as a Latin translation of a treatise by the Arab mathematician Thâbit ibn Qurra (Thâbit ibn Qurra 1960; Neugebauer and Thâbit ibn Qurra 1962), was commonly called by the Latin astronomers trepidation (trepidatio), or motion of access and recess (accessus et recessus) (Neugebauer 1975, 298, 598, 631-34;Nothaft 2017). While trepidation was initially admitted as a correction of the motion of precession of the equinoxes, it came to be considered in the Latin world as a motion independent of the latter, requiring it to be accounted for by a separate sphere, distinct from the ninth, to which the precession of the equinoxes had been previously attributed (Dobrzycki 2010(Dobrzycki [1965Neugebauer 1975, 633;Grant 1994, 315-16;Nothaft 2017). 221 Although the addition of a ninth and a tenth sphere, just as the admission of partial orbs, stemmed from the will on the part of astronomers to account for the apparent motions of the stars through a system that would conform to the principles of Aristotelian natural philosophy (Morelon 1999) (at least to some of them), 222 certain reservations were raised with regards to the ontological status of these spheres, as the fact that they did not carry any star made it difficult to prove their physical reality, just as it was to prove the existence of epicycles and of the eccentric spheres.…”

The Alfonsine Tables mentioned in 1304

“…One possibility would be Paris, where the newly founded College of Sorbonne (1257) had quickly established itself as a leading centre for astronomical studies in Europe, with scholars such as Peter of Limoges, Giles of Lessines, William of Saint-Cloud, Franco of Poland, Peter of Dacia, Peter of Saint-Omer, John of Sicily and Peter of Abano, among others, and it is noticeable that the value of the precession was a recurrent subject of enquiry among them. 7 It is also documented that new Alfonsine material travelled from Toledo to Paris at an early date. This is shown by Peter of Limoges (fl.…”