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)

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 surveys measurements of celestial (chiefly solar) altitudes documented from twelfth- and thirteenth-century Latin Europe. It consists of four main parts providing (i) an overview of the instruments available for altitude measurements and described in contemporary sources, viz. astrolabes, quadrants, shadow sticks, and the torquetum; (ii) a survey of the role played by altitude measurements in the determination of geographic latitude, which takes into account more than 70 preserved estimates; (iii) case studies of four sets of measured solar altitudes (...) in twelfth-century Latin sources; (iv) an in-depth discussion of the evidence relating to altitude measurements performed in Paris in the period 1281–1290. The findings from the last part indicate that by the end of the thirteenth century Parisian astronomer had developed rigorous standards of observational practice in which altitudes were typically measured to a precision of minutes of arc and with a level of accuracy higher than ± 0;5°, and sometimes exceeding ± 0;1°. (shrink)