The Concept and Practice of Fitting in Medieval Islamic Astronomy: The Data and Models for the Sun and Trepidation

This study investigates the concept of fitting as a fundamental epistemic operation in Ptolemaic astronomy, following the methodological precept in Almagest IX.2, and its medieval Islamic reception, where newly observed empirical anomalies necessitated the construction of novel models through the adaptation of established hypotheses and model components. Situating Ptolemy’s fitting and typology of errors at the core of medieval astronomy’s evolution, the paper analyzes historical procedures for reconciling theoretical constructs with discrepant data. Central to this analysis are the models devised by Abū Jaʿfar al-Khāzin ( ca. 900– ca. 971) and Ibn al-Zarqālluh (d. 1100) to account for variations in precession, the obliquity of the ecliptic, and solar eccentricity. We introduce a core portion of al-Khāzin’s original account of his non-Ptolemaic physical ( hayʾa ) model and clarify its historiographical misinterpretation. We further reconstruct the rationale behind Ibn al-Zarqālluh’s fitting of his kinematic models to historical empirical data, detailing the necessary incorporation of a pivotal value for the solar eccentricity from pre-Islamic Persian astronomy.