 Solution

A useful distinction is between preserving an inherited text, correcting a particular prediction, and changing the standards by which an explanation is judged. Work in the medieval Islamic world did all three. It did not form one homogeneous programme, and its significance should not be measured only by how nearly it anticipated later European theories. Mathematical astronomy provides a particularly clear example of critical development within, rather than simple abandonment of, an inherited physical framework.

Aristotle's account of celestial motion privileged uniform circular movements, whereas the computational models associated with Ptolemy used constructions whose physical interpretation was contested. An astronomical device could reproduce observed positions yet leave a question about whether the corresponding arrangement of celestial bodies could actually execute those motions. The dispute therefore concerned the relation between mathematical prediction and physical explanation, not merely improved arithmetic.

The Tusi couple, associated with Nasir al-Din al-Tusi, demonstrates the resources of this tradition. In modern Cartesian notation, combine two equal-radius uniform circular motions with opposite angular rates:Their resultant is a straight oscillation. Thus circular component motions need not produce a circular resultant. The plane construction offers a way of representing a required oscillatory displacement using circular components; it does not itself establish a new force law or the actual constitution of the heavens. The distinction between plane and spherical versions also matters: one should not transfer the planar identity to a sphere without a separate geometric argument.^[ref]

Ibn al-Shatir went beyond transmitting a computational recipe by producing revised planetary models. The surviving treatise and its manuscript differences are material evidence of active theoretical construction, not a fixed body of knowledge passing unchanged through translators. The critical edition of his work also distinguishes the extant exposition from a lost work to which it refers for observations and demonstrations. That limits what can responsibly be claimed about the surviving text: a modern mathematical reconstruction is not a newly discovered original experimental record.^[ref]

These cases show enrichment and modification through new geometry and models, and dispute over the adequacy of inherited physical assumptions. They do not justify labeling every participant anti-Aristotelian. A demand for physically admissible uniform component motions could itself be motivated by Aristotelian commitments. Nor does a geometrical resemblance between a model and a later one prove direct transmission or establish that their authors shared the same cosmology. The historical achievement is more precise: inherited authority supplied resources and problems, while astronomers developed new constructions and criticized the relation between prediction and physical explanation. That is a substantive transformation of a research tradition, even where geocentric assumptions remained.