ABSTRACT
Planetary theory in the ninth century? How was this achieved? It occurred when scholars at or before the mid-ninth century found in studying the astronomical book of Martianus Capella (fl c. 475) that certain texts needed clarification, which they provided through diagrams. In one notable case clarification involved investigation and comparison of other authorities on the topic. Here diagrams were invented to question and compare more sharply than the texts themselves allowed. This process is correctly called model-building, an essentia] part of theorizing. Carolingian scholars (under the dynasty that included Charlemagne (768814)) not only studied and taught the four mathematical subjects of the quadrivium. In the case of astronomy, at least, they questioned and suggested theoretical complexities not found in the texts. Whether or not they mathematized these views in the form of equations is totally irrelevant. The resultant theory was used or referred to in manuscripts over the rest of the Middle Ages.
