The medieval notion of contractio in Michael Stifel's Arithmetica integra (1544))

摘要

The notion of "contractio" appears in the Middle Ages in various contexts, in particular in Robert Kilwardby's De ortu scientiarum (ca. 1215-1279), on the question of the subordination of sciences. Kilwardby then takes the example of Book X of Euclid's Elements to show how the classification of irrational lines is subordinated to arithmetic by means of the contraction of numbers into geometric quantities. We shall see that Michael Stifel's interpretation of Book X of Euclid's Elements in his Arithmetica integra (1544) may shed some light on Kilwardby's remarks.