Points and Atoms, between kalam, falsafa and geometry

While Aristotle considered, in De caelo iii, that geometry could only support continuism (i.e. the doctrine of the infinite divisibility of magnitudes), in the 9^th century each of the two camps relies on geometry. The upholders of the continuum appealed to the infinite divisibility implied by the incommensurability of the side and the diameter of the square, while the supporters of infinitesimal thresholds (beyond which matter could no longer be divided) also looked to Euclid for arguments in their favour. Will shall try to explain this new situation by taking new texts into account.

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