ABSTRACT
Cartesian mechanical philosophy brought about changed conditions that were more favourable to a conjunction of probability and mathematics. Nevertheless, practitioners of the magical science based their predictions on precise determinations of successively repeated conjunctions, oppositions and other planetary aspects. Geometry argues that if her hypothesis were adopted, the beauty of the universe and the goodness of the gods would increase, since there would be a mixture of uniform and difform elements. The art of combinations is intimately connected with probability, for without its help the enumeration of equally possible cases cannot be accomplished. The widespread interest in combinatorial problems from the early part of the seventeenth century coincides with the revival of materialistic atomism and the appearance of the mechanical philosophy of Rene Descartes. Starting with mechanics, therefore, the natural sciences, along with their methods of probable inference depending on fair sampling, gain in prominence.
