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algebraic analysis argument Aristotelian Aristotle atomistic atoms Beeckman body career of Descartes Cartesian chapter circle classical geometrical sciences classical mechanics compass concepts concerning conic sections construction corpuscular corpuscular-mechanical cosmological cubic cubic equations cultural curves deductive demonstration Descartes Discours discovery distance doctrine dreams early seventeenth century emergence equations example explain fact finding two mean force of motion Galileo Gassendi generalisation geometrical optics Hermeticism heuristic hydrostatics manuscript idea inquiry insight instant interpretation intuition Isaac Beeckman Kepler knowledge KoyrS later latus rectum lines mean proportionals mechanical philosophy mechanistic optics Menaechmus Mersenne metaphysics methodological micro-mechanical Milhaud mixed mathematics natural philosophy November objects parabola philosophy of nature physical Popkin posed precisely principles problem procedures Proclus quantity question Regulae relations reveal role rule 4B scientific sixteenth century solved sort speculations speed Stevin structure tendency to motion theological theory tradition truth unity universal mathematics universal method