Ideal Construction and Genesis of the Mathematical Science

The birth of a new cognitive strategy and a corresponding world view during the Scientific Revolution of the XVII century is reviewed in the article. The basis of this strategy is the ideal (theoretic) construction implemented by means of mathematics. The latter is viewed as an alternative to qualitative ideal construction peculiar to Aristotle and late Middle Ages. Mathematized ideal constructions create a special means of world apprehension, grounded in developing the initial theoretic scheme. Within its framework the connection of elementary ideal objects accessible for quantative description is defined.