Taking the development of mathematics in western rational tradition as the basic thread and springboard , reviewing the influence of rebound of the view of the nature in greece and religionary reform , combining the characteristics of the " science of quantum " of western mathematics in 17th century , the article not only provides abundant blurry continuum of quantity directly and defends for the " rationality of arithmetic " indirectly but also expatiated that the philosophy of the nature whose characteristics are the quantification of the nature and the mechanization of the universe has a great influence over 17th century ' s " mathematics of arithmetic " , especially over the birth and the development of analytic geometry and calculus 本文以西方理性传统中的数学发展为基本线索和出发点，通过考察文艺复兴以来希腊自然观的复兴和宗教改革的影响，结合十七世纪西方数学明显的“量的科学”的特点，说明以自然的数量化和宇宙的机械化为特征的新的自然哲学，通过直接提供模糊而丰富的“量的连续统”和间接的为“算法合理性”辩护，对十七世纪的“算法数学” ? ?特别是解析几何和微积分的产生和发展的影响。
The article goes along cartesian train of thoughts , clarifies that while the new mathematics whose commissary is calculus is the new byproduct of " retrieving phenomena " in the western traditional logos , the philosophy of the nature after revival of learning which was greatly influenced by the western logos of tradition has already formed a new effective way of " retrieving phenomena " in west logos from the quantification of the prospect of the world to the mathematication of the philosophy of the nature 全文沿着笛卡尔的“思”路，说明深受西方理性传统影响的文艺复兴时期以来的自然哲学，从世界图景的数量化到自然哲学的数学化，形成西方理性“拯救现象”的新的有效方式，而以微积分为代表的新的数学正是西方传统理性以新的方式“拯救现象”的副产品。
And it is nothing other than the new philosophy of the nature whose characteristics are the quantification of substance and the mechanization of the movement that defends the existence and the property of this quantum second , the quantification of substance and the mechanization of the movement which are emphasized by the new philosophy of the nature offers a intuitionistic continuun which takes the extension of the space - time for the birth of calculous 正是以物质的数量化和运动的机械化为特征的新的自然哲学为这种量的存在及性质(特别是拓扑性质)和程序化的算法提供辩护。其次，新的自然哲学所强调的物质的数量化和运动的机械化为微积分的产生提供了以时空广延为模型的直观连续统。
