A Pilot Study On The Consistency And Difference Between Newton's Principia And Classic Geometry

This thesis aims to show the difference and consistency between classic geometryand the mathematical foundation in solving the inverse problem in Newton's Principia. Newtonthought the mathematical proposition is synthetical, which was inherited from classic geometry;Newton's method "finite witnesses" was similar to "reduction to absurdity" which was used inclassic geometry. In the other hand, in classic geometry a mathematical object should be eternal,construct and finite, but in Newton's opinion, a variant, unconstructible and infinite object still canbe studied by mathematics. Last, only single-dimension magnitude can be found in classicgeometry, but in Principia , double-dimension magnitude was used, the difference is similar to thedifference between iterated integral and multiple integral.