Sir Isaac Newton's philosophi Naturalis Principia Mathematica'(the
Principia) contains a prose-style mixture of geometric and limit
reasoning that has often been viewed as logically vague. In A
Combination of Geometry Theorem Proving and Nonstandard Analysis,
Jacques Fleuriot presents a formalization of Lemmas and
Propositions from the Principia using a combination of methods from
geometry and nonstandard analysis. The mechanization of the
procedures, which respects much of Newton's original reasoning, is
developed within the theorem prover Isabelle. The application of
this framework to the mechanization of elementary real analysis
using nonstandard techniques is also discussed.
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