Newton's argument for Proposition 1 of the \textit{Principia}
Proposition 1 of \textit{Principia} says that orbital motions have both the fixed plane property (FPP) and the area property (AP), and Newton's proof is based upon the impulse assumption (IA): an orbital motion can be represented as a limit of polygonal impulse motions. Newton takes IA for granted and it is the aim of this paper to consider the validity of that assumption. More precisely, the author considers two possible meanings of an ``orbital'' motion and the validity of Newton's proof in each case. If ``orbital'' means ``centripetal'' (a traditional view), then there is a gap in the argument: only a nontrivial analysis, using FPP, shows IA, and so Newton's argument is ultimately valid for AP but not for FPP. And if ``orbital'' means ``impulse limit'' (IA becomes a definition), then one can deduce both AP and FPP, but there appears another crucial question: ``How plentiful are these impulse motions? Are there enough of them to sustain Newton's subsequent study?'' The paper is completed by two sophisticated proofs which ``Newton could have given'' of both AP and FPP for orbital motions in the traditional sense.
scientific article; zbMATH DE number 1931212