Visiting Newton's Atelier before the Principia, 1679-1684

TL;DR

This paper reconstructs Newton's early development of fundamental concepts leading to the Principia by analyzing historical letters and diagrams, revealing how Newton formulated key propositions and developed a rapid method for orbital calculations.

Contribution

It presents a novel reconstruction of Newton's thought process before the Principia using historical correspondence and diagram analysis, offering new insights into his development of orbital methods.

Findings

Reconstruction of Newton's early ideas based on letters and diagrams

Identification of a rapid convergence method for orbital curves

Insights into how Newton formulated key propositions in the Principia

Abstract

The manuscripts that presumably contained Newton's early development of the fundamental concepts that led to his Principia have been lost. A plausible reconstruction of this development is presened based on Newton's exchange of letters with Robert Hooke in 1679, with Edmund Halley in 1686, and on some clues in the diagram associated with Proposition1 in Book1 of the Principia that have been ignored in the past. The graphical method associated with this proposition leads to a rapidly convergent method to obtain orbital curves for central forces, and elucidates how Newton may have have been led to formulate some of his other propositions in the Principia.