![]() ![]() "Ī striking feature of Newton’s thought is the very broad reach of his empiricism, potentially extending even to immaterial substances, including God, minds, and should one exist, a non-perceiving immaterial medium. The consequences of this law when applied specifically to elliptical, hyperbolic and parabolic orbits are remarkable and, lead directly to proof of the inverse square law of gravity. The general applicability of Kepler's second law is first demonstrated as set out in the Principia for a body subject to any central force. It also shows that it is more likely than not that Newton did actually arrive at his results using only geometrical constructs. The derivation uses the same traditional geometrical approach that Newton used, however, the line of reasoning is considered to be more straight forward than that presented by Newton and, it is believed that it may represent the way he actually arrived at this monumental discovery. This paper presents a modified version of Newton's proof of the inverse square law of gravity, as presented in Proposition XI, Problem VI of his Philosophiae Naturalis Principia Mathematica (now almost universally known as the Principia). ![]() In addition, it has been argued, and Newton tended to encourage the idea, that he must have used The Calculus to have arrived at his results, and only then worked out his geometric proofs. For approximately three hundred years scholars have painstakingly ploughed through the original proofs and have almost unanimously found them difficult modern scholars are no exception. "The view has long been held by historians of science, that Sir Isaac Newton's original derivation of the inverse square law of gravity, whilst certainly not lacking brevity, most definitely provides little indication of the original thought processes that led him to the final results.
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