If the limiting procedure is logically incoherent without the rigorous epsilon-delta foundations unavailable to Newton, the derived ratio v²/r inherits that foundational illegitimacy.

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Epsilon-delta(as used in calculus foundations): A rigorous mathematical method for proving limits work correctly, using two small numbers (epsilon and delta) to show that you can get arbitrarily close to a desired value.
Foundational illegitimacy(as used in philosophy of mathematics): A flaw or invalidity that comes from a weak or broken starting point; if your foundation is shaky, anything built on it is also questionable.
Limiting procedure(as used in calculus and mathematical foundations): A mathematical technique where you get closer and closer to a target value by taking smaller and smaller steps, eventually reaching a precise answer.
Newton: # Newton A Newton is a unit of measurement that describes force—basically, the push or pull needed to move something. It's named after Sir Isaac Newton, an English scientist from the 1600s who discovered the fundamental laws explaining how objects move and how gravity works. You encounter Newtons all the time: for example, the force you apply when pushing a door or the weight of an apple falling from a tree can be measured in Newtons.

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