Help with Newton quote
- From: "DMF" <me@xxxxxxxxxxxxx>
- Date: Tue, 3 Jan 2006 00:44:56 -0800
All,
I am reading "Infinite Ascent: A Short History of Mathematics"
by David Berlinski. In the chapter on Calculus page 47 he is
discussing objections raised against Newton's conception of
instantaneous speed. One objection raised is that the concept
gives rise to the mathematically meaningless term 0/0.
Berlinski writes....
> In a section of the Principia Mathematica titled The Nature
> of the First and Last Ratios, Newton addressed this
> objection. His argument has all the force of his implacable
> genius. If an object in motion has no discernable speed at
> any given time, then "by the same argument," Newton
> observed, "it may be alleged that a body arriving at a certain
> place, and then stopping, has no ultimate velocity; because
> the velocity, before the object comes to the place, is not its
> ultimate velocity; when it has arrived, there is none." This
> Newton remarks, is absurd. And so it is.
I don't see the absurdity... can someone explain or help me to
understand Newton's point?
Regards,
David
.
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