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Re: reason for "s = distance traveled"



Hi all-
In response to:
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At 19:42 8/24/97 EDT, Tom Wayburn wrote:
...
I would have wished to consult an English translation of
"Principia..." where I fancy Newton may possibly have used
the symbol; but I have no copy.

It would be particularly pleasing if he used s as a reasonable
initial letter for a term in his written language; something like
s - secta (path, method etc.) but this is wild speculation.

....
Leibnitz and Gauss are candidates for first use of
lower-case ess for arclength.
... The style of Newton is not entirely accessible, is it?

Tom

It is not, as Chandrasekhar found to his cost in the final
year of his life on the publication of his review of Newton's
major works.
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I think that Newton can safely be eliminated as the source.
The Principia was written for people who understood geometry, so
all curves are identified by their end points (as in, "the curve AB").
Sommerfeld (Lectures, Vol. I) does not seem to use it, although
he introduces an "s" as a complex parameter in discussing Foucalt's
pendulum (Sec. 31).
I don't find Einstein using ds prior to his 1911 paper. Minkowski,
in his 1908 lecture used c*dtau where tau stands for time interval.
It would have been natural to replace c*dtau by ds, s standing for space.
That's the best that I can do from home, I think. The relativity
papers are in "The Principles of Relativity", by Einstein and Others.
Regards,
Jack