Pat:
I was wrong about squares and cubes being called "powers" of numbers.
The word I was thinking of from Euclid was "apotome," which is really an
irrational remainder after starting to divide two numbers. It occurs in
the context that squares and cubes of irrational numbers are also
irrational, but Euclid only refers to squares and cubes, not exponents
in general. He does use expressions for power (potensis) in other
contexts.
The real study of exponents got going in the mid-16th c with the study
of logarithms. I could not find any use of the terminology of "power"
earlier than that period, although it could certainly have escaped my
cursory look. We have a history of math expert in the building with whom
I'll consult, when our spring break is over. I'll let you all know what
he says.
Regards,
Chuck Blatchley
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