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Re: [HM] Origin of the term "indeterminate" in algebra
Posted:
Mar 23, 2004 4:14 AM
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Dear Matt and all the others,
First of all, indeterminates and variables are two different things. One
sees this immediately, if one considers the ring of polynomials and the ring
of polynomial functions over a finite field. The former one is infinite, the
latter one finite.
The word "inderterminatum", plural "indeterminata" occurs in the following
paper by Gauss:
Demonstratio nova altera theorematis omnem functionem algebraicam
rationalem integram unius variabilis in factores reales primi vel
secundi gradus resolvi posse. Commentationes soc. reg. scient.
Gottingensis rec. III, 1816. Collected papers, vol 3, 31-56. Second
reprint of the edition Goettingen 1866. Hildesheim, New York 1981
I did not find the word in Lagrange's big papers of 1770, 1771:
Re/flexions sur la Re/solution alge/brique des e/quations. Nouveaux
Me/moires de l'Acade/mie royale des Sciences et Belles-Lettres de Berlin,
anne/es 1770 et 1771. Oeuvres, vol. 3, 205-421
But the idea is there. Lagrange distinguishes e/quations algebriques and
e/quations nume/riques. The first ones have indeterminates as coefficients
and the second ones numbers. We would call all of them algebraic equations.
The first ones are also called "e/quations lite/rales" in one place.
What about Euler? I don't know.
Heinz Lueneburg
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