Tuesday, 11 October 2011

Il teorema degli zeri - Bernard Bolzano (1817)


Purely Analytic
Proof of the Theorem
that
between any two Values, which give Results of Opposite Sign,
there lies at least one real Root of the Equation
by
Bernard Bolzano
Priest, Doctor of Philosophy, Professor of Theology and Ordinary Member of the Royal Society of Sciences at Prague
For the Proceedings of the Royal Society of Sciences
Prague, 1817 Printed by Gottlieb Haase



Theorem. If two functions of x, fx and φx, vary according to the law of continuity either for all values of x or for all those lying between α and β, and furthermore if fα < φα and fβ > φβ, then there is always a certain value of x between α and β for which fx = φx.

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