  Heisenberg's uncertainty principle was originally posed for the limit of the
accuracy of simultaneous measurement of non-commuting observables as stating
that canonically conjugate observables can be measured simultaneously only with
the constraint that the product of their mean errors should be no less than a
limit set by Planck's constant. However, Heisenberg with the subsequent
completion by Kennard has long been credited only with a constraint for state
preparation represented by the product of the standard deviations. Here, we
show that Heisenberg actually proved the constraint for the accuracy of
simultaneous measurement but assuming an obsolete postulate for quantum
mechanics. This assumption, known as the repeatability hypothesis, formulated
explicitly by von Neumann and Schr\"{o}dinger, was broadly accepted until the
1970s, but abandoned in the 1980s, when completely general quantum measurement
theory was established. We also survey the author's recent proposal for a
universally valid reformulation of Heisenberg's uncertainty principle under the
most general assumption on quantum measurement.
