Carl Friedrich Gauss Quote

The function just found cannot, it is true, express rigorously the probabilities of the errors: for since the possible errors are in all cases confined within certain limits, the probability of errors exceeding those limits ought always to be zero, while our formula always gives some value. However, this defect, which every analytical function must, from its nature, labor under, is of no importance in practice, because the value of our function decreases so rapidly... that it can safely be considered as vanishing. Besides, the nature of the subject never admits of assigning with absolute rigor the limits of error.


Theoria motus corporum coelestium in sectionibus conicis solem ambientum (1809) Tr. Charles Henry Davis as Theory of the Motion of the Heavenly Bodies moving about the Sun in Conic Sections (1857)

Picture Quote 1

The function just found cannot, it is true, express rigorously the probabilities of the errors: for since the possible errors are in all cases...

Picture Quote 2

The function just found cannot, it is true, express rigorously the probabilities of the errors: for since the possible errors are in all cases...

Picture Quote 3

The function just found cannot, it is true, express rigorously the probabilities of the errors: for since the possible errors are in all cases...

Picture Quote 4

The function just found cannot, it is true, express rigorously the probabilities of the errors: for since the possible errors are in all cases...