Do we have anything of what Gauss thought of these people from his works or anecdotes ?
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There is a quote where Gauss mentions Laplace:
Sin^2 φ is odious to me, even though Laplace made use of it; should it be feared that sin^2 φ might become ambiguous, which would perhaps never occur, or at most very rarely when speaking of sin(φ^2),well then, let us write (sin φ)^2, but not sin^2 φ, which by analogy should signify sin (sin φ).
This quote suggests that Gauss respected Laplace, even if Laplace used a formula that he (Gauss) disliked.
Link: http://mathshistory.st-andrews.ac.uk/Quotations/Gauss.html
Gauss worked on a few of Euler's integrals and rediscovered other pieces of his work, according to this link:
http://mathshistory.st-andrews.ac.uk/Biographies/Euler.html
This may imply that Gauss admired Euler's work to the point of studying it intensely.
As for Lagrange, for whom Euler was a mentor, the sources for any idea of their thoughts about each other remain elusive as of this writing.
