Physicists and engineers think about things like that all the time (e.g. "gravity dies off like 1/r^2"), so I'd guess it was just a physics idea that got applied to algorithms. Probably not an "aha!" moment.
> the labour required here is proportional to a power of the logarithm of the modulus, not to the modulus itself or its square root as in the indirect processes, and hence see that in the case of a large modulus the direct process will be much quicker than the indirect
Specifically, he's pointing out that asymptotically any power of the logarithm of n will be smaller than a constant times n.
Physicists also naturally know about asymptotic comparisons, but the "this algorithm asymptotically beats that algorithm because it's (log n)^k₁ vs. k₂*n" is pretty darn similar to the way we think about this today!