Gauss indeed wrote "methodisches tatonniren"[1], the latter of which is not a common German word, nor does it suggest grouping. I believe it to be an expression used at the time which was borrowed from French "tâtonner", which means "fumble", to describe a step-by-step process, "approaching" a solution. The closest I get in modern German is "herantasten", which in turn does not have an elegant English translation; you will have to take its elements "heran" (onto) and "tasten" (touch/feel/grope) individually to judge how close it is to fumble.
So, methodical groping is not as far off as you might have thought!
The word "tâtonner" should be the same as Italian "procedere (proceed) a tastoni", since usually the circumflex accent in French correspond to an "s" in Italian.
The meaning is "feel your way"---proceed carefully and at every step feel what is around you, as if you were walking on complete darkness.
Gauss indeed wrote "methodisches tatonniren"[1], the latter of which is not a common German word, nor does it suggest grouping. I believe it to be an expression used at the time which was borrowed from French "tâtonner", which means "fumble", to describe a step-by-step process, "approaching" a solution. The closest I get in modern German is "herantasten", which in turn does not have an elegant English translation; you will have to take its elements "heran" (onto) and "tasten" (touch/feel/grope) individually to judge how close it is to fumble.
So, methodical groping is not as far off as you might have thought!
[1] https://books.google.com/books?id=3jEDAAAAQAAJ&pg=RA1-PA106&... This may be a typo—the regular verb form would be "tatonnieren"—then again a lot of German spelling has changed since the time of those letters.