Consider the Germanic root "mid/mit" (e.g. middle, Mittel, Mitte), the Slavic root "сред" (e.g. средство, среда), and the Latin root "medio" (e.g. median, medios, mean, moyen).
Their derived terms in all three language families have both meanings of "center, intermediate" and "method or course of action used to achieve some result".
Since it seems highly unlikely that three different roots in three different language families would have the same two meanings independently, I wondered whether only one of the two meanings is native to all three families, with the second meaning developing initially in one language family only and then spreading to the other two via calques (e.g. first developing in French, and then copied via calque by the English, Russians, and Germans).
I tried checking etymological dictionaries (e.g. Wiktionary), but none compare the etymologies of related words in different languages so as to check for calques. Thus I don't know how to confirm or deny this hypothesis. Generalizing this specific situation leads to my overall
Question. Does anyone know or can anyone suggest a standardized procedure for checking for calques obscuring a word's true etymology?