Did Euler found Continuum Mechanics on Balance Laws? "Argumentum ab auctoritate est infirmissimum"

The content of this paper is not a historiographical reconstruction.Instead, it intends to give a documented opinion, based also on historicalconsiderations, about the postulation scheme which must be preferred informulating novel mechanical models. Truesdell has claimed that his ownpreferred postulation to continuum mechanics, which builds the theorybased on local integral balance laws, is historically grounded in the workof Leonhard Euler. Is this position, so strongly advocated by Truesdell,tenable? In the present paper, based on circumstantial evidence and byusing the technique of logical reconstruction of “lacking” mathematicaldetails in a “corrupted” flow of mathematical reasonings, as proposed in[63, 62], we conjecture that, most likely, Euler’s preferred postulation ofmechanics was based on variational principles. This conjecture will need tobe further substantiated, as, unfortunately, the greatest part of the corpusof Euler’s works (mainly published in Latin only or even not completelyprinted, yet) is not easily accessible: therefore the careful philologicalanalysis needed to fully confirm the proposed conjecture is, at the moment,impossible. In the literature one finds two argumenta ab actoritate: thefirst, used by Truesdell, claims that balance laws postulation must beaccepted because Euler is assumed to have chosen it; the second, used byTruesdellians, claims that such a postulation must be accepted becauseTruesdell has shown us the light. However it is well-known that argumentaab auctoritate sunt infirmissima (The arguments based on the authorityof a “bigger” thinker are the weakest).