E110 -- Scientia Navalis, volume 1

(Naval Science, volume 1)

Originally published with the full title: Scientia navalis seu tractatus de construendis ac dirigendis navibus Pars prior complectens theoriam universam de situ ac motu corporum aquae innatantium. Auctore Leonhardo Euler prof. honorario academiae imper. scient. et directore acad. reg. scient. Borussicae. Instar supplementi ad tom. I. novorum commentar. acad. scient. imper. Petropoli typis academiae scientiarum MDCCXLIX.

(based on C. Truesdell's An idiot's fugitive essays on science: methods, criticisms, training, circumstances and his introduction to Opera Omnia Series II, Volume 12)
Together with E111, Euler establishes his principles of hydrostatics, providing a basis for the scientific foundation for the theory of naval architecture. Together, these are second among the great treatises on rational mechanics by which Euler created the field as we now know it. Among the topics mentioned in these two volumes are: Euler also shows that the principle, written in modern notation as F = -∫p dS and p = rgh, where p is pressure, r is density, g is the force of gravity per unit mass, and F is the force, is both necessary and sufficient for the equlibrium of incompressible fluids near the earth's surface. It is on this principle that he builds a "mansion of analysis" that includes all the elementary parts of hydrostatics as we know them today. In addition, Euler proves that one can obtain a complete solution to the problem of finding the restoring moment for a body in any position by first finding all the positions of equilibrium; once this is done, determine the direction of the turning moment that is acting on the body when it is infinitesimally displaced from each of these equilibrium positions.

In particular, this volume looks at the general theory of the location and motion of bodies floating in water. In chapter 3, Euler gives a general and precise definition of stability that applies to all systems that are in equilibrium; this definition is still commonly used today. More specifically, Euler considers:


In addition to the dedication (to Graf Rasumowski), which is dated January 25, 1749, it contains 7 chapters listed above.

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