## Scientia navalis seu tractatus de construendis ac dirigendis navibus.

St. Petersburg: Typis Academiae Scientiarum, 1749.

First edition of the work, which enunciated for the first time the principles of hydrostatics, with outstanding provenance: the copy of the great explorer and mathematician Charles Marie de La Condamine (1701–1774). A very good and entirely unrestored copy, in contemporary binding, of Euler’s first large work on fluid mechanics. “Together, these [two volumes] are second among the great treatises on rational mechanics by which Euler created the field as we now know it… [in this work Euler] builds a ‘mansion of analysis’ that includes all the elementary parts of hydrostatics as we know them today.” (Enetröm).

“Together with [the second volume of this work], Euler establishes his principles of hydrostatics, providing a basis for the scientific foundation for the theory of naval architecture… Among the topics mentioned in these two volumes are: the idea of centroid and metacenter as distinct from center of gravity; a theory of stability based on the direction of the restoring torque in a small displacement; the earliest treatment of three-dimensional motion of a general rigid body in response to an applied torque; the theory of small oscillations of floating bodies; solutions of specific problems based on local use of Newton’s Law of Resistance.

“Euler also shows that the principle, written in modern notation as *F = -∫p dS* and *p = *r*gh*, 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: the equilibrium of floating bodies; the restitution of floating bodies to equilibrium; the stability of floating bodies in equilibrium; the effects of external forces upon floating bodies; the resistance of water to moved plane figures; the resistance of water to moved bodies; the progressive motion of floating bodies.

“In [the second] volume, Euler looks at the rules and precepts for constructing and steering ships. In chapter 4, given an arbitrary floating body in various modes of oscillation, he calculates the length of an equivalent pendulum. This technique has become a part of modern hydrostatics. More specifically, he considers ships in general; the equilibrium of ships; the stability of equilibrium; the oscillations of ships; inclination under the influence of arbitrary forces; the effect of rudders; the effect of oars; the construction of rowed ships; the force exerted by the ind on a sail; masting of sailing ships; a ship on a skew course.” (Eneström no, 110 & 111).

4to. Two volumes in contemporary mottled calf with richly gilt spines. (2),44,444,(2) pp. and 37 plates; (2),534 pp. and 28 plates.

Item #6036

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Price:
$5,000.00
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