Scientia Navalis, seu Tractatus de construendis ac dirigendis navibus pars prior complectens theoriam universam de situ ac motu corporum aquae innatantium. [And:] Pars posterior in qua rationes ac praecepta navium construendarum et gubernandarum fusius exponuntur.

St Petersburg: Typis Academiae Scientiarum, 1749.

First edition of one of Euler’s rarer books, his highly original and important contribution to fluid mechanics and shipbuilding. “Any reader who can put himself in the position of the times will be astounded by the breadth, depth, and originality of Euler’s great book. In Mr. Habicht’s words, ‘here for the first time the principles of hydrostatics are established in full clarity, on the basis of which a scientific foundation for the theory of naval architecture is provided’” (Truesdell, p. 329). “His Scientia navalis and his articles on elasticity initiated continuum mechanics” (Calinger, p. 303). “With this work Euler made a major contribution to the study of fluid mechanics. In the first volume he presents a general theory of equilibrium of floating bodies with an original theory of stability and small oscillations in the neighborhood of the equilibrium position. The second volume applies the general theory to ship design, and deals with ships in general, stability and equilibrium, the motion of ships, and the wind; as well, it treats of such parts as masts, sails, oars, and rudder” (Roberts & Trent). “In the domain of hydromechanics, the first big work of Euler was his extensive opus on vessels, the Scientia navalis (1749). This work represents, after the Mechanica (1736), the second milestone in the development of rational mechanics and it has lost nothing of its importance up to the present day. Not only, for the first time, were the principles of hydrostatics set out in splendid clarity and, based on it, the scientific fundamentals of the theory of ship­building, but the subjects covered gave an overview of almost all relevant lines of development in mechanics during the 18th century. In the first volume Euler deals with the general theory of the equilibrium of floating bodies – at that time a ‘novum’ – pro­blems of stability as well as small oscilla­tions in the neighbourhood of the state of equilibrium. In this connexion he defined, via the pressure of liquids (independent of the direction), the ‘ideal liquid’, which unquestionably provided Cauchy later on with the pattern for his definition of the strain tensor. The second volume gives the applications of the general theory to the special case of a ship. With the Scientia navalis, Euler established a new science and influenced markedly the development of navigation and marine engineering. Only a few specialists are aware of the fact that it is due to none other than Leonhard Euler that we first understood the technically realisable principles of the impeller drive and the propeller. The bold projects of Euler’s time for its application were, of course, condemned to remain theoretical, since the necessary propulsion energies were not yet available” (Fellman, p. 45). “Here we find the concepts of centroid and metacenter as distinct from center of gravity; a theory of stability based upon the direction of the restoring torque in a small displacement; the earliest treatment of three-dimensional motion of a rigid body of general form in response to applied torque; the theory of small oscillations of floating bodies; and a cornucopia of solutions of specific problems based upon local use of ‘Newton’s law of resistance.’ The astonishing courage of the work may be guessed from the titles of the chapters” (Truesdell, ibid.).

After 14 years in Russia, Euler had moved to Berlin in 1741. The Scientia navalis had been completed no later than the spring of 1743, for Euler informed the astronomer Christian Nicolaus Winsheim then that the book was finished. The St. Petersburg Academy had agreed to fund its publication, but difficulties had arisen. Euler then tried to have the book published at London. “Euler was in 1746 seeking to be elected a fellow of the Royal Society of London, and he offered to present to the society a manuscript copy of his Scientia navalis, which the Petersburg Academy had not yet published. Euler wanted it published as quickly as possible, because he was worried that others would make discoveries similar to his and publish them first. He promised to compare Scientia navalis with Pierre Bouguer’s Traité du navire on navigation and naval architecture, which appeared that year. Euler’s ship theory and computations agreed with experience, he asserted, while Bouguer had made mistakes in calculations – especially on rowing – and had failed to cover the field. Euler offered to pay for the printing of Scientia navalis, but Royal Society president Folkes would not agree to it. Razumovskii [President of the St. Petersburg Imperial Academy of Sciences, 1746-98] had Schumacher [councillor of the Academy] write in August 1747 … that the Russian academic chancellery, with support of the Russian admiralty, had renewed its rights to have both volumes of the Scientia navalis printed in Berlin at the expense of the Petersburg Academy. Razumovskii allocated 500 rubles for the publication, a decision that drew criticism. Possibly because of costs and uncertainty over who would pay it was impossible to find a publisher in Berlin willing to undertake the difficult project” (Calinger, p. 269).

“After more than a decade’s delay, Euler’s two-volume Scientia navalis on the construction and propulsion of ships was finally published in 1749. That it appeared even then was due to the initiative of Razumovskii the previous year; when he and the Russian Admiralty approved funds for printing both volumes, Razumovskii had ordered that it be printed as quickly as possible … Euler dated the prologue of the Scientia navalis 25 January 1749. For the title page he asked that in addition to ‘Prof. Honorario Academiae Imper. Scient.’ after his name, the position ‘et Directore Acad. Scient. Borussicae.’ be inserted, and he requested copies of the work. Both wishes were granted.

Scientia navalis, Euler’s third landmark book during his tenure in the Prussian Academy, provided optimal ship designs, a precise general definition of stability, and positions of the equilibrium of ships. A general theory of navigation was insufficient to attain these. The second volume of Scientia navalis particularly treats the maximum stability, handling, and speed of ships, features that often come at the expense of others: gaining the greatest speed and maintaining exact direction, for example, may impede each other; the water also produces such effects as swaying and rolling. Euler endeavoured to perfect naval theory by reconciling with ship construction the art of piloting, knowing to what extent to use one method to enhance a variety of properties. The previous lack of mathematical methods and computations in naval construction and naval science meant that progress had been piecemeal, misapprehended, and intermittent” (Calinger, pp. 301-2).

“Euler 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 equilibrium 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.

“The first volume considers 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, which is still commonly used today. More specifically, in this volume Euler considers: the equilibrium and stability of floating bodies; the restitution of floating bodies to equilibrium; the effects of external forces upon floating bodies; the resistance of water to moved bodies; the progressive motion of floating bodies … [In the second volume], Euler describes some 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. Some other topics he considers are: the equilibrium and oscillations of ships; inclination under the influence of arbitrary forces; the effects of rudders and oars; the force exerted by the wind on a sail; masting of sailing ships; a ship on a skew course” (Euler Archive).

“Exceptional in both theoretical and applied mathematics, the Scientia navalis continued Euler’s program for founding rational mechanics. Soon after its release, he was concerned that the text was too difficult for navigators and quickly began a revision to simplify it. The long delay in publishing the two-volume text allowed Euler’s competitor Pierre Bouguer, the winner of the Prix de Paris in 1727, to precede him in print, getting out his magnum opus Traité du navire, de sa construction et de ses mouvements in 1746 and thereby to claim priority for central concepts in naval science, such as the metacentre that Euler had earlier discovered. Probably to avoid a dispute over priority, Euler recognized the contributions of Bouguer twice near the close of his prologue. But Euler was the first to clearly establish the principles of hydrostatics, providing variational solutions using differential equations” (Calinger, pp. 303).

Poggendorff I, 690; Gascoigne 535; Roberts & Trent 105; Libri rari 97; Sotheran I, 1257 (“This work first expresses mathematically the resistance meeting a ship on its path through the water”). Fellmann, Leonhard Euler, 2007. Truesdell, An Idiot’s Fugitive Essays on Science, 2012. For a detailed account of the Scientia navalis, see the Introduction by Walter Habicht to Euler’s Commentationes mechanicae et astronomicae as Scientiam navalem pertinentes, Volumen posterius (Opera Omnia, Ser. 2, Vol. 21), 1978.



Two vols., 4to, pp. [ii], 44, [2], 444; [ii], 534, with 65 folding engraved plates (occasional light browning, a few rust spots). Early 19th-century half-calf and marbled boards (slightly rubbed). A large, clean and fresh copy.

Item #5251

Price: $7,500.00

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