Both volumes are dedicated to "Monseigneur le Comte de Maurepas. Ministère et Secretaire d'Etat," and have the dedication signed and dated by the author, the first "Paris le 21 Mars 1732," and the second "Versailles, le 19 Avril 1734." The Scott Catalogue identifies the arms on the rich crimson morocco binding as those of the dedicatee.

The Marquis de Maurepas (1701-81) had succeeded his father as Secretary of State for the Marine, was deeply interested in scientific matters and patron of several French scientists and mathematicians. Little is known of De La Croix except that he became Commissaire-Général de la Marine, and may therefore have acted for Maurepas in a civil service capacity. His work describes methods of calculation of plans of ships based on mathematical principles and deals with the theory of hydrostatics and stability. Betty Cooper states that "In 1735, extracts from vol. 2 were published in Paris under the title Extrait du méchanisme des mouvemens des corps flotants. An English translation was made by Admiral Sir Charles Knowles entitled An abstract on the motion of floating bodies and published in London, 1775. Knowles wrote of the work, 'This little treatise contains more knowledge on the art of shipbuilding, than any book hitherto published that I have met with.'"