Thoughts on a nautical problem, proposed by the illustrious Royal Academy of Sciences in Paris
Paris prize article
Euler uses mechanics to design ships. He adopts Newton's law of resistance (which says that the pressure exerted by a fluid acting against a plane surface is proportional to the square of the speed, neglecting back pressure) by interpreting it as a statement about differential elements of surface. He calls this assumption "the common hypothesis" and uses it to calculate the total resistance, via integration. In this way, he arrives at definite answers (often in elegant, explicit forms) that allow for both quantitative and qualitative conclusions that he develops and interprets clearly. (Based on Clifford Truesdell's An idiot's fugitive essays on science: methods, criticisms, training, circumstances.)
Original Source Citation
Pièce qui ont remporté le prix de l'académie royale des sciences, Volume 1727, pp. 1-48.
Opera Omnia Citation
Series 2, Volume 20, pp.1-35.