Mechanica Vol. II (1736)

...ch they arise, so that we may distinctly derive each individual case in the following chapters.

Scholion 5.

10. In these motions, whether upon given lines or surfaces, we exclude all friction from our consideration, and we shall assume no retardation of motion. Therefore, the lines and surfaces upon which the points are assumed to move must be conceived as perfectly smooth and devoid of all roughness, lest the motion be subject to slowing because of it. Rotational motion original: "Motum rotatorium"; Euler is distinguishing between simple translation (moving from A to B) and rotation (spinning), which complicates the energy and path equations. must also be entirely banished from our thoughts, since changes in motion arise from it which can only be explained in the following sections. For this reason, the point must be conceived as moving as if by sliding original: "rependo"; literally "creeping" or "crawling," used here to denote pure translational motion without rolling., so that every part of it—if indeed parts can be conceived in a mathematical point—possesses the same motion.

Scholion 6.

11. Therefore, those things that were presented in the preceding book, and those that will be presented in this one regarding the motion of points, can also be adapted to bodies of finite magnitude original: "corpora finitae magnitudinis"; these are physical objects with length, width, and height, as opposed to dimensionless points., provided that their motion is perpetually parallel to itself and all parts of the body are endowed with equal motion. This will appear more clearly from the subsequent books: specifically, in which cases the motion of finite bodies does not differ from the motion of points. On this account, we consider only points in these books because, as they lack parts, different motions cannot exist within those parts.