r ’s Gravesande’s Foundations for Mechanics Steffen Ducheyne and Jip van Besouw Centre for Logic and Philosophy of Science, Vrije Universiteit Brussel, Brussels, Belgium Related Topics ’ s Gravesande · Foundations of mechanics · Vis viva controversy Introduction This entry deals with foundational issues in the mechanics of ’ s Gravesande. First, it deals with how he defined the fundamental concepts of his mechanics. Second, it looks at his use of the concept “force” and his intervention in the vis viva controversy. The first part of this entry examines W.J. ’ s Gravesande’ s views on space, time, body, and force and is based on the various editions of his Elements and Institutions, and his 1722 “Essay” (These works refer to Mathematical elements of physics confirmed by experiments, its abridgment, Institutions of Newtonian philosophy , and “Essay on a new theory of the collision of bodies.” See “Works cited.” For contextualization of ’ s Gravesande’ s natural philosophy, his specific way of appropriating Newton’ s natural- philosophical work, and his early career, see Ducheyne (2014a, b) and Van Besouw (2016).). In all three editions of the Elements, “place” (locus) is defined by ’ s Gravesande as the space (spatium) occupied by a body. (In this and the following quotations, one finds clear parallels with the following sentences from Newton’ s scho- lium on space and time: “Absolute, true, and mathematical time, in and of itself and of its own nature, without reference to anything external, flows uniformly [...]. Relative, apparent, and common time is any sensible and external mea- sure (precise or imprecise) of duration by means of motion [...]. [...] Absolute space, of its own nature without reference to anything external, always remains homogeneous and immovable. Relative space is any movable measure or dimen- sion of this absolute space; such a measure or dimension is determined by our senses from the situation [per situm] of the space with respect to bodies [...]. [...] Place is the part of space that a body occupies, and it is, depending on the space, either absolute of relative [...].” (1999: 408–409). Note however that ’ s Gravesande applies the adjectives absolute and relative to place rather than to space.) Place and time can be absolute or relative. Throughout these works, ’ s Gravesande defines true or absolute place as “a part of immo- bile space, which is occupied by a body”; relative place, “which can only be distinguished by the senses,” as the position (situs) of a body with respect to other bodies; true or absolute time as having “no relation to the motion of bodies, nor to the succession of ideas in an intelligent Being” and as flowing “always equally by its nature”; and © Springer Nature Switzerland AG 2020 D. Jalobeanu, C. T. Wolfe (eds.), Encyclopedia of Early Modern Philosophy and the Sciences, https://doi.org/10.1007/978-3-319-20791-9_40-1