Chapter Five of the Paris Manuscript of Du Châtelet‘s Institutions de Physique is now online here. The chapter deals with “the notion of space,” as she puts it in the earliest extant draft.
An excerpt from the Introduction by Aaron Wells:
One interesting revision appears at the end of section LXXVII. Having traced the origins of the idea of extension to unity and diversity, Du Châtelet now diagnoses an error made by materialist philosophers. They inferred, from the fact that the “soul” exhibits both unity and diversity, and that unity and diversity are also characteristic of extended things, that the soul is extended. In version B, her response simply appeals to the fact that anything extended has parts outside one another (whereas the soul lacks this property). A possible problem with this response is that the property of having parts outside one another, unless it is further disambiguated, may just presuppose the property of being extended. So the response would just amount to asserting that the soul is non-extended, which is precisely the point of contention. A marginal note in her hand signals that she aims to expand on this reasoning: it reads “mettre la, la raison.” Indeed, an important sentence is added to this passage in version D, at which point the marginal note is canceled out. In this later version, she puts the point in terms that do not presuppose space. Rather, she appeals to metaphysical separability to distinguish between two cases of unity in diversity. In extended things, there is unity in diversity and the diverse parts are separable from the whole; in the soul, there is also unity in diversity, but the diverse faculties are not separable from the soul as substance: the soul’s attributes and its modes “sont inseparables del’etre quils modifient et font un avec lui” (105v). So she now has an objection to the materialist’s inference that does not simply assert that the soul is non-extended.