Note 13 — Chapter I

Lacroix has justly criticised the expression of solid, commonly used by geometers to designate a volume. It is certain, in fact, that when we wish to consider separately a certain portion of indefinite space, conceived as gaseous, we mentally solidify its exterior envelope, so that a line and a surface are habitually, to our minds, just as solid as a volume. It may also be remarked that most generally, in order that bodies may penetrate one another with more facility, we are obliged to imagine the interior of the volumes to be hollow, which renders still more sensible the impropriety of the word solid.