It is fitting to treat the science of the weight and of the equilibrium of fluids and solids in fluids by a twofold method. To the extent that it appertains to the mathematical sciences, it is reasonable that I largely abstract it from physical considerations. And for this reason I have undertaken to demonstrate its individual propositions from abstract principles, sufficiently well known to the student, strictly and geometrically. Since this doctrine may be judged to be somewhat akin to natural philosophy, in so far as it may be applied to making clear many of the phenomena of natural philosophy and in order, moreover, that its usefulness may be particularly apparent and the certainty of its principles perhaps confirmed, I shall not be reluctant to illustrate the propositions abundantly from experiments as well, in such a way, however, that this freer method of discussion, disposed in scholia, may not be confused with the former, which is treated in lemmas, propositions and corollaries.

The foundations from which this science may be demonstrated are either definitions of certain words, or axioms and postulates no one denies. And of these I treat directly.

Definitions

The terms ‘quantity’, ‘duration’, and ‘space’ are too well known to be susceptible of definition by other words.