Let A and B be two Solids. I say, that the Absolute Gravity of A, hath to the Absolute Gravity of B, a proportion compounded of the proportions of the specificall Gravity of A, to the Specificall Gravity of B, and of the Mass A to the Mass B. Let the Line D have the same proportion to E, that the specifick Gravity of A, hath to the specifick Gravity of B; and let E be to F, as the Mass A to the Mass B: It is manifest, that the proportion of D to F, is compounded of the proportions D and E; and E and F. It is requisite, therefore, to demonstrate, that as D is to F, so the absolute Gravity of A, is to the absolute Gravity of B. Take the Solid C, equall in Mass to the Solid A, and of the same Gravity _in specie_ with the Solid B. Because, therefore, A and C are equall in Mass, the absolute Gravity of A, shall have to the absolute Gravity of C, the same proportion, as the specificall Gravity of A, hath to the specificall Gravity of C, or of B, which is the same _in specie_; that is, as D is to E. And, because, C and B are of the same Gravity _in specie_, it shall be, that as the absolute weight of C, is to the absolute weight of B, so the Mass C, or the Mass A, is to the Mass B; that is, as the Line E to the Line F. As therefore, the absolute Gravity of A, is to the absolute Gravity of C, so is the Line D to the Line E: and, as the absolute Gravity of C, is to the absolute Gravity of B, so is the Line E to the Line F: Therefore, by Equality of proportion, the absolute Gravity of A, is to the absolute Gravity of B, as the Line D to the Line F: which was to be demonstrated. I proceed now to demonstrate, how that, THEOREME IV. [Sidenote: The proportion of water requisite to make a Solid swim:] _If a Solid, Cylinder, or Prisme, lesse grave specifically than the Water, being put into a Vessel, as above, of whatsoever greatnesse, and the Water, be afterwards infused, the Solid shall rest in the bottom, unraised, till the Water arrive to that part of the Altitude, of the said Prisme, to which its whole Altitude hath the same proportion, that the Specificall Gravity of the Water, hath to the Specificall Gravity of the said Solid: but infusing more Water, the Solid shall ascend._ [Illustration]