[Sidenote: The absolute Gravity of Solids, are in a proportion
compounded of their Specifick Gravities, and of their Masses.]
_The absolute Gravities of Solids, have a proportion compounded of
the proportions of their specificall Gravities, and of their
Masses._
[Illustration]
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,