[Sidenote: Solids whose Masses are in contrary proportion to
their Specifick Gravities are equall in absolute Gravity.]
_Solids whose Masses answer in proportion contrarily to their
Specificall Gravities, are equall in Absolute Gravities._
[Illustration]
Let A C and B be two Solids, and let the Mass A C be to the Mass B,
as the Specificall Gravity of the Solid B, is to the Specificall
Gravity of the Solid A C: I say, the Solids A C and B are equall in
absolute weight, that is, equally grave. For if the Mass A C be equall
to the Mass B, then, by the Assumption, the Specificall Gravity of B,
shall be equall to the Specificall Gravity of A C, and being equall in
Mass, and of the same Specificall Gravity they shall absolutely weigh
one as much as another. But if their Masses shall be unequall, let the
Mass A C be greater, and in it take the part C, equall to the Mass B.
And, because the Masses B and C are equall; the Absolute weight of B,
shall have the same proportion to the Absolute weight of C, that the
Specificall Gravity of B, hath to the Specificall Gravity of C; or of
C A, which is the same _in specie_: But look what proportion the
Specificall Gravity of B, hath to the Specificall Gravity of C A, the
like proportion, by the Assumption, hath the Mass C A, to the Mass B,
that is, to the Mass C: Therefore, the absolute weight of B, to the
absolute weight of C, is as the Mass A C to the Mass C: But as the
Mass A C, is to the Mass C, so is the absolute weight of A C, to the
absolute weight of C: Therefore the absolute weight of B, hath the
same proportion to the absolute weight of C, that the absolute weight
of A C, hath to the absolute weight of C: Therefore, the two Solids A
C and B are equall in absolute Gravity: which was to be demonstrated.
Having demonstrated this, I say,