Galilei, Galileo, Discourse concerning the natation of bodies, 1663

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The abſolute
Gravity of So­
lids, are in a pro­
portion com­
pounded of their
Specifick Gravi­
ties, and of their
Maſſes.
Let A and B be two Solids. I ſay, that the Abſolute Gravity
of A, hath to the Abſolute Gravity of B, a proportion com­
pounded 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

Figure: /permanent/archimedes/galil_natat_074_en_1663/figures not scanned
[Figure 4]

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 pro­
portion, 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, be­
cauſe, 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 Gra­
vity 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 demon­
ſtrate, how that,

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