LEMMA I.
The abſolute Gravities of Solids, have a proportion com-
pounded of the proportions of their ſpecificall Gravities,
and of their Maſſes.
The abſolute
Gravity of
lids, are in a
portion
pounded of their
Specifick
ties, and of their
Maſſes.
Gravity of
lids, are in a
portion
pounded of their
Specifick
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
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
305[Figure 305]
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
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,
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
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
ſtrate, how that,
of A, hath to the Abſolute Gravity of B, a proportion
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
305[Figure 305]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
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,
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
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
ſtrate, how that,
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