ARCHIMEDES,
HIS TRACT
DE
INSIDENTIBUS HUMIDO,
OR,
Of the NATATION of BODIES Upon, or
Submerſion In the WATER, or other LIQUIDS.
HIS TRACT
DE
INSIDENTIBUS HUMIDO,
OR,
Of the NATATION of BODIES Upon, or
Submerſion In the WATER, or other LIQUIDS.
BOOK II.
PROP. I. THEOR. I.
If any Magnitude lighter than the Liquid be demitted
into the ſaid Liquid, it ſhall have the ſame proporti
on in Gravity to a Liquid of equal Maſſe, that the
part of the Magnitude demerged hath unto the
whole Magnitude.
into the ſaid Liquid, it ſhall have the ſame proporti
on in Gravity to a Liquid of equal Maſſe, that the
part of the Magnitude demerged hath unto the
whole Magnitude.
For let any Solid Magnitude, as for in
ſtance F A, lighter than the Liquid, be de
merged in the Liquid, which let be F A:
And let the part thereof immerged be A,
and the part above the Liquid F, It is to
be demonſtrated that the Magnitude F A
hath the ſame proportion in Gravity to a
Liquid of Equall Maſſe that A hath to F
A. Take any Liquid Magnitude, as ſup
poſe N I, of equall Maſſe with F A; and let F be equall to N, and
A to I: and let the Gravity of the whole Magnitude F A be B, and
let that of the Magnitude N I be O,
and let that of I be R. Now the
245[Figure 245]
Magnitude F A hath the ſame pro
portion unto N I that the Gravity B
hath to the Gravity O R: But for
aſmuch as the Magnitude F A demit
ted into the Liquid is lighter than
the ſaid Liquid, it is manifeſt that a Maſſe of the Liquid, I, equall
to the part of the Magnitude demerged, A, hath equall Gravity
with the whole Magnitnde, F A: For this was (a) above demon
ſtrated: But B is the Gravity of the Magnitude F A, and R of I:
ſtance F A, lighter than the Liquid, be de
merged in the Liquid, which let be F A:
And let the part thereof immerged be A,
and the part above the Liquid F, It is to
be demonſtrated that the Magnitude F A
hath the ſame proportion in Gravity to a
Liquid of Equall Maſſe that A hath to F
A. Take any Liquid Magnitude, as ſup
poſe N I, of equall Maſſe with F A; and let F be equall to N, and
A to I: and let the Gravity of the whole Magnitude F A be B, and
let that of the Magnitude N I be O,
and let that of I be R. Now the
245[Figure 245]Magnitude F A hath the ſame pro
portion unto N I that the Gravity B
hath to the Gravity O R: But for
aſmuch as the Magnitude F A demit
ted into the Liquid is lighter than
the ſaid Liquid, it is manifeſt that a Maſſe of the Liquid, I, equall
to the part of the Magnitude demerged, A, hath equall Gravity
with the whole Magnitnde, F A: For this was (a) above demon
ſtrated: But B is the Gravity of the Magnitude F A, and R of I: