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: