Salusbury, Thomas
,
Mathematical collections and translations (Tome I)
,
1667
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>ARCHIMEDES,
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HIS TRACT
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DE
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INSIDENTIBUS HUMIDO,
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OR,
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Of the NATATION of BODIES Upon, or
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Submerſion In the WATER, or other LIQUIDS.</
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BOOK
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II.</
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>PROP. I. THEOR. I.</
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If any Magnitude lighter than the Liquid be demitted
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into the ſaid Liquid, it ſhall have the ſame proporti
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on in Gravity to a Liquid of equal Maſſe, that the
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part of the Magnitude demerged hath unto the
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whole Magnitude.
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>For let any Solid Magnitude, as for in
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ſtance F A, lighter than the Liquid, be de
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merged in the Liquid, which let be F A:
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And let the part thereof immerged be A,
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and the part above the Liquid F, It is to
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be demonſtrated that the Magnitude F A
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hath the ſame proportion in Gravity to a
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Liquid of Equall Maſſe that A hath to F
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A. </
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>Take any Liquid Magnitude, as ſup
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poſe N I, of equall Maſſe with F A; and let F be equall to N, and
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A to I: and let the Gravity of the whole Magnitude F A be B, and
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let that of the Magnitude N I be O,
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and let that of I be R. </
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<
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>Now the
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Magnitude F A hath the ſame pro
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portion unto N I that the Gravity B
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hath to the Gravity O R: But for
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aſmuch as the Magnitude F A demit
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ted into the Liquid is lighter than
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the ſaid Liquid, it is manifeſt that a Maſſe of the Liquid, I, equall
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to the part of the Magnitude demerged, A, hath equall Gravity
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with the whole Magnitnde, F A: For this was
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(a)
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above demon
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ſtrated: But B is the Gravity of the Magnitude F A, and R of I: </
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