Archimedes
,
Natation of bodies
,
1662
Text
Text Image
XML
Document information
None
Concordance
Figures
Thumbnails
page
|<
<
of 68
>
>|
<
archimedes
>
<
text
>
<
body
>
<
chap
>
<
pb
xlink:href
="
073/01/024.jpg
"
pagenum
="
353
"/>
<
p
type
="
head
">
<
s
>ARCHIMEDES,
<
lb
/>
HIS TRACT
<
lb
/>
<
emph
type
="
italics
"/>
DE
<
lb
/>
INSIDENTIBUS HUMIDO,
<
emph.end
type
="
italics
"/>
<
lb
/>
OR,
<
lb
/>
Of the NATATION of BODIES Upon, or
<
lb
/>
Submerſion In the WATER, or other LIQUIDS.</
s
>
</
p
>
<
p
type
="
head
">
<
s
>
<
emph
type
="
italics
"/>
BOOK
<
emph.end
type
="
italics
"/>
II.</
s
>
</
p
>
<
p
type
="
head
">
<
s
>PROP. I. THEOR. I.</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
If any Magnitude lighter than the Liquid be demitted
<
lb
/>
into the ſaid Liquid, it ſhall have the ſame proporti
<
lb
/>
on in Gravity to a Liquid of equal Maſſe, that the
<
lb
/>
part of the Magnitude demerged hath unto the
<
lb
/>
whole Magnitude.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>For let any Solid Magnitude, as for in
<
lb
/>
ſtance F A, lighter than the Liquid, be de
<
lb
/>
merged in the Liquid, which let be F A:
<
lb
/>
And let the part thereof immerged be A,
<
lb
/>
and the part above the Liquid F, It is to
<
lb
/>
be demonſtrated that the Magnitude F A
<
lb
/>
hath the ſame proportion in Gravity to a
<
lb
/>
Liquid of Equall Maſſe that A hath to F
<
lb
/>
A. </
s
>
<
s
>Take any Liquid Magnitude, as ſup
<
lb
/>
poſe N I, of equall Maſſe with F A; and let F be equall to N, and
<
lb
/>
A to I: and let the Gravity of the whole Magnitude F A be B, and
<
lb
/>
let that of the Magnitude N I be O,
<
lb
/>
and let that of I be R. </
s
>
<
s
>Now the
<
lb
/>
<
figure
id
="
id.073.01.024.1.jpg
"
xlink:href
="
073/01/024/1.jpg
"
number
="
19
"/>
<
lb
/>
Magnitude F A hath the ſame pro
<
lb
/>
portion unto N I that the Gravity B
<
lb
/>
hath to the Gravity O R: But for
<
lb
/>
aſmuch as the Magnitude F A demit
<
lb
/>
ted into the Liquid is lighter than
<
lb
/>
the ſaid Liquid, it is manifeſt that a Maſſe of the Liquid, I, equall
<
lb
/>
to the part of the Magnitude demerged, A, hath equall Gravity
<
lb
/>
<
arrow.to.target
n
="
marg1163
"/>
<
lb
/>
with the whole Magnitnde, F A: For this was
<
emph
type
="
italics
"/>
(a)
<
emph.end
type
="
italics
"/>
above demon
<
lb
/>
ſtrated: But B is the Gravity of the Magnitude F A, and R of I: </
s
>
</
p
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>