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
="
073/01/012.jpg
"
pagenum
="
341
"/>
<
p
type
="
head
">
<
s
>PROP. IV. THEOR. IV.</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Solid Magnitudes that are lighter than the Liquid,
<
lb
/>
being demitted into the ſetled Liquid, will not total
<
lb
/>
ly ſubmerge in the ſame, but ſome part thereof will
<
lb
/>
lie or ſtay above the Surface of the Liquid.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>NIC. </
s
>
<
s
>In this fourth
<
emph
type
="
italics
"/>
Propoſition
<
emph.end
type
="
italics
"/>
it is concluded, that every Body or Solid that is
<
lb
/>
lighter (as to Specifical Gravity) than the
<
emph
type
="
italics
"/>
L
<
emph.end
type
="
italics
"/>
iquid, being put into the
<
lb
/>
<
emph
type
="
italics
"/>
L
<
emph.end
type
="
italics
"/>
iquid, will not totally ſubmerge in the ſame, but that ſome part of it
<
lb
/>
will ſtay and appear without the
<
emph
type
="
italics
"/>
L
<
emph.end
type
="
italics
"/>
iquid, that is above its Surface.</
s
>
</
p
>
<
p
type
="
main
">
<
s
>For ſuppoſing, on the contrary, that it were poſſible for a Solid
<
lb
/>
more light than the Liquid, being demitted in the Liquid to ſub
<
lb
/>
merge totally in the ſame, that is, ſo as that no part thereof re
<
lb
/>
maineth above, or without the ſaid Liquid, (evermore ſuppoſing
<
lb
/>
that the Liquid be ſo conſtituted as that it be not moved,) let us
<
lb
/>
imagine any Plane produced thorow the Center of the Earth, tho
<
lb
/>
row the Liquid, and thorow that Solid Body: and that the Surface
<
lb
/>
of the Liquid is cut by this Plane according to the Circumference
<
lb
/>
A
<
emph
type
="
italics
"/>
B
<
emph.end
type
="
italics
"/>
G, and the Solid
<
emph
type
="
italics
"/>
B
<
emph.end
type
="
italics
"/>
ody according to the Figure R; and let the
<
lb
/>
Center of the Earth be K. </
s
>
<
s
>And let there be imagined a Pyramid
<
lb
/>
<
figure
id
="
id.073.01.012.1.jpg
"
xlink:href
="
073/01/012/1.jpg
"
number
="
6
"/>
<
lb
/>
that compriſeth the Figure
<
lb
/>
R, as was done in the pre.
<
lb
/>
</
s
>
<
s
>cedent, that hath its Ver
<
lb
/>
tex in the Point K, and let
<
lb
/>
the Superficies of that
<
lb
/>
Pyramid be cut by the
<
lb
/>
Superficies of the Plane
<
lb
/>
A
<
emph
type
="
italics
"/>
B
<
emph.end
type
="
italics
"/>
G, according to A K
<
lb
/>
and K
<
emph
type
="
italics
"/>
B
<
emph.end
type
="
italics
"/>
. </
s
>
<
s
>And let us ima
<
lb
/>
gine another Pyramid equal and like to this, and let its Superficies
<
lb
/>
be cut by the Superficies A
<
emph
type
="
italics
"/>
B
<
emph.end
type
="
italics
"/>
G according to K
<
emph
type
="
italics
"/>
B
<
emph.end
type
="
italics
"/>
and K
<
emph
type
="
italics
"/>
G
<
emph.end
type
="
italics
"/>
; and let
<
lb
/>
the Superficies of another Sphære be deſcribed in the Liquid, upon
<
lb
/>
the Center K, and beneath the Solid R; and let that be cut by the
<
lb
/>
ſame Plane according to
<
emph
type
="
italics
"/>
X
<
emph.end
type
="
italics
"/>
O P. And, laſtly, let us ſuppoſe ano
<
lb
/>
ther Solid taken ^{*} from the Liquid, in this ſecond Pyramid, which
<
lb
/>
<
arrow.to.target
n
="
marg1133
"/>
<
lb
/>
let be H, equal to the Solid R. </
s
>
<
s
>Now the parts of the Liquid, name
<
lb
/>
ly, that which is under the Spherical Superficies that proceeds ac
<
lb
/>
cording to the Superficies or Circumference
<
emph
type
="
italics
"/>
X
<
emph.end
type
="
italics
"/>
O, in the firſt Py
<
lb
/>
ramid, and that which is under the Spherical Superficies that pro
<
lb
/>
ceeds according to the Circumference O P, in the ſecond Pyramid,
<
lb
/>
are equijacent, and contiguous, but are not preſſed equally; for </
s
>
</
p
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>