Archimedes
,
Natation of bodies
,
1662
Text
Text Image
XML
Document information
None
Concordance
Figures
Thumbnails
page
|<
<
of 68
>
>|
<
archimedes
>
<
text
>
<
body
>
<
chap
>
<
p
type
="
main
">
<
s
>
<
pb
xlink:href
="
073/01/011.jpg
"
pagenum
="
340
"/>
contained between the Sphærical Superficies that proceed accord
<
lb
/>
ing to P O and M N and the Planes of the Pyramid; and the Gra
<
lb
/>
vity of the Liquid, which is according to M N O P, ſhall be leſſer
<
lb
/>
than that which is according to L M X O; becauſe that Solid of
<
lb
/>
Liquor which proceeds according to R S C Y is leſs than the Solid
<
lb
/>
E Z H T (having been ſuppoſed to be equal in quantity to only
<
lb
/>
the part H B G T of that:) And the ſaid Solid E Z H T hath been
<
lb
/>
ſuppoſed to be equally grave with the Liquid: Therefore the Gra
<
lb
/>
vity of the
<
emph
type
="
italics
"/>
L
<
emph.end
type
="
italics
"/>
iquid compriſed betwixt the two Sphærical Superfi
<
lb
/>
cies L M and
<
emph
type
="
italics
"/>
X
<
emph.end
type
="
italics
"/>
O, and betwixt the ſides L
<
emph
type
="
italics
"/>
X
<
emph.end
type
="
italics
"/>
and M O of the
<
lb
/>
<
figure
id
="
id.073.01.011.1.jpg
"
xlink:href
="
073/01/011/1.jpg
"
number
="
5
"/>
<
lb
/>
Pyramid, together with
<
lb
/>
the whole Solid EZHT,
<
lb
/>
ſhall exceed the Gravity
<
lb
/>
of the Liquid compri
<
lb
/>
ſed betwixt the other
<
lb
/>
two Sphærical Superfi
<
lb
/>
cies M N and O P, and
<
lb
/>
the Sides M O and N P
<
lb
/>
of the Pyramid, toge
<
lb
/>
ther with the Solid of Liquor R S C Y by the quantity of the Gra
<
lb
/>
vity of the part E B Z G, ſuppoſed to remain above the Surface of
<
lb
/>
the Liquid: And therefore it is manifeſt that the part which pro
<
lb
/>
ceedeth according to the Circumference O P is preſſed, driven, and
<
lb
/>
repulſed, according to the
<
emph
type
="
italics
"/>
Suppoſition,
<
emph.end
type
="
italics
"/>
by that which proceeds ac
<
lb
/>
cording to the Circumference X O, by which means the Liquid
<
lb
/>
would not be ſetled and ſtill: But we did preſuppoſe that it was
<
lb
/>
ſetled, namely ſo, as to be without motion: It followeth, therefore,
<
lb
/>
that the ſaid Solid cannot in any part of it exceed or lie above the
<
lb
/>
Superficies of the Liquid: And alſo that being dimerged in the Li
<
lb
/>
quid it cannot deſcend to the Bottom, for that all the parts of the
<
lb
/>
Liquid equijacent, or diſpoſed equally, are equally preſſed, becauſe
<
lb
/>
the Solid is equally grave with the Liquid, by what we preſuppoſed.</
s
>
</
p
>
<
p
type
="
main
">
<
s
>RIC. </
s
>
<
s
>I do underſtand your Argumentation, but I underſtand not that Phraſe
<
lb
/>
<
emph
type
="
italics
"/>
Solid Magnitudes.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>NIC. </
s
>
<
s
>I will declare this Term unto you.
<
emph
type
="
italics
"/>
Magnitude
<
emph.end
type
="
italics
"/>
is a general Word that
<
lb
/>
reſpecteth all the Species of Continual Quantity; and the Species of Continual
<
lb
/>
Quantity are three, that is, the
<
emph
type
="
italics
"/>
L
<
emph.end
type
="
italics
"/>
ine, the Superficies, and the Body; which Body
<
lb
/>
is alſo called a Solid, as having in it ſelf
<
emph
type
="
italics
"/>
L
<
emph.end
type
="
italics
"/>
ength, Breadth, and Thickneſs, or Depth:
<
lb
/>
and therefore that none might equivocate or take that Term
<
emph
type
="
italics
"/>
Magnitudes
<
emph.end
type
="
italics
"/>
to be
<
lb
/>
meant of
<
emph
type
="
italics
"/>
L
<
emph.end
type
="
italics
"/>
ines, or Superficies, but only of Solid
<
emph
type
="
italics
"/>
Magnitudes,
<
emph.end
type
="
italics
"/>
that is, Bodies, he
<
lb
/>
did ſpecifie it by that manner of expreſſion, as was ſaid. </
s
>
<
s
>The truth is, that he
<
lb
/>
might have expreſt that
<
emph
type
="
italics
"/>
Propoſition
<
emph.end
type
="
italics
"/>
in this manner:
<
emph
type
="
italics
"/>
Solids (or Bodies) which being
<
lb
/>
of equal Gravity with an equal Maſs of the Liquid,
<
emph.end
type
="
italics
"/>
&c. </
s
>
<
s
>And this
<
emph
type
="
italics
"/>
Propoſition
<
emph.end
type
="
italics
"/>
would have
<
lb
/>
been more cleer and intelligible, for it is as ſignificant to ſay, a
<
emph
type
="
italics
"/>
Solid,
<
emph.end
type
="
italics
"/>
or, a
<
emph
type
="
italics
"/>
Body,
<
emph.end
type
="
italics
"/>
as
<
lb
/>
to ſay, a
<
emph
type
="
italics
"/>
Solid Magnitude:
<
emph.end
type
="
italics
"/>
therefore wonder not if for the future I uſe theſe three
<
lb
/>
kinds of words indifferently.</
s
>
</
p
>
<
p
type
="
main
">
<
s
>RIC. </
s
>
<
s
>You have ſufficiently ſatisfied me, wherefore that we may loſe no time
<
lb
/>
let us go forwards to the fourth
<
emph
type
="
italics
"/>
Propoſition.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>