Salusbury, Thomas, Mathematical collections and translations (Tome I), 1667

#### Table of figures

< >
[Figure 211]
[Figure 212]
[Figure 213]
[Figure 214]
[Figure 215]
[Figure 216]
[Figure 217]
[Figure 218]
[Figure 219]
[Figure 220]
[Figure 221]
[Figure 222]
[Figure 223]
[Figure 224]
[Figure 225]
[Figure 226]
[Figure 227]
[Figure 228]
[Figure 229]
[Figure 230]
[Figure 231]
[Figure 232]
[Figure 233]
[Figure 234]
[Figure 235]
[Figure 236]
[Figure 237]
[Figure 238]
[Figure 239]
[Figure 240]
< >
page |< < of 701 > >|
<archimedes>
<text>
<body>
<chap>
<p type="main">
<s>
tions of a Sphære, ſhall have its Axis in the Perpendicular, that is
<lb/>
drawn through the point K; and its Centre of Gravity, for the ſame
<lb/>
reaſon, ſhall be in the Line N K: let us ſuppoſe it to be the Point R:
<lb/>
<arrow.to.target n="marg1141"/>
<lb/>
But the Centre of Gravity of the whole Portion is in the Line F T,
<lb/>
betwixt the Point R and
<lb/>
<lb/>
the Point F; let us ſuppoſe
<lb/>
it to be the Point
<emph type="italics"/>
X
<emph.end type="italics"/>
: The re­
<lb/>
mainder, therefore, of that
<lb/>
<arrow.to.target n="marg1142"/>
<lb/>
Figure elivated above the
<lb/>
Surface of the Liquid, hath
<lb/>
its Centre of Gravity in
<lb/>
the Line R X produced or
<lb/>
continued right out in the
<lb/>
Part towards X, taken ſo,
<lb/>
that the part prolonged may
<lb/>
have the ſame proportion to
<lb/>
X R, that the Gravity of
<lb/>
that Portion that is demer­
<lb/>
ged in the Liquid hath to
<lb/>
the Gravity of that Figure which is above the Liquid; let us ſuppoſe
<lb/>
<arrow.to.target n="marg1143"/>
<lb/>
that ^{*} that Centre of the ſaid Figure be the Point S: and thorow that
<lb/>
<arrow.to.target n="marg1144"/>
<lb/>
ſame Centre S draw the Perpendicular L S. </s>
<s>Now the Gravity of the Fi­
<lb/>
gure that is above the Liquid ſhall preſſe from above downwards ac­
<lb/>
cording to the Perpendicular S L; & the Gravity of the Portion that
<lb/>
is ſubmerged in the Liquid, ſhall preſſe from below upwards, accor­
<lb/>
ding to the Perpendicular R L. </s>
<s>Therefore that Figure will not conti­
<lb/>
nue according to our Adverſaries Propoſall, but thoſe parts of the
<lb/>
ſaid Figure which are towards E, ſhall be born or drawn downwards,
<lb/>
& thoſe which are towards H ſhall be born or driven upwards, and
<lb/>
this ſhall be ſo long untill that the Axis F T comes to be according
<lb/>
to the Perpendicular.</s>
</p>
<p type="margin">
<s>
<margin.target id="marg1139"/>
(a)
<emph type="italics"/>
Perpendicular
<lb/>
is taken kere, as
<lb/>
in all other places,
<lb/>
by this Author for
<lb/>
the Line K L
<lb/>
drawn thorow the
<lb/>
Centre and Cir­
<lb/>
cumference of the
<lb/>
Earth.
<emph.end type="italics"/>
</s>
</p>
<p type="margin">
<s>
<margin.target id="marg1140"/>
C</s>
</p>
<p type="margin">
<s>
<margin.target id="marg1141"/>
D</s>
</p>
<p type="margin">
<s>
<margin.target id="marg1142"/>
E</s>
</p>
<p type="margin">
<s>
<margin.target id="marg1143"/>
*
<emph type="italics"/>
i. </s>
<s>e,
<emph.end type="italics"/>
The Center
<lb/>
of Gravity.</s>
</p>
<p type="margin">
<s>
<margin.target id="marg1144"/>
F</s>
</p>
<p type="main">
<s>And this ſame Demonſtration is in the ſame manner verified in
<lb/>
the other
<emph type="italics"/>
P
<emph.end type="italics"/>
ortions. </s>
<s>As, firſt, in the Hæmiſphere that lieth with its
<lb/>
whole Baſe above or without the
<emph type="italics"/>
L
<emph.end type="italics"/>
iquid, the Centre of the Sphære
<lb/>
hath been ſuppoſed to be the
<emph type="italics"/>
P
<emph.end type="italics"/>
oint T; and therefore, imagining T
<lb/>
to be in the place, in which, in the other above mentioned, the
<lb/>
<emph type="italics"/>
P
<emph.end type="italics"/>
oint R was, arguing in all things elſe as you did in that, you ſhall
<lb/>
find that the Figure which is above the
<emph type="italics"/>
L
<emph.end type="italics"/>
iquid ſhall preſs from
<lb/>
above downwards according to the
<emph type="italics"/>
P
<emph.end type="italics"/>
erpendicular S
<emph type="italics"/>
L
<emph.end type="italics"/>
; and the
<lb/>
<emph type="italics"/>
P
<emph.end type="italics"/>
ortion that is ſubmerged in the
<emph type="italics"/>
L
<emph.end type="italics"/>
iquid ſhall preſs from below up­
<lb/>
wards according to the
<emph type="italics"/>
P
<emph.end type="italics"/>
erpendicular R
<emph type="italics"/>
L.
<emph.end type="italics"/>
And therefore it ſhall
<lb/>
follow, as in the other, namely, that the parts of the whole Figure
<lb/>
which are towards E, ſhall be born or preſſed downwards, and thoſe
<lb/>
<arrow.to.target n="marg1145"/>
<lb/>
that are towards H, ſhall be born or driven upwards: and this ſhall
<lb/>
be ſo long untill that the Axis F T come to ſtand ^{*}
<emph type="italics"/>
P
<emph.end type="italics"/>
</s>
</p>
</chap>
</body>
</text>
</archimedes>