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 > >|
1
PROP. IV. THEOR. IV.
Solid Magnitudes that are lighter than the Liquid,
being demitted into the ſetled Liquid, will not total­
ly ſubmerge in the ſame, but ſome part thereof will
lie or ſtay above the Surface of the Liquid.
NIC. In this fourth Propoſition it is concluded, that every Body or Solid that is
lighter (as to Specifical Gravity) than the Liquid, being put into the
Liquid, will not totally ſubmerge in the ſame, but that ſome part of it
will ſtay and appear without the Liquid, that is above its Surface.
For ſuppoſing, on the contrary, that it were poſſible for a Solid
more light than the Liquid, being demitted in the Liquid to ſub­
merge totally in the ſame, that is, ſo as that no part thereof re­
maineth above, or without the ſaid Liquid, (evermore ſuppoſing
that the Liquid be ſo conſtituted as that it be not moved,) let us
imagine any Plane produced thorow the Center of the Earth, tho­
row the Liquid, and thorow that Solid Body: and that the Surface
of the Liquid is cut by this Plane according to the Circumference
A B G, and the Solid Body according to the Figure R; and let the
Center of the Earth be K.
And let there be imagined a Pyramid

that compriſeth the Figure
R, as was done in the pre.
cedent, that hath its Ver­
tex in the Point K, and let
the Superficies of that
Pyramid be cut by the
Superficies of the Plane
A B G, according to A K
and K B. And let us ima­
gine another Pyramid equal and like to this, and let its Superficies
be cut by the Superficies A B G according to K B and K G; and let
the Superficies of another Sphære be deſcribed in the Liquid, upon
the Center K, and beneath the Solid R; and let that be cut by the
ſame Plane according to X O P. And, laſtly, let us ſuppoſe ano­
ther Solid taken ^{*} from the Liquid, in this ſecond Pyramid, which

let be H, equal to the Solid R.
Now the parts of the Liquid, name­
ly, that which is under the Spherical Superficies that proceeds ac­
cording to the Superficies or Circumference X O, in the firſt Py­
ramid, and that which is under the Spherical Superficies that pro­
ceeds according to the Circumference O P, in the ſecond Pyramid,
are equijacent, and contiguous, but are not preſſed equally; for