[Sidenote: Much less shall the said Cone swim, if one immerge a
part thereof.]
_I say farther; that much lesse shall the said Cone stay afloat, if
one immerge a part thereof._
Which you may see, comparing with the water as well the part that
shall immerge as the other above water. Let us therefore of the Cone A
B D, submergeth part N T O S, and advance the Point N S F above water.
The Altitude of the Cone F N S, shall either be more than half the
whole Altitude of the Cone F T O, or it shall not be more: if it shall
be more than half, the Cone F N S shall be more than half of the
Cylinder E N S C: for the Altitude of the Cone F N S, shall be more
than Sesquialter of the Altitude of the Cylinder E N S C: And, because
the Matter of the Cone is supposed to be double in Specificall Gravity
to the water, the water which would be contained within the Rampart E
N S C, would be less grave absolutely than the Cone F N S; so that the
whole Cone F N S cannot be sustained by the Rampart: But the part
immerged N T O S, by being double in Specificall Gravity to the water,
shall tend to the bottom: Therefore, the whole _C_one F T O, as well
in respect of the part submerged, as the part above water shall
descend to the bottom. But if the Altitude of the Point F N S, shall
be half the Altitude of the whole Cone F T O, the same Altitude of the
said Cone F N S shall be Sesquialter to the Altitude E N: and,
therefore, E N S C shall be double to the Cone F N S; and as much
water in Mass as the _C_ylinder E N S C, would weigh as much as the
part of the _C_one F N S. But, because the other immerged part N T O
S, is double in Gravity to the water, a Mass of water equall to that
compounded of the _C_ylinder E N S C, and of the Solid N T O S, shall
weigh less than the _C_one F T O, by as much as the weight of a Mass
of water equall to the Solid N T O S: Therefore, the _C_one sha{l}l
also descend. Again, because the Solid N T O S, is septuple to the
Cone F N S, to which the _C_ylinder E S is double, the proportion of
the Solid N T O S, shall be to the _C_ylinder E N S C, as seaven to
two: Therefore, the whole Solid compounded of the _C_ylinder E N S C,
and of the Solid N T O S, is much less than double the Solid N T O S:
Therefore, the single Solid N T O S, is much graver than a Mass of
water equall to the Mass, compounded of the _C_ylinder E N S C, and of
N T O S.