1tend to the bottom: Therefore, the whole Cone F T O, as well in
reſpect of the part ſubmerged, as the part above water ſhall
ſcend 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 Cylinder E N S C, would weigh as much as the
part of the Cone 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 Cylinder E N S C, and of the Solid N T O S,
ſhall weigh leſs than the Cone F T O, by as much as the weight of
a Maſs of water equall to the Solid N T O S: Therefore, the Cone
ſha l alſo deſcend. Again, becauſe the Solid N T O S, is ſeptuple
to the Cone F N S, to which the Cylinder E S is double, the
tion of the Solid N T O S, ſhall be to the Cylinder E N S C, as ſeaven
to two: Therefore, the whole Solid compounded of the Cylinder
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
linder E N S C, and of N T O S.
reſpect of the part ſubmerged, as the part above water ſhall
ſcend 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 Cylinder E N S C, would weigh as much as the
part of the Cone 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 Cylinder E N S C, and of the Solid N T O S,
ſhall weigh leſs than the Cone F T O, by as much as the weight of
a Maſs of water equall to the Solid N T O S: Therefore, the Cone
ſha l alſo deſcend. Again, becauſe the Solid N T O S, is ſeptuple
to the Cone F N S, to which the Cylinder E S is double, the
tion of the Solid N T O S, ſhall be to the Cylinder E N S C, as ſeaven
to two: Therefore, the whole Solid compounded of the Cylinder
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
linder E N S C, and of N T O S.
COROLARY
Part of the
Cones towards
the Cuſpis
ved, it ſhall ſtill
ſink.
Cones towards
the Cuſpis
ved, it ſhall ſtill
ſink.
From whence it followeth, that though one ſhould remove and take
way the part of the Cone F N S, the ſole remainder N T O S would
go to the bottom.
way the part of the Cone F N S, the ſole remainder N T O S would
go to the bottom.
COROLARY III.
And if we ſhould more depreſs the Cone F T O, it would be ſo much the
more impoſſible that it ſhould ſuſtain it ſelf afloat, the part ſubmerged
N T O S ſtill encreaſing, and the Maſs of Air contained in the Rampart
diminiſhing, which ever grows leſs, the more the Cone ſubmergeth.
The more the
Cone is
ged, the more
impoſſible is its
floating.
Cone is
ged, the more
impoſſible is its
floating.
That Cone, therefore, that with its Baſe upwards, and its
Cuſpis downwards doth ſwimme, being dimitted with its Baſe
downward muſt of neceſſity ſinke. They have argued farre
from the truth, therefore, who have aſcribed the cauſe of Natation
to waters reſiſtance of Diviſion, as to a paſſive principle, and to the
breadth of the Figure, with which the diviſion is to be made, as the
Efficient.
Cuſpis downwards doth ſwimme, being dimitted with its Baſe
downward muſt of neceſſity ſinke. They have argued farre
from the truth, therefore, who have aſcribed the cauſe of Natation
to waters reſiſtance of Diviſion, as to a paſſive principle, and to the
breadth of the Figure, with which the diviſion is to be made, as the
Efficient.
I come in the fourth place, to collect and conclude the reaſon of
that which I have propoſed to the Adverſaries, namely,
that which I have propoſed to the Adverſaries, namely,