THE OREME XII.
That it is poſſible to fo m Solid Bodies, of what Figure
and greatneſs ſoever, that of their own Nature goe
to the Bottome; But by the help of the Air
tained in the Rampart, reſt without ſubmerging.
and greatneſs ſoever, that of their own Nature goe
to the Bottome; But by the help of the Air
tained in the Rampart, reſt without ſubmerging.
The truth of this Propoſition is ſufficiently manifeſt in all thoſe
Solid Figures, that determine in their uppermoſt part in a plane
Superficies: for making ſuch Figures of ſome Matter
cally as grave as the water, putting them into the water, ſo that the
whole Maſs be covered, it is manifeſt, that they ſhall reſt in all
places, provided, that ſuch a Matter equall in weight to the water,
may be exactly adjuſted: and they ſhall by conſequence, reſt or
lie even with the Levell of the water, without making any Rampart.
If, therefore, in reſpect of the Matter, ſuch Figures are apt to reſt
without ſubmerging, though deprived of the help of the Rampart,
it is manifeſt, that they may admit ſo much encreaſe of Gravity,
(without encreaſing their Maſſes) as is the weight of as much water
as would be contained within the Rampart, that is made about their
upper plane Surface: by the help of which being ſuſtained, they
ſhall reſt afloat, but being bathed, they ſhall deſcend, having been
made graver than the water. In Figures, therefore, that determine
above in a plane, we may cleerly comprehend, that the Rampart
added or removed, may prohibit or permit the deſcent: but in thoſe
Figures that go leſſening upwards towards the top, ſome Perſons
may, and that not without much ſeeming Reaſon, doubt whether
the ſame may be done, and eſpecially by thoſe which terminate in a
very acute Point, ſuch as are your Cones and ſmall Piramids.
ing theſe, therefore, as more dubious than the reſt, I will endeavour
to demonſtrate, that they alſo lie under the ſame Accident of going,
or not going to the Bottom, be they of any whatever bigneſs. Let
therefore the Cone be A B D, made of a matter
ſpecifically as grave as the water; it is manifeſt
16[Figure 16]
that being put all under water, it ſhall reſt in
all places (alwayes provided, that it ſhall weigh
exactly as much as the water, which is almoſt
impoſſible to effect) and that any ſmall weight
being added to it, it ſhall ſink to the bottom:
but if it ſhall deſcend downwards gently, I ſay,
that it ſhall make the Rampart E S T O, and
that there ſhall ſtay out of the water the point A S T, tripple in
height to the Rampart E S: which is manifeſt, for the Matter of the
Solid Figures, that determine in their uppermoſt part in a plane
Superficies: for making ſuch Figures of ſome Matter
cally as grave as the water, putting them into the water, ſo that the
whole Maſs be covered, it is manifeſt, that they ſhall reſt in all
places, provided, that ſuch a Matter equall in weight to the water,
may be exactly adjuſted: and they ſhall by conſequence, reſt or
lie even with the Levell of the water, without making any Rampart.
If, therefore, in reſpect of the Matter, ſuch Figures are apt to reſt
without ſubmerging, though deprived of the help of the Rampart,
it is manifeſt, that they may admit ſo much encreaſe of Gravity,
(without encreaſing their Maſſes) as is the weight of as much water
as would be contained within the Rampart, that is made about their
upper plane Surface: by the help of which being ſuſtained, they
ſhall reſt afloat, but being bathed, they ſhall deſcend, having been
made graver than the water. In Figures, therefore, that determine
above in a plane, we may cleerly comprehend, that the Rampart
added or removed, may prohibit or permit the deſcent: but in thoſe
Figures that go leſſening upwards towards the top, ſome Perſons
may, and that not without much ſeeming Reaſon, doubt whether
the ſame may be done, and eſpecially by thoſe which terminate in a
very acute Point, ſuch as are your Cones and ſmall Piramids.
ing theſe, therefore, as more dubious than the reſt, I will endeavour
to demonſtrate, that they alſo lie under the ſame Accident of going,
or not going to the Bottom, be they of any whatever bigneſs. Let
therefore the Cone be A B D, made of a matter
ſpecifically as grave as the water; it is manifeſt
that being put all under water, it ſhall reſt in
all places (alwayes provided, that it ſhall weigh
exactly as much as the water, which is almoſt
impoſſible to effect) and that any ſmall weight
being added to it, it ſhall ſink to the bottom:
but if it ſhall deſcend downwards gently, I ſay,
that it ſhall make the Rampart E S T O, and
that there ſhall ſtay out of the water the point A S T, tripple in
height to the Rampart E S: which is manifeſt, for the Matter of the