Priſmes and
Cylinders
ving the ſame
Baſe, are to one
another as their
heights.
Cylinders
ving the ſame
Baſe, are to one
another as their
heights.
THEOREME.
All Figures
of all Matters,
float by hep of
the Rampart
pleniſhed with
Air, and ſome
but only touch
the water.
of all Matters,
float by hep of
the Rampart
pleniſhed with
Air, and ſome
but only touch
the water.
All ſorts of Figures of whatſoever Matter, albeit more
grave than the Water, do by Benefit of the ſaid
part, not only float, but ſome Figures, though of the
graveſt Matter, do ſtay wholly above Water, wetting
only the inferiour Surface that toucheth the Water.
grave than the Water, do by Benefit of the ſaid
part, not only float, but ſome Figures, though of the
graveſt Matter, do ſtay wholly above Water, wetting
only the inferiour Surface that toucheth the Water.
And theſe ſhall be all Figures, which from the inferiour Baſe up
wards, grow leſſer and leſſer; the which we ſhall exemplifie for
this time in Piramides or Cones, of which Figures the paſſions sre
common. We will demonſtrate therefore, that,
wards, grow leſſer and leſſer; the which we ſhall exemplifie for
this time in Piramides or Cones, of which Figures the paſſions sre
common. We will demonſtrate therefore, that,
It is poſſible to form a Piramide, of any whatſoever Matter propoſed,
which being put with its Baſe upon the Water, reſts not only
ſubmerging, but without wetting it more then its Baſe.
which being put with its Baſe upon the Water, reſts not only
ſubmerging, but without wetting it more then its Baſe.
For the explication of which it is requiſite, that we firſt
the ſubſequent Lemma, namely, that,
the ſubſequent Lemma, namely, that,
LEMMA II.
Solids whoſe Maſſes anſwer in proportion contrarily to
their Specificall Gravities, are equall in Abſolute
Gravities.
Solids whoſe
Maſſes are in
contrary
portion to their
Specifick
vities, are equall
in abſolute Gra
vity.
Maſſes are in
contrary
portion to their
Specifick
vities, are equall
in abſolute Gra
vity.
Let A C and B be two Solids, and let the Maſs A C be to the
Maſs B, as the Specificall Gravity of the Solid B, is to the Speci
ficall Gravity of the Solid A C: I ſay, the Solids A C and B are
equall in abſolute weight, that is, equally grave. For
12[Figure 12]
if the Maſs A C be equall to the Maſs B, then, by the
Aſſumption, the Specificall Gravity of B, ſhall be
quall to the Specificall Gravity of A C, and being
quall in Maſs, and of the ſame Specificall Gravity
ſhall abſolutely weigh one as much as another. But
if their Maſſes ſhall be unequall, let the Maſs A C be greater, and in it
take the part C, equall to the Maſs B. And, becauſe the Maſſes B
and C are equall; the Abſolute weight of B, ſhall have the ſame
portion to the Abſolute weight of C, that the Specificall Gravity of
B, hath to the Specificall Gravity of C; or of C A, which is the
ſame in ſpecie: But look what proportion the Specificall Gravity of
B, hath to the Specificall Gravity of C A, the like proportion, by the
Aſſumption, hath the Maſs C A, to the Maſs B; that is, to the Maſs C:
Maſs B, as the Specificall Gravity of the Solid B, is to the Speci
ficall Gravity of the Solid A C: I ſay, the Solids A C and B are
equall in abſolute weight, that is, equally grave. For
if the Maſs A C be equall to the Maſs B, then, by the
Aſſumption, the Specificall Gravity of B, ſhall be
quall to the Specificall Gravity of A C, and being
quall in Maſs, and of the ſame Specificall Gravity
ſhall abſolutely weigh one as much as another. But
if their Maſſes ſhall be unequall, let the Maſs A C be greater, and in it
take the part C, equall to the Maſs B. And, becauſe the Maſſes B
and C are equall; the Abſolute weight of B, ſhall have the ſame
portion to the Abſolute weight of C, that the Specificall Gravity of
B, hath to the Specificall Gravity of C; or of C A, which is the
ſame in ſpecie: But look what proportion the Specificall Gravity of
B, hath to the Specificall Gravity of C A, the like proportion, by the
Aſſumption, hath the Maſs C A, to the Maſs B; that is, to the Maſs C: