[Sidenote: There may be Cones and Piramides of any Matter, which
demitted into the water, rest only their Bases.]
_That it is possible of any assigned Matter, to form a Piramide or
Cone upon any Base, which being put upon the Water shall not
submerge, nor wet any more than its Base._
[Illustration]
Let the greatest possible Altitude of the Rampart be the Line D B,
and the Diameter of the Base of the Cone to be made of any Matter
assigned B C, at right angles to D B: And as the Specificall Gravity
of the Matter of the Piramide or Cone to be made, is to the
Specificall Gravity of the water, so let the Altitude of the Rampart D
B, be to the third part of the Piramide or Cone A B C, described upon
the Base, whose Diameter is B C: I say, that the said Cone A B C, and
any other Cone, lower then the same, shall rest upon the Surface of
the water B C without sinking. Draw D F parallel to B C, and suppose
the Prisme or Cylinder E C, which shall be tripple to the Cone A B C.
And, because the Cylinder D C hath the same proportion to the Cylinder
C E, that the Altitude D B, hath to the Altitude B E: But the Cylinder
C E, is to the Cone A B C, as the Altitude E B is to the third part of
the Altitude of the Cone: Therefore, by Equality of proportion, the
Cylinder D C is to the Cone A B C, as D B is to the third part of the
Altitude B E: But as D B is to the third part of B E, so is the
Specificall Gravity of the Cone A B C, to the Specificall Gravity of
the water: Therefore, as the Mass of the Solid D C, is to the Mass of
the Cone A _B_ C, so is the Specificall Gravity of the said Cone, to
the Specificall Gravity of the water: Therefore, by the precedent
Lemma, the Cone A B C weighs in absolute Gravity, as much as a Mass of
Water equall to the Mass D C: But the water which by the imposition of
the Cone A B C, is driven out of its place, is as much as would
precisely lie in the place D C, and is equall in weight to the Cone
that displaceth it: Therefore, there shall be an _Equilibrium_, and
the Cone shall rest without farther submerging. And its manifest,